×

Singular or non-Fermi liquids. (English) Zbl 1001.82118

Summary: An introductory survey of the theoretical ideas and calculations and the experimental results which depart from Landau Fermi liquids is presented. The common themes and possible routes to the singularities leading to the breakdown of Landau Fermi liquids are categorized following an elementary discussion of the theory. Soluble examples of singular or non-Fermi liquids include models of impurities in metals with special symmetries and one-dimensional interacting fermions. A review of these is followed by a discussion of singular Fermi liquids in a wide variety of experimental situations and theoretical models. These include the effects of low-energy collective fluctuations, gauge fields due either to symmetries in the Hamiltonian or possible dynamically generated symmetries, fluctuations around quantum critical points, the normal state of high-temperature superconductors and the two-dimensional metallic state. For the last three systems, the principal experimental results are summarized and the outstanding theoretical issues are highlighted.

MSC:

82D50 Statistical mechanics of superfluids
82B10 Quantum equilibrium statistical mechanics (general)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Abrahams, E.; Anderson, P. W.; Licciardo, D. C.; Ramakrishnan, T. V., Scaling theory of localization: absence of quantum diffusion in two dimensions, Phys. Rev. Lett., 42, 673 (1979)
[2] Abrahams, E.; Varma, C. M., What angle-resolved photoemission experiments tell about the microscopic theory for high-temperature superconductors, Proc. Nat. Acad. Sci., 97, 5714 (2000)
[3] E. Abrahams, S.V. Kravchenko, M.P. Sarachik, Metallic behavior and related phenomena in two dimensions, cond-mat/0006055, Rev. Mod. Phys. 73 (2001) 251.; E. Abrahams, S.V. Kravchenko, M.P. Sarachik, Metallic behavior and related phenomena in two dimensions, cond-mat/0006055, Rev. Mod. Phys. 73 (2001) 251.
[4] Abrikosov, A. A.; Gorkov, L. P.; Dzyaloshinskii, I., Methods of Quantum field Theory in Statistical Physics (1963), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0135.45003
[5] Abrikosov, A. A., Fundamentals of the Theory of Metals (1988), North-Holland: North-Holland Amsterdam
[6] Affleck, I.; Kennedy, T.; Lieb, E. H.; Tasaki, H., Rigorous results on valence-bond ground states in antiferromagnets, Phys. Rev. Lett., 59, 799 (1987)
[7] Affleck, I.; Ludwig, A. W.W.; Pang, H.-B.; Cox, D. L., Relevance of anisotropy in the multichannel Kondo effect: comparison of conformal field theory and numerical renormalization-group results, Phys. Rev. B, 45, 7918 (1992)
[8] Affleck, I.; Ludwig, A. W.W., Exact critical theory of the two-impurity Kondo model, Phys. Rev. Lett., 68, 1046 (1992)
[9] Affleck, I.; Ludwig, A. W.; Jones, B. A., Conformal-field-theory approach to the two-impurity Kondo problem: comparison with numerical renormalization-group results, Phys. Rev. B, 52, 9528 (1995)
[10] Alloul, H., Comment on “Nature of the conduction-band states in \(YBa_2 Cu_3O_7\) as revealed by its yttrium knight shift”, Phys. Rev. Lett., 63, 689 (1989)
[11] Altshuler, B. L.; Aronov, A. G.; Lee, P. A., Interaction effects in disordered Fermi systems in two dimensions, Phys. Rev. Lett., 44, 1288 (1980)
[12] Altshuler, B. L.; Aronov, A. G.; Khmelnitskii, D. E., Suppression of localization effects by the high frequency field and the Nyquist noise, Solid State Commun., 39, 619 (1981)
[13] Altshuler, B. L.; Aronov, A. G.; Khmelnitskii, D. E., Effects of electron-electron collisions with small energy transfers on quantum localization, J. Phys. C, 15, 7367 (1982)
[14] Altshuler, B. L.; Aronov, A. G., (Efros, A. L.; Pollak, M., Electron-Electron Interactions in Disordered Systems (1985), Elsevier Science Publishers: Elsevier Science Publishers New York)
[15] Altshuler, B. L.; Maslov, D. L., Theory of metal-insulator transitions in gated semiconductors, Phys. Rev. Lett., 82, 145 (1999)
[16] Altshuler, B. L.; Maslov, D. L.; Pudalov, V. M., Metal-insulator transition in 2D: resistance in the critical region, Physica E, 9, 209 (2001)
[17] B.L. Altshuler, G.W. Martin, D.L. Maslov, V.M. Pudalov, A. Prinz, G. Brunthaler, G. Bauer, Weak-localization type description of conduction in the “anomalous” metallic state, cond-mat/0008005.; B.L. Altshuler, G.W. Martin, D.L. Maslov, V.M. Pudalov, A. Prinz, G. Brunthaler, G. Bauer, Weak-localization type description of conduction in the “anomalous” metallic state, cond-mat/0008005.
[18] Anderson, P. W., Absence of diffusion in certain random lattices, Phys. Rev., 109, 1492 (1958)
[19] Anderson, P. W., Localized Magnetic States in Metals, Phys. Rev., 124, 41 (1961)
[20] Anderson, P. W., Infrared catastrophe in Fermi gases with local scattering potential, Phys. Rev. Lett., 18, 1049 (1967)
[21] Anderson, P. W., A poor man’s derivation of scaling laws for the Kondo problem, J. Phys. C, 3, 2436 (1970)
[22] Anderson, P. W.; Yuval, G., Exact results in the Kondo problem: equivalence to a classical one-dimensional Coulomb gas, Phys. Rev. Lett., 23, 89 (1969)
[23] Anderson, P. W.; Yuval, G.; Hamann, D. R., Exact results in the Kondo problem II. Scaling theory, qualitatively correct solution, and some new results on one-dimensional classical statistical models, Phys. Rev. B, 1, 4464 (1970)
[24] Anderson, P. W., The Theory of Superconductivity in the High \(T_c\) Cuprates (1997), Princeton University Press: Princeton University Press Princeton
[25] Anderson, P. W., Mater. Res. Bull., 8, 153 (1973)
[26] Ando, T.; Fowler, A. B.; Stern, F., Electronic properties of two-dimensional systems, Rev. Mod. Phys., 54, 437 (1982)
[27] Andraka, B.; Tsvelik, A. M., Observation of non-Fermi-liquid behavior in \(U_{0.2}Y_{0.8}Pd_3\), Phys. Rev. Lett., 67, 2886 (1991)
[28] Andres, K.; Graebner, J. E.; Ott, H. R., \(4f\)-virtual-bound-state formation in \(CeAl_3\) at low temperatures, Phys. Rev. Lett., 35, 1779 (1975)
[29] Aronson, M. C.; Maple, M. B.; Chau, R.; Georges, A.; Tsvelik, A. M.; Osborn, R., Non-Fermi-liquid scaling in \(UCu_{5−x}Pd_x (x=1, 1.5)\), J. Phys.: Condens. Matter, 8, 9815 (1996)
[30] Aronson, M. C.; Maple, M. B.; de Sa, P.; Chau, R.; Tsvelik, A. M.; Osborn, R., Non-Fermi-liquid scaling in \(UCu_{5−x}Pd_x (x=1, 1.5)\), a phenomenological description, Europhys. Lett., 46, 245 (1997)
[31] Auerbach, A., Interacting Electrons and Quantum Magnetism (1994), Springer: Springer New York
[32] Auslaender, O. M.; Yacoby, A.; de Picciotto, R.; Pfeiffer, L. N.; West, K. W., Experimental evidence for resonant-tunneling in a Luttinger-liquid, Phys. Rev. Lett., 84, 1756 (2000)
[33] Balents, L.; Fisher, M. P.A., Weak-coupling phase diagram of two-chain Hubbard model, Phys. Rev. B, 53, 12133 (1996)
[34] Balents, L.; Varma, C. M., Ferromagnetism in doped excitonic insulators, Phys. Rev. Lett., 84, 1264 (2000)
[35] Batlogg, B.; Varma, C. M., The underdoped phase of cuprate superconductors, Phys. World, 13, 33 (2000)
[36] Barzykin, V.; Gorkov, L. P., Ferromagnetism and superstructure in \(Ca_{1−x}La_xB_6\), Phys. Rev. Lett., 84, 2207 (2000)
[37] Baym, G.; Pethick, C., Landau Fermi Liquid Theory (1991), Wiley: Wiley New York
[38] Béal-Monod, M. T.; Maki, K., Renormalizability of paramagnon theories, Phys. Rev. Lett., 34, 1461 (1975)
[39] Bedell (Ed.), K. S., Strongly Correlated Electronic Materials (1989), Addison Wesley: Addison Wesley New York
[40] Belitz, D.; Kirkpatrick, T. R., The Anderson-Mott transition, Rev. Mod. Phys., 66, 261 (1994)
[41] Bergmann, G., Weak localization in thin films, Phys. Rep., 107, 1 (1984)
[42] Bernal, O. O.; MacLaughlin, D. E.; Lukefahr, H. G.; Andraka, B., Copper NMR and thermodynamics of \(UCu_{5−x}Pd_x\): evidence for Kondo disorder, Phys. Rev. Lett., 75, 2023 (1995)
[43] Betbeder-Matibet, O.; Nozières, P., Transport equation for quasiparticles in a system of interacting fermions colliding on dilute impurities, Ann. Phys. (NY), 37, 17 (1966)
[44] Bogenberger, B.; von Löhneysen, H., Tuning of non-Fermi-liquid behavior with pressure, Phys. Rev. Lett., 74, 1016 (1995)
[45] Bogolubov, N., On the theory of superfluidity, J. Phys. (USSR), XI, 23 (1947)
[46] Bucher, B.; Steiner, P.; Karpinski, J.; Kaldis, E.; Wachter, P., Influence of the spin gap on the normal state transport in \(YBa_2 Cu_4O_8\), Phys. Rev. Lett., 70, 2012 (1993)
[47] B. Bernu, L. Candido, D.M. Ceperley, Exchange frequencies in the 2d Wigner crystal, cond-mat/0008062.; B. Bernu, L. Candido, D.M. Ceperley, Exchange frequencies in the 2d Wigner crystal, cond-mat/0008062.
[48] Bishop, D. J.; Tsui, D. C.; Dynes, R. C., Nonmetallic conduction in electron inversion layers at low temperatures, Phys. Rev. Lett., 44, 1153 (1980)
[49] Brunthaler, G.; Prinz, A.; Bauer, G.; Pudalov, V. M.; Dizhur, E. M.; Jaroszynski, J.; Glod, P.; Dietl, T., Weak localization in the 2D metallic regime of Si-MOS, Ann. Phys. (Leipzig), 8, 579 (1999)
[50] Castella, H.; Zotos, X., Exact calculation of spectral properties of a particle interacting with a one dimensional fermionic system, Phys. Rev., 47, 16186 (1993)
[51] Castellani, C.; Di Castro, C.; Metzner, W., Dimensional crossover from Fermi to Luttinger liquid, Phys. Rev. Lett., 72, 316 (1994)
[52] Castellani, C.; Di Castro, C.; Lee, P. A.; Ma, M., Interaction-driven metal-insulator transitions in disordered fermion systems, Phys. Rev. B, 30, 527 (1984)
[53] Castellani, C.; Di Castro, C.; Forgacs, G.; Tabet, E., Towards a microscopic theory of the metal-insulator transition, Nucl. Phys. B, 225, 441 (1983)
[54] Castellani, C.; Di Castro, C.; Lee, P. A.; Ma, M.; Sorella, S.; Tabet, E., Spin fluctuations in disordered interacting electrons, Phys. Rev. B, 30, 1596 (1984)
[55] Castro Neto, A. H.; Castilla, G.; Jones, B. A., Non-Fermi liquid behavior and Griffiths phase in f-electron compounds, Phys. Rev. Lett., 81, 3531 (1998)
[56] Chakravary, S.; Halperin, B. I.; Nelson, D., Low temperature behavior of two-dimensional quantum antiferromagnets, Phys. Rev. B, 39, 2344 (1989)
[57] Chakravarty, S.; Kivelson, S.; Nayak, C.; Voelker, K., Wigner glass, spin liquids, and the metal-insulator transition, Philos. Mag. B, 79, 859 (1999)
[58] Chakravarty, S.; Laughlin, R. B.; Morr, D. K.; Nayak, C., Hidden order in the cuprates, Phys. Rev. B, 63, 094503 (2001)
[59] Cheong, S.-W.; Hwang, H. Y.; Chen, C. H.; Batlog, B.; Rupp, L. W.; Carter, S. A., Charge-ordered states in (La,Sr)\(_2 NiO_4\) for hole concentrations \(n_h=1/3\) and 1/2, Phys. Rev. B, 49, 7088 (1994)
[60] Chen, Y. H.; Wilczek, F.; Witten, E.; Halperin, B. I., Int. J. Mod. Phys. B, 3, 1001 (1989)
[61] Chitra, P.; Giamarchi, T.; Le Doussal, P., Dynamical properties of the pinned Wigner crystal, Phys. Rev. Lett., 80, 3827 (1998)
[62] Coleridge, P. T.; Williams, R. L.; Feng, Y.; Zawadzki, P., Metal-insulator transition at \(B=0\) in p-type SiGe, Phys. Rev. B, 56, R12764 (1997)
[63] P.T. Coleridge, A.S. Sachrajda, P. Zawadski, Weak localisation, interaction effects and the metallic phase of SiGe, cond-mat/9912041.; P.T. Coleridge, A.S. Sachrajda, P. Zawadski, Weak localisation, interaction effects and the metallic phase of SiGe, cond-mat/9912041.
[64] Combescot, M.; Nozières, P., Infrared catastrophy and excitations in the X-ray spectra of metals, J. Phys., 32, 913 (1971)
[65] Continentino, M. A., Universal behavior in heavy fermions, Phys. Rev. B, 47, 11587 (1993)
[66] Continento, M. A., Quantum scaling in many body systems, Phys. Rep., 239, 179 (1994)
[67] J. Corson, J. Orenstein, Normal state conductivity varies as fractional power of transport lifetime in a cuprate superconductor, cond-mat/0006027.; J. Corson, J. Orenstein, Normal state conductivity varies as fractional power of transport lifetime in a cuprate superconductor, cond-mat/0006027.
[68] Cox, D. L., Quadrupolar Kondo effect in uranium heavy-electron materials? Phys. Rev. Lett., 59, 1993 (1240)
[69] Cox, D. L.; Jarrell, M., The two-channel Kondo route to non-Fermi-liquid metals, J. Phys.: Condens. Matter, 8, 9825 (1996)
[70] Cox, D. L.; Zawadowski, A., Exotic Kondo effects in metals: magnetic ion in a crystalline electric field and tunneling centers, Adv. Phys., 47, 599 (1999)
[71] Das Sarma, S.; Pinczuk (Eds.), A., Perspectives in Quantum Hall Effects (1997), Wiley: Wiley New York
[72] Das Sarma, S.; Hwang, E. H., Charged impurity-scattering-limited low-temperature resistivity of low-density silicon inversion layers, Phys. Rev. Lett., 83, 164 (1999)
[73] Dekker, C., Carbon nanotubes as molecular quantum wires, Phys. Today, 52, 22 (1999)
[74] de Visser, A.; Graf, M. J.; Estrela, P.; Amato, A.; Baines, C.; Andreica, D.; Gygax, F. N.; Schenck, A., Magnetic quantum critical point in \(UPt_3\) doped with Pd, Phys. Rev. Lett., 85, 3005 (2000)
[75] de Picciotto, R.; Stormer, H. L.; Pfeiffer, L. N.; Baldwin, K. W.; West, K. W., Four-terminal resistance of a ballistic quantum wire, Nature, 411, 51 (2001)
[76] Dobrosavljević, V.; Abrahams, E.; Miranda, E.; Chakravarty, S., Scaling theory of two-dimensional metal-insulator transitions, Phys. Rev. Lett., 79, 455 (1997)
[77] Doniach, S., The Kondo lattice and weak antiferromagnetism, Physica B, 91, 231 (1977)
[78] Doniach, S.; Englesberg, S., Low-temperature properties of nearly ferromagnetic Fermi liquids, Phys. Rev. Lett., 17, 750 (1966)
[79] Doniach, S.; Sondheimer, E. H., Green’s functions for Solid State Physicists (1974), Benjamin/Cummings: Benjamin/Cummings London · Zbl 1058.82001
[80] Dultz, S. C.; Jiang, H. W., Thermodynamic signature of a two-dimensional metal-insulator transition, Phys. Rev. Lett., 84, 4689 (2000)
[81] Dzyaloshinskii, I.; Polyakov, A. M.; Wiegmann, P., Phys. Lett., 127A, 112 (1988)
[82] Emery, V. J., (Jérome, D.; Larson, L. G., Low-Dimensional Conductors and Superconductors (1987), Plenum: Plenum New York), 47
[83] Emery, V. J., (Devreese, J. T.; Evrard, R. P.; van Doren, V. E., Highly Conducting One-Dimensional Solids (1979), Plenum: Plenum New York), 247
[84] Emery, V. J.; Kivelson, S., Mapping of the two-channel Kondo problem to a resonant-level model, Phys. Rev. B, 46, 10812 (1992)
[85] Emery, V. J.; Kivelson, S., Frustrated electronic phase separation and high temperature superconductors, Physica C, 209, 597 (1993)
[86] Eskes, H. J.; Grimberg, R.; van Saarloos, W.; Zaanen, J., Quantizing charged magnetic domain walls: strings on a lattice, Phys. Rev. B, 54, R724 (1996)
[87] P. Estrela, Non-Fermi liquid behavior in uranium based heavy-fermion compounds, Thesis, University of Amsterdam, 2000.; P. Estrela, Non-Fermi liquid behavior in uranium based heavy-fermion compounds, Thesis, University of Amsterdam, 2000.
[88] Estrela, P.; Pereira, L. C.J.; de Visser, A.; de Boer, F. R.; Almeida, M.; Godinho, M.; Rebizant, J.; Spirlet, J. C., Structural, magnetic and transport properties of single-crystalline \(U_2 Pt_2In\), J. Phys.: Condens. Matter, 10, 9465 (1998)
[89] Fabrizio, M., Role of transverse hopping in a two-coupled-chains model, Phys. Rev. B, 48, 15838 (1993)
[90] Fetter, A.; Hanna, C.; Laughlin, R. B., The random phase approximation in the fractional-statistics gas, Phys. Rev. B, 39, 9679 (1998)
[91] A.M. Finkel’stein, Influence of Coulomb interaction on the properties of disordered metals, Zh. Eksp. Teor. Fiz 84 (1983) 168 [Sov. Phys. JETP 57 (1983) 97].; A.M. Finkel’stein, Influence of Coulomb interaction on the properties of disordered metals, Zh. Eksp. Teor. Fiz 84 (1983) 168 [Sov. Phys. JETP 57 (1983) 97].
[92] Finkel’stein, A. M., Weak localization and Coulomb interaction in disordered systems, Z. Phys., 56, 189 (1984)
[93] Finkelstein, A. I., Soviet Sci. Rev., 3 (1990)
[94] Finkelstein, A. I.; Larkin, A. I., Two coupled chains with Tomonaga-Luttinger interactions, Phys. Rev. B, 47, 10461 (1993)
[95] Fjaerstad, J. O.; Sudbo, A.; Luther, A., Correlation functions for a two-dimensional electron system with bosonic interactions and a square Fermi surface, Phys. Rev. B, 60, 13361 (1999)
[96] Fisher, M. E., (Hahne, F. J.W., Critical Phenomena, Vol. 186. Critical Phenomena, Vol. 186, Lecture Notes in Physics (1983), Springer: Springer Berlin)
[97] Fisher, M. P.A.; Glazman, L. I., Transport in a one-dimensional Luttinger liquid, (Kouwenhoven, L.; Schön, G.; Sohn, L., Mesoscopic Electron Transport, NATO ASI Series E (1997), Kluwer: Kluwer Dordrecht)
[98] Forro, L.; Gaál, R.; Berger, H.; Fazekas, P.; Penc, K.; Készmárki, I.; Mihály, G., Pressure induced quantum critical point and non-Fermi-liquid behavior in \(BaVS_3\), Phys. Rev. Lett., 85, 1938 (2000)
[99] Fowler, M.; Zawadowski, A., Scaling and the renormalization group in the Kondo effect, Solid State Commun., 9, 471 (1971)
[100] Fulde, P.; Keller, J.; Zwicknagel, G., Theory of heavy fermion systems, (Ehrenreich, H.; Turnbull, D., Solid State Physics, Vol. 41 (1988), Academic Press: Academic Press New York)
[101] Fulde, P., Electron Correlations in Molecules and Solids (1995), Springer: Springer Berlin
[102] Fukuyama, H., Effects of mutual interactions in weakly localized regime of disordered two-dimensional systems. II. Intervalley impurity scattering, J. Phys. Soc. Japan, 50, 3562 (1981)
[103] Galitski, The energy spectrum of a non-ideal fermi gas, Sov. Phys. JETP 7 (1958) 104.; Galitski, The energy spectrum of a non-ideal fermi gas, Sov. Phys. JETP 7 (1958) 104.
[104] Georges, A.; Kotliar, G.; Krauth, W.; Rozenberg, M. J., Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys., 68, 13 (1996)
[105] Giamarchi, T.; Millis, A. J., Conductivity of a Luttinger Liquid, Phys. Rev. B, 46, 9325 (1992)
[106] Giamarchi, T.; Varma, C. M.; Ruckenstein, A. E.; Nozières, P., Singular low-energy properties of an impurity model with finite range interactions, Phys. Rev. Lett., 70, 3967 (1993)
[107] Giamarchi, T.; Schulz, H. J., Anderson localization and interactions in one dimensional metals, Phys. Rev. B, 37, 325 (1988)
[108] Giamarchi, T.; Le Doussal, P., Phase diagrams of flux lattices with disorder, Phys. Rev. B, 55, 6577 (1997)
[109] D.M. Ginsberg (Ed.), Physical Properties of High Temperature Superconductors Vol. I (1989), Vol. II (1990), Vol. III (1992), Vol. IV (1994), World Scientific, Singapore.; D.M. Ginsberg (Ed.), Physical Properties of High Temperature Superconductors Vol. I (1989), Vol. II (1990), Vol. III (1992), Vol. IV (1994), World Scientific, Singapore.
[110] S.M. Girvin, The quantum Hall effect: novel excitation and broken symmetries, cond-mat/9907002.; S.M. Girvin, The quantum Hall effect: novel excitation and broken symmetries, cond-mat/9907002. · Zbl 0993.81068
[111] Glyde, H. R., Excitations in Liquid and Solid Helium (1994), Clarendon: Clarendon Oxford
[112] Gogolin, A. O.; Nersesyan, A. A.; Tsvelik, A. M., Bosonization and Strongly correlated Systems (1998), Cambridge University Press: Cambridge University Press Cambridge
[113] Grayson, M.; Tsui, D. C.; Pfeiffer, L. N.; West, K. W.; Chang, A. M., Continuum of chiral Luttinger liquids at the fractional quantum Hall edge, Phys. Rev. Lett., 80, 1062 (1998)
[114] Grosche, F. M.; Pfleiderer, C.; McMullan, G. J.; Lonzarich, G. G.; Bernhoeft, N. R., Critical behaviour of \(ZrZn_2\), Physica B, 206-207, 20 (1995)
[115] Halbroth, C. J.; Metzner, W., d-Wave superconductivity and Pomeranchuk instability in the two-dimensional Hubbard model, Phys. Rev. Lett., 85, 5162 (2000)
[116] Halperin, B. I.; Hohenberg, P. C., Theory of dynamic critical phenomena, Rev. Mod. Phys., 49, 435 (1977)
[117] Halperin, B. I.; Lee, P. A.; Read, N., Theory of the half-filled Landau level, Phys. Rev. B, 47, 7312 (1993)
[118] Hamilton, A. R.; Simmons, M. Y.; Pepper, M.; Linfeld, E. H.; Rose, P. D.; Ritchie, D. A., Reentrant insulator-metal transition at \(B=0\) in a two-dimensional hole gas, Phys. Rev. Lett., 82, 1542 (1999)
[119] Hanein, Y.; Meirav, U.; Shahar, D.; Li, C. C.; Tsui, D. C.; Shtrikman, H., The metalliclike conductivity of a two-dimensional hole system, Phys. Rev. Lett., 80, 1288 (1998)
[120] Harris, A. B., Effects of random defects on the critical behavior of Ising models, J. Phys. C, 7, 1671 (1974)
[121] Hayden, S. M.; Doubble, R.; Aeppli, G.; Perring, T. G.; Fawcett, E., Strongly enhanced magnetic excitations near the quantum critical point of \(Cr_{1−x}V_x\) and why strong exchange enhancement need not imply heavy fermion behavior, Phys. Rev. Lett., 84, 999 (2000)
[122] Hertz, J. A., Quantum critical phenomena, Phys. Rev. B, 14, 1165 (1976)
[123] Hewson, A. C., The Kondo Problem to Heavy Fermions (1993), Cambridge University Press: Cambridge University Press Cambridge
[124] Hikami, S.; Larkin, A. I.; Nagaoka, Y., Spin-orbit interaction and magnetoresistance in the two-dimensional random system, Progr. Theor. Phys., 63, 707 (1980)
[125] Hlubina, R.; Rice, T. M., Resistivity as a function of temperature for models with hot spots on the Fermi surface, Phys. Rev. B, 51, 9253 (1995)
[126] Holstein, T.; Norton, R. E.; Pincus, P., de Haas-van Alphen effect and the specific heat of an electron gas, Phys. Rev. B, l8, 2647 (1973)
[127] Houghton, A.; Marston, J. B., Bosonization and fermion liquids in dimensions greater than one, Phys. Rev. B, 48, 7790 (1993)
[128] Ilani, S.; Yacoby, A.; Mahalu, D.; Shtrikman, H., Unexpected behavior of the local compressibility near the \(B=0\) metal-insulator transition, Phys. Rev. Lett., 84, 3133 (2000)
[129] S. Ilani, A. Yacoby, D. Mihalu, H. Shtrikman, Microscopic structure of the metal-insulator transition in two-dimensions, Science, submitted for publication.; S. Ilani, A. Yacoby, D. Mihalu, H. Shtrikman, Microscopic structure of the metal-insulator transition in two-dimensions, Science, submitted for publication.
[130] Imry, Y.; Ma, S.-K., Random-field instability of the ordered state of continuous symmetry, Phys. Rev. Lett., 35, 1399 (1975)
[131] Imry, Y.; Wortis, M., Influence of quenched impurities on first order phase transitions, Phys. Rev. B, 19, 3580 (1979)
[132] Imry, Y., Introduction to Mesoscopic Physics (1997), Oxford University Press: Oxford University Press Oxford
[133] Ioffe, L. B.; Larkin, A. I., Gapless fermions and gauge fields in dielectrics, Phys. Rev. B, 39, 8988 (1989)
[134] Jacklič, J.; Prelovšek, P., Finite-temperature properties of doped antiferromagnets, Adv. Phys., 49, 1 (2000)
[135] Jones, B. A.; Varma, C. M., Study of two magnetic impurities in a Fermi gas, Phys. Rev. Lett., 58, 843 (1987)
[136] Jones, B. A.; Varma, C. M.; Wilkins, J. W., Low-temperature properties of the two-impurity Kondo Hamiltonian, Phys. Rev. Lett., 61, 125 (1988)
[137] Kalmeyer, V.; Laughlin, R. B., Equivalence of the resonating-valence-bond and quantum Hall states, Phys. Rev. Lett., 59, 2095 (1987)
[138] Kaminski, A.; Mesot, A. J.; Fretwell, H.; Campuzano, J. C.; Norman, M. R.; Randeria, M.; Ding, H.; Sato, T.; Takahashi, T.; Mochiku, T.; Kadowaki, K.; Hoechst, H., Quasiparticles in the superconducting state of \(Bis_2 Sr_2 CaCu_2 O_8\), Phys. Rev. Lett., 84, 1788 (2000)
[139] Kane, C. L.; Fisher, M. P.A., Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas, Phys. Rev. B, 46, 15233 (1992)
[140] Kane, C. L.; Balents, L.; Fisher, M. P.A., Coulomb interactions and mesoscopic effects in carbon nanotubes, Phys. Rev. Lett., 79, 5086 (1997)
[141] H.-Y. Kee, Effect of doping-induced disorder on \(T_c\); H.-Y. Kee, Effect of doping-induced disorder on \(T_c\)
[142] Kim, T. S.; Cox, D. L., Scaling analysis of a model Hamiltonian for \(Ce^{3+}\) impurities in a cubic metal, Phys. Rev. B, 54, 6494 (1996)
[143] Kivelson, S. A.; Rokshar, D. S.; Sethna, J. P., Topology of the resonating valence-bond state: solitons and high \(T_c\) superconductivity, Phys. Rev. B, 35, 8865 (1987)
[144] Klapwijk, T. M.; Das Sarma, S., A few electrons per ion scenario for the \(B=0\) metal-insulator transition in two dimensions, Solid State Commun., 110, 581 (1999)
[145] Kondo, J., Resistance minimum in dilute magnetic alloys, Progr. Theor. Phys., 32, 37 (1964)
[146] Kosterlitz, J. M.; Thouless, D., Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C, 6, 1181 (1973)
[147] Kotliar, G., Resonating valence bonds and d-wave superconductivity, Phys. Rev. B, 37, 3664 (1988)
[148] Kravchenko, S. V.; Mason, W. E.; Bowker, G. E.; Furneaux, J. E.; Pudalov, V. M.; D’Iorio, M., Scaling of an anomalous metal-insulator transition in a two-dimensional system in silicon at \(B=0\), Phys. Rev. B, 51, 7038 (1995)
[149] Kravchenko, S. V.; Klapwijk, T. M., Metallic low-temperature resistivity in a 2D electron system over an extended temperature range, Phys. Rev. Lett., 84, 2909 (2000)
[150] Krishna-murthy, H. R.; Wilkins, J. W.; Wilson, K. G., Renormalization-group approach to the Anderson model of dilute magnetic alloys. I. Static properties for the symmetric case, Phys. Rev. B, 21, 1003 (1980)
[151] L.D. Landau, The theory of a Fermi liquid, Zh. Eksp. Teor. Fiz. 30 (1956) 1058 [Sov. Phys. JETP 3 (1957) 920].; L.D. Landau, The theory of a Fermi liquid, Zh. Eksp. Teor. Fiz. 30 (1956) 1058 [Sov. Phys. JETP 3 (1957) 920].
[152] L.D. Landau, Oscillations in a Fermi liquid, Zh. Eksp. Teor. Fiz. 32 (1957) 59 [Sov. Phys. JETP 5 (1957) 101].; L.D. Landau, Oscillations in a Fermi liquid, Zh. Eksp. Teor. Fiz. 32 (1957) 59 [Sov. Phys. JETP 5 (1957) 101]. · Zbl 0086.44403
[153] E.M. Lifshitz, L.P. Pitaevskii, Statistical Physics, Part 2, Pergamon, New York, 1980 (Chapter III).; E.M. Lifshitz, L.P. Pitaevskii, Statistical Physics, Part 2, Pergamon, New York, 1980 (Chapter III).
[154] Larkin, A. I.; Melnikov, V. I., Magnetic impurity in an almost magnetic metal, Sov. Phys. JETP, 34, 656 (1972)
[155] Laughlin, R. B., The relationship between high temperature superconductors and the fractional quantum Hall effect, Science, 242, 525 (1988)
[156] Lee, P. A.; Ramakrishnan, T. V., Disordered electronic systems, Rev. Mod. Phys., 57, 287 (1985)
[157] Lee, P. A., Pseudogaps in underdoped cuprates, Physica C, 317-318, 194 (1999)
[158] Lin, H.; Balents, L.; Fisher, M. P.A., Exact SO(8) Symmetry in the weakly-interacting two-leg ladder, Phys. Rev. B, 58, 1794 (1998)
[159] Lonzarich, G. G.; Taillefer, L., Effect of spin fluctuations on the magnetic equation of state of ferromagnetic or nearly ferromagnetic metals, J. Phys. C, 18, 4339 (1985)
[160] G. Lonzarich, private communication to CMV, June 2000.; G. Lonzarich, private communication to CMV, June 2000.
[161] Loram, J. W.; Mirza, K. A.; Cooper, J. R.; Tallon, J. L., Superconducting and normal state energy gaps in \(Y_{0.8}Ca_{0.2}Ba_2 Cu_3O_{7−δ}\) from the electronic specific heat, Physica C, 282-287, 1405 (1997)
[162] Luther, A.; Emery, V. J., Backward scattering in the one-dimensional electron gas, Phys. Rev. Lett., 33, 589 (1974)
[163] Ma, S. K., Modern Theory of Critical Phenomena (1976), Benjamin Cummings: Benjamin Cummings Reading
[164] Maclaughlin, D. E.; Bernal, O. O.; Heffner, R. H.; Nieuwenhuis, G. J.; Rose, M. C.; Sonier, J. E.; Andraka, B.; Chau, R.; Maple, M. P., Glassy dynamics in non-Fermi-liquid \(UCu_{5−x}Pd_x, x=1.0\) and 1.5, Phys. Rev. Lett., 87, 066402 (2001)
[165] H. Maebashi, K. Miyake, C.M. Varma, Singular effects of impurities near the ferromagnetic quantum critical point, cond-mat/0109276.; H. Maebashi, K. Miyake, C.M. Varma, Singular effects of impurities near the ferromagnetic quantum critical point, cond-mat/0109276.
[166] Mahan, G. D., Excitons in degenerate semiconductors, Phys. Rev., 153, 882 (1967)
[167] Mahan, G. D., Many-Particle Physics (1990), Plenum: Plenum New York
[168] Maple, M. B.; Dickey, R. P.; Herrman, J.; de Andrade, M. C.; Freeman, E. J.; Gajewski, D. A.; Chau, R., Single-ion scaling of the low-temperature properties of f-electron materials with non-Fermi-liquid ground states, J. Phys.: Condens. Matter, 8, 9773 (1996)
[169] Mathur, N. D.; Grosche, F. M.; Julian, S. R.; Walker, I. R.; Freye, D. M.; Haselwimmer, R. K.W.; Lonzarich, G. G., Magnetically mediated superconductivity in heavy fermion compounds, Nature, 394, 39 (1998)
[170] Maclaughlin, D. E.; Bernal, O. O.; Lukefahr, H. G., NMR and \(μ\) SR studies of non-Fermi-liquid behavior in disordered heavy-fermion systems, J. Phys.: Condens. Matter, 8, 9855 (1996)
[171] Manousakis, E., The Spin 1/2 Heisenberg antiferromagnet on a square lattice and its application to the cuprous oxides, Rev. Mod. Phys., 63, 1 (1991)
[172] J.O. Fjaerestad, J.B. Marston, Staggered orbital currents in the half-filled two-leg ladder, cond-mat/0107094.; J.O. Fjaerestad, J.B. Marston, Staggered orbital currents in the half-filled two-leg ladder, cond-mat/0107094.
[173] G.B. Martins, J.C. Xavier, C. Gazza, M. Vojta, E. Dagotto, Indications of spin-charge separation at short distance and stripe formation in the extended t-J model on ladders and planes, cond-mat/0007196.; G.B. Martins, J.C. Xavier, C. Gazza, M. Vojta, E. Dagotto, Indications of spin-charge separation at short distance and stripe formation in the extended t-J model on ladders and planes, cond-mat/0007196.
[174] K. Salama, W-K. Chen, P.C.W. Chu (Eds.), Materials and Mechanisms of Superconductivity: High Temperature Superconductivity VI (Houston, 1999), North-Holland, Amsterdam, 2000, reprinted from Physica C (2000) 341-348.; K. Salama, W-K. Chen, P.C.W. Chu (Eds.), Materials and Mechanisms of Superconductivity: High Temperature Superconductivity VI (Houston, 1999), North-Holland, Amsterdam, 2000, reprinted from Physica C (2000) 341-348.
[175] Mason, N.; Kapitulnik, A., Dissipation effects on the superconductor-insulator transition in 2D superconductors, Phys. Rev. Lett., 82, 5341 (1999)
[176] Mason, N.; Kapitulnik, A., True superconductivity in 2D “superconducting-insulating” system, Phys. Rev. B, 64, 060504 (2001)
[177] Meir, Y., Percolation-type description of the metal-insulator transition in two dimensions, Phys. Rev. Lett., 83, 3506 (1999)
[178] Metzner, W.; Di Castro, C., Conservation laws and correlation functions in the Luttinger liquid, Phys. Rev. B, 47, 16107 (1993)
[179] Metzner, W.; Vollhardt, D., Correlated lattice fermions in \(d\)=∞ dimensions, Phys. Rev. Lett., 62, 324 (1989)
[180] Metzner, W.; Castellani, C.; Di Castro, C., Fermi systems with strong forward scattering, Adv. Phys., 47, 317 (1998)
[181] Millikan, F. P.; Umbach, C. P.; Webb, R. A., Indications of a Luttinger-liquid in the fractional quantum Hall regime, Solid State Commun., 97, 309 (1996)
[182] Millis, A. J., Effect of a nonzero temperature on quantum critical points in itinerant fermion systems, Phys. Rev. B, 48, 7183 (1993)
[183] A.J. Mills, et al., unpublished.; A.J. Mills, et al., unpublished.
[184] Miranda, E.; Dobrosavlijevic, V.; Kotliar, G., Kondo disorder: a possible route towards non-Fermi-liquid behavior, J. Phys.: Condens. Matter, 8, 9871 (1996)
[185] Mishra, S. G.; Ramakrishnan, T. V., Temperature dependence of the spin susceptibility of nearly ferromagnetic Fermi systems, Phys. Rev. B, 18, 2308 (1978)
[186] Miyake, K.; Schmitt-Rink, S.; Varma, C. M., Spin-fluctuation-mediated even-parity paring in heavy-fermion superconductors, Phys. Rev. B, 34, 6554 (1986)
[187] Moessner, R.; Sondhi, S. L., Ising models of quantum frustration, Phys. Rev. B, 63, 224401 (2001)
[188] Moriya, T.; Kawabata, A., Effect of spin fluctuations on itinerant electron ferromagnetism, J. Phys. Soc. Japan, 34, 639 (1973)
[189] Moriya, T.; Kawabata, A., Effect of spin fluctuations on itinerant electron ferromagnetism II, J. Phys. Soc. Japan, 35, 669 (1973)
[190] Nagaoka, Y., Ferromagnetism in a narrow almost half-filled s band, Phys. Rev., 147, 392 (1966)
[191] Nagaosa, N., Quantum field theory in Condensed Matter Physics (1999), Springer: Springer Berlin · Zbl 0998.81533
[192] Nagaosa, N., Quantum field theory in Strongly Correlated Electronic Systems (1999), Springer: Springer Berlin · Zbl 0967.82003
[193] Noack, R.; White, S.; Scalapino, D., Correlations in a two-chain Hubbard model, Phys. Rev. Lett., 73, 882 (1994)
[194] Nozières, P., Interacting Fermi Systems (1963), Benjamin: Benjamin New York · Zbl 0129.22003
[195] Nozières, P.; deDominicis, C., Singularities in the X-ray absorption and emission of metals III. One body theory exact solutions, Phys. Rev., 178, 1097 (1969)
[196] Nozieres, P., A “Fermi-liquid” description of the Kondo problem at low temperatures, J. Low Temp. Phys., 17, 31 (1974)
[197] Nozières, P.; Blandin, A., Kondo effect in real metals, J. Phys., 41, 193 (1980)
[198] Nozières, P., The effect of recoil on edge singularities, J. Phys. I France, 4, 1275 (1994)
[199] Oganesyan, V.; Kivelson, S.; Fradkin, E., Quantum theory of a nematic Fermi liquid, Phys. Rev. B, 64, 195109 (2001)
[200] Orenstein, J.; Millis, A. J., Advances in the physics of high temperature superconductivity, Science, 288, 468 (2000)
[201] Orgad, D., Spectral functions for the Tomonaga-Luttinger and Luther-Emery liquids, Philos. Mag. B, 81, 375 (2001)
[202] Orignac, E.; Giamarchi, T., Effects of disorder on two strongly correlated coupled chains, Phys. Rev. B, 56, 7167 (1997)
[203] Perakis, I. E.; Varma, C. M.; Ruckenstein, A. E., Non-Fermi-liquid states of a magnetic ion in a metal, Phys. Rev. Lett., 70, 3467 (1993)
[204] Pfleiderer, C.; McMullan, G. J.; Lonzarich, G. G., Pressure induced crossover of the magnetic transition from second to first order near the quantum critical point in MnSi, Physica B, 206, 207, 847 (1995)
[205] Pfleiderer, C.; Friend, R. H.; Lonzarich, G. G.; Bernhoeft, N. R.; Flouquet, J., Transition from a magnetic to a nonmagnetic state as a function of pressure in MnSi, Int. J. Mod. Phys. B, 7, 887 (1993)
[206] Phillips, P.; Wan, Y.; Martin, I.; Knysh, S.; Dalidovich, D., Superconductivity in a two-dimensional electron gas, Nature, 395, 253 (1998)
[207] Pines, D.; Nozieres, P., The Theory of Quantum Liquids, Vol. I (1990), Addison-Wesley: Addison-Wesley New York · Zbl 0083.45201
[208] Polchinski, J., Low-energy dynamics of the spinon-gauge system, Nucl. Phys. B, 422, 617 (1994)
[209] Popović, D.; Fowler, A. B.; Washburn, S., Metal-insulator transition in two dimensions: effects of disorder and magnetic field, Phys. Rev. Lett., 79, 1543 (1990)
[210] Postma, H. W.Ch.; de Jonge, M.; Yao, Z.; Dekker, C., Electrical transport through carbon nanotube junctions created by mechanical manipulation, Phys. Rev. B, 62, R10653 (2000)
[211] Prange, R.; Kadanoff, L. P., Transport theory for electron-phonon interactions in metals, Phys. Rev., 134, A566 (1964) · Zbl 0124.23501
[212] Prange, R. E.; Girvin (Eds.), S. H., The Quantum Hall Effect (1985), Springer: Springer Berlin
[213] A. Prinz, V.M. Pudalov, G. Brunthaler, G. Bauer, Metal-insulator transition in Si-MOS structure in: K. Hess (Ed.), Proceedings International Meeting SIMD-99, Mauri, 1999, Superlattices Microstruct., 2000, in press.; A. Prinz, V.M. Pudalov, G. Brunthaler, G. Bauer, Metal-insulator transition in Si-MOS structure in: K. Hess (Ed.), Proceedings International Meeting SIMD-99, Mauri, 1999, Superlattices Microstruct., 2000, in press.
[214] Pudalov, V. M.; Brunthaler, G.; Prinz, A.; Bauer, G., Breakdown of the anomalous two-dimensional metallic phase in a parallel magnetic field, Physica B, 249-251, 697 (1998)
[215] Pudalov, V. M.; Brunthaler, G.; Prinz, A.; Bauer, G., Maximum metallic conductivity in Si MOS structures, Phys. Rev. B, 60, R2154 (1999)
[216] V.M. Pudalov, M. Gershenson, H. Kojima, N. Butch, E.M. Dizhur, G. Brunthaler, A. Prinz, G. Bauer, Fermi-liquid renormalization of the g-factor and effective mass in Si inversion layer, cond-mat/0105081.; V.M. Pudalov, M. Gershenson, H. Kojima, N. Butch, E.M. Dizhur, G. Brunthaler, A. Prinz, G. Bauer, Fermi-liquid renormalization of the g-factor and effective mass in Si inversion layer, cond-mat/0105081.
[217] S. Rabello, Q. Si, Spectral functions in a magnetic field as a probe of spin-charge separation in a Luttinger liquid, cond-mat/0008065.; S. Rabello, Q. Si, Spectral functions in a magnetic field as a probe of spin-charge separation in a Luttinger liquid, cond-mat/0008065.
[218] Ralph, D. C.; Ludwig, A. W.W.; von Delft, J.; Buhrman, R. A., 2-channel Kondo scaling in conductance signals from 2-level tunneling systems, Phys. Rev. Lett., 72, 1064 (1994)
[219] Ralph, D. C.; Ludwig, A. W.W.; von Delft, J.; Buhrman, R. A., Reply to “comment on: 2-channel Kondo scaling in conductance signals from 2-level tunneling systems”, Phys. Rev. Lett., 75, 770 (1995)
[220] Reizer, M. Yu., Effective electron-electron interaction in metals and superconductors, Phys. Rev. B, 39, 1602 (1989)
[221] Rickayzen, X., Green’s functions and Condensed Matter (1980), Academic: Academic London · Zbl 0573.34025
[222] M. Sarachik, private communication.; M. Sarachik, private communication.
[223] Sachdev, S.; Read, N., Metallic spin glasses, J. Phys.: Condens. Matter, 8, 9723 (1996)
[224] Sachdev, S., Quantum Phase Transitions (1999), Cambridge University Press: Cambridge University Press Cambridge
[225] Sarachik, M. P.; Kravchenko, S. V., Novel phenomena in dilute electron systems in two dimensions, Proc. Nat. Acad. USA, 96, 5900 (1999)
[226] Schlottman, P.; Sacramento, P. D., Multichannel Kondo problem and some applications, Adv. Phys., 42, 641 (1993)
[227] Schmitt-Rink, S.; Varma, C. M.; Ruckenstein, A. E., Spectral tion of holes in a quantum antiferromagnet, Phys. Rev. Lett., 60, 2793 (1998)
[228] Schröder, A.; Aeppli, G.; Bucher, E.; Ramazashvili, R.; Coleman, P., Scaling of magnetic fluctuations near a quantum phase transition, Phys. Rev. Lett., 80, 5623 (1998)
[229] Schröder, A.; Aeppli, G.; Coldea, R.; Adams, M.; Stockert, O.; Lohneysen, H.v.; Bucher, E.; Ramazashvili, R.; Coleman, P., Onset of antiferromagnetism in heavy-fermion metals, Nature, 407, 351 (2000)
[230] Schulz, H. J., Phases of two coupled Luttinger liquids, Phys. Rev. B, 53, 2959 (1996)
[231] H.J. Schulz, G. Cuniberti, P. Pieri, Fermi liquids and Luttinger liquids, Lecture notes of the Chia Laguna summer school, 1998 [cond-mat/9807366].; H.J. Schulz, G. Cuniberti, P. Pieri, Fermi liquids and Luttinger liquids, Lecture notes of the Chia Laguna summer school, 1998 [cond-mat/9807366].
[232] Sengupta, A., Spin in a fluctuating field: the Bose(+Fermi) Kondo models, Phys. Rev. B, 61, 4041 (2000)
[233] T. Senthil, M.P.A. Fisher, Fractionalization, topological order, and cuprate superconductivity, cond-mat/0008082.; T. Senthil, M.P.A. Fisher, Fractionalization, topological order, and cuprate superconductivity, cond-mat/0008082.
[234] Senthil, T.; Fisher, M. P.A., Fractionalization and confinement in the \(U(1)\) and \(Z_2\) gauge theories of strongly correlated electron systems, J. Phys. A, 10, L119 (2001) · Zbl 0978.82519
[235] Shankar, R., Renormalization-group approach to interacting fermions, Rev. Mod. Phys., 66, 129 (1994)
[236] A.A. Shashkin, S.V. Kravchenko, T.M. Klapwijk, Evolution of the metal-insulator transition in two dimensions with parallel magnetic field, cond-mat/0009180.; A.A. Shashkin, S.V. Kravchenko, T.M. Klapwijk, Evolution of the metal-insulator transition in two dimensions with parallel magnetic field, cond-mat/0009180.
[237] Shklovskii, B. I.; Efros, A. L., Electronic Properties of doped Semiconductors (1984), Springer: Springer Berlin
[238] Si, Q.; Kotliar, G., Fermi-liquid and non-Fermi-liquid phases of an extended Hubbard model in infinite dimensions, Phys. Rev. Lett., 70, 3143 (1993)
[239] Si, Q.; Varma, C. M., Metal-insulator transition of disordered interacting electrons, Phys. Rev. Lett., 81, 4951 (1998)
[240] Si, Q.; Rabello, S.; Ingersent, K.; Smith, J. L., Locally critical quantum phase transition in strongly correlated metals, Nature, 413, 804 (2001)
[241] Simonian, D.; Kravchenko, S. V.; Sarachik, M. P., Magnetic field suppression of the conducting phase in two dimensions, Phys. Rev. Lett., 79, 2304 (1997)
[242] Sire, C.; Varma, C. M.; Krishnamurthy, H. R., Theory of the non-Fermi-liquid transition in the two-impurity Kondo Model, Phys. Rev. B, 48, 13833 (1993)
[243] Sire, C.; Varma, C. M.; Rukenstein, A. E.; Giamarchi, T., Theory of the marginal-Fermi-liquid spectrum and pairing in a local copper oxide model, Phys. Rev. Lett., 72, 2478 (1994)
[244] Sólyom, J., The Fermi gas model of one-dimensional conductors, Adv. Phys., 28, 201 (1979)
[245] Sondhi, S. L.; Girvin, S. M.; Carini, J. P.; Sahar, D., Continuous quantum phase transitions, Rev. Mod. Phys., 69, 315 (1997)
[246] Spielman, S.; Fesler, F.; Eom, C. B.; Geballe, T. H.; Fejer, M. M.; Kapitulnik, A., Test of nonreciprocal circular birefringence in \(YBa_2 Cu_3O_7\) thin films as evidence for broken time-reversal symmetry, Phys. Rev. Lett., 65, 123 (1990)
[247] Stechel, E. B.; Sudbo, A.; Giamarchi, T.; Varma, C. M., Pairing fluctuations in a one-dimensional copper oxide model, Phys. Rev. B, 51, 553 (1995)
[248] Steglich, F.; Buschinger, B.; Gegenwart, P.; Lohmann, M.; Helfrich, R.; Langhammer, C.; Hellmann, P.; Donnevert, L.; Thomas, S.; Link, A.; Geibel, C.; Lang, M.; Sparn, G.; Assmus, W., Quantum critical phenomena in undoped heavy-fermion metals, J. Phys.: Condens. Matter, 8, 9909 (1996)
[249] Stockert, O.; Löhneysen, H.v.; Rosch, A.; Pyka, N.; Loewenhaupt, M., Two-dimensional fluctuations at the quantum-critical point of \(CeCu_{6−x}Au_x\), Phys. Rev. Lett., 80, 5627 (1998)
[250] Sudbo, A.; Varma, C. M.; Giamarchi, T.; Stechel, E. B.; Scalettar, R. T., Flux quantization and paring in one-dimensional copper-oxide models, Phys. Rev. Lett., 70, 978 (1993)
[251] Tanatar, B.; Ceperley, D. M., Ground state of the two-dimensional electron gas, Phys. Rev. B, 39, 5005 (1989)
[252] Thessieu, C.; Floquet, J.; Lapertot, G.; Stepanov, A. N.; Jaccard, D., Magnetism and spin fluctuations in a weak itinerant ferromagnet: MnSi, Solid State Commun., 96, 707 (1995)
[253] Thouless, D. J., Electrons in disordered systems and the theory of localization, Phys. Rep., 13, 93 (1974)
[254] Thouless, D., Percolation and localization, (Balian, R.; Maynard, R.; Toulouse, G., Ill Condensed Matter (1979), North-Holland: North-Holland Amsterdam) · Zbl 0097.43602
[255] Tranquada, J. M.; Sternlleb, B. J.; Axe, J. D.; Nakamura, Y.; Uchida, S., Evidence for stripe correlations of spins and holes in copper oxide superconductors, Nature, 375, 561 (1995)
[256] Trovarelli, O.; Geibel, C.; Mederle, S.; Langhammer, C.; Grosche, F. M.; Gegenwart, P.; Lang, M.; Sparn, G.; Steglich, F., \(YbRh_2 Si_2\): Pronounced non-Fermi-liquid effects above a low-lying magnetic phase transition, Phys. Rev. Lett., 85, 626 (2000)
[257] Tsvelik, A. M., Quantum Field Theory in Condensed Matter Physics (1995), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0968.82001
[258] Uren, M. J.; Davies, R. A.; Pepper, M., The observation of interaction and localisation effects in a two-dimensional electron gas at low temperatures, J. Physica C, 13, L985 (1980)
[259] Valla, T.; Fedorov, A. V.; Johnson, P. D.; Wells, B. O.; Hulbert, S. L.; Li, Q.; Gu, G. D.; Khoshizuka, N., Evidence for quantum critical behavior in the optimally doped cuprate \(Bi_2 Sr_2CaCu_2 O_{8+δ}\), Science, 285, 2110 (1999)
[260] Valla, T.; Fedorov, A. V.; Johnson, P. D.; Li, Q.; Gu, G. D.; Koshizuka, N., Temperature dependent scattering rates at the Fermi surface of optimally doped Bi2212, Phys. Rev. Lett., 85, 828 (2000)
[261] Varma, C. M., Mixed valence compounds, Rev. Mod. Phys., 48, 219 (1976)
[262] Varma, C. M.; Zawadowski, A., Scaling in an interacting two-component (valence-fluctuating) electron gas, Phys. Rev. B, 32, 7399 (1985)
[263] Varma, C. M., Phenomenological Aspects of Heavy Fermions, 55, 2723 (1985)
[264] Varma, C. M.; Schmitt-Rink, S.; Abrahams, E., Charge transfer excitation and superconductivity in “Ionic” metals, Solid State Commun., 62, 681 (1987)
[265] Varma, C. M.; Schmitt-Rink, S.; Abrahams, E., (Kresin, V.; Wolf, S., Novel Mechanisms of Superconductivity (1987), Plenum: Plenum New York)
[266] Varma, C. M.; Littlewood, P. B.; Schmitt-Rink, S.; Abrahams, E.; Ruckenstein, A. E., Phenemenology of the normal state of Cu-O high-temperature superconductors, Phys. Rev. Lett., 63, 1996 (1989)
[267] Varma, C. M., Phenomenolgical constraints on theories for high temperature superconductivity, Int. J. Mod. Phys. B, 3, 2083 (1998)
[268] Varma, C. M., Non-Fermi-liquid states and pairing instability of a general model of copper oxide metals, Phys. Rev. B, 55, 14554 (1997)
[269] Varma, C. M., Only Fermi-liquids are metals, Phys. Rev. Lett., 79, 1535 (1997)
[270] Varma, C. M., Pseudogap phase and the quantum-critical point in copper-oxide metals, Phys. Rev. Lett., 83, 3538 (1999)
[271] Varma, C. M., Proposal for an experiment to test a theory of high-temperature superconductors, Phys. Rev. B, 61, R3804 (2000)
[272] Varma, C. M.; Abrahams, E., Effective Lorentz force due to small-angle impurity scattering: magnetotransport in high-\(T_c\) superconductors, Phys. Rev. Lett., 86, 4652 (2001)
[273] Vitkalov, S. A.; Sarachik, M. P.; Klapwijk, T. M., Spin polarization of two-dimensional electrons determined from Shubnikov-de Haas oscillations as a function of angle, Phys. Rev. B, 64, 073101 (2001)
[274] Voit, J., One-dimensional Fermi liquids, Rep. Progr. Phys., 58, 97 (1995)
[275] Voit, J., Charge-spin separation and the spectral properties of Luttinger liquids, Phys. Rev. B, 47, 6740 (1993)
[276] B.A. Volkov, Yu.V. Kopaev, A.I. Rusinov, Theory of “excitonic” ferromagnetism, Zh. Eksp. Teor. Fyz. 68 (1975) 1899 [Sov. Phys. JETP 41 (1976) 952].; B.A. Volkov, Yu.V. Kopaev, A.I. Rusinov, Theory of “excitonic” ferromagnetism, Zh. Eksp. Teor. Fyz. 68 (1975) 1899 [Sov. Phys. JETP 41 (1976) 952].
[277] Vollhardt, D., High dimensions—a new approach to fermionic lattice models, Physica B, 169, 277 (1991)
[278] von Löhneysen, H.; Pietrus, T.; Portisch, G.; Schlager, H. G.; Schröder, A.; Sieck, M.; Trappmann, M., Non-Fermi-liquid behavior in a heavy-fermion alloy at a magnetic instability, Phys. Rev. Lett., 72, 3262 (1994)
[279] von Löhneysen, H., Non-Fermi-liquid behavior in heavy-fermion systems, Physica, 206, 101 (1995)
[280] Löhneysen, H.v., Non-Fermi-liquid behaviour in the heavy fermion system \(CeCu_{6−x}Au_x\), J. Phys.: Condens. Matter, 8, 9689 (1996)
[281] Löhneysen, H.v.; Neubert, A.; Schröder, A.; Stockert, O.; Tutsch, U.; Loewenhaupt, M.; Rosch, A.; Wölfle, P., Magnetic order and transport in the heavy-fermion system \(CeCu_{6−x}Au_x\), Eur. Phys. J. B, 5, 447 (1999)
[282] Löhneysen, H.v.; Pietrus, T.; Portish, G.; Schlager, H. G.; Schröder, A.; Sieck, M.; Trappmann, T., Non-Fermi-liquid behavior in a heavy-fermion alloy at a magnetic instability, Phys. Rev. Lett., 72, 3262 (1994)
[283] Wegner, F. J., (Nagaoka, H.; Fukuyama, H., Anderson Localisation (1982), Springer: Springer Berlin)
[284] Wen, X. G., Chiral Luttinger liquid and the edge excitations in the fractional quantum Hall states, Phys. Rev. B, 41, 12838 (1990)
[285] White, S. R.; Scalapino, D. J., Density matrix renormalization group study of the striped phase in the 2D t-J model, Phys. Rev. Lett., 80, 1272 (1998)
[286] Wilson, K. G., The renormalization group: critical phenomena and the Kondo problem, Rev. Mod. Phys., 47, 773 (1975)
[287] Wingreen, N. S.; Altshuler, B. L.; Meir, Y., Comment on “2-channel Kondo scaling in conductance signals from 2-level tunneling systems”, Phys. Rev. Lett., 75, 769 (1995)
[288] Wuyts, B.; Moschalkov, V. V.; Bruynseraede, Y., Resistivity and hall effect of metallic oxygen-deficient \(YBa_2 Cu_3O_x\) films in the normal state, Phys. Rev., B 53, 9418 (1996)
[289] Yaish, Y.; Prus, O.; Buchstab, E.; Shapira, S.; Yoseph, G. B.; Sivan, U.; Stern, A., Interband scattering and the “metallic phase” of two-dimensional holes in GaAs/AlGaAs, Phys. Rev. Lett., 84, 4954 (2000)
[290] Yasuoka, H., Hyperfine Interactions, 105, 27 (1997)
[291] Yoon, J.; Li, C. C.; Shahar, D.; Tsui, D. C.; Shayegan, M., Parallel magnetic field induced transition in transport in the dilute two-dimensional hole system in GaAs, Phys. Rev. Lett., 84, 4421 (2000)
[292] Young, D. R.; Hall, D.; Torelli, M. E.; Fisk, Z.; Sarrao, J. L.; Thompson, J. D.; Ott, H.-R.; Oseroff, S. B.; Goodrich, R. G.; Zysler, R., High-temperature weak ferromagnetism in a low-density free-electron gas, Nature, 387, 2219 (1999)
[293] Zaanen, J.; Sawatsky, G.; Allen, J. W., Band gaps and electronic structure of transition-metal compounds, Phys. Rev. Lett., 55, 418 (1985)
[294] Zaanen, J.; Gunnarson, O., Charged domain lines and the magnetism of high-\(T_c\) oxides, Phys. Rev. B, 40, 7391 (1989)
[295] Zaanen, J.; Horbach, M.; van Saarloos, W., Charged domain-wall dynamics in doped antiferromagnets and spin fluctuations in cuprate superconductors, Phys. Rev. B, 53, 8671 (1996)
[296] Zaanen, J., Order out of disorder in a gas of elastic quantum strings in 2+1 dimensions, Phys. Rev. Lett., 84, 753 (2000)
[297] F.-C. Zhang, T.M. Rice, An anyon superconducting groundstate in Si MOSFETS? cond-mat/9708050.; F.-C. Zhang, T.M. Rice, An anyon superconducting groundstate in Si MOSFETS? cond-mat/9708050.
[298] Zarand, G.; Zawadowski, A., Theory of tunneling centers in metallic systems: role of excited states and orbital Kondo effect, Phys. Rev. Lett., 72, 542 (1991)
[299] Zhitomirsky, M. E.; Rice, T. M.; Anisimov, V. I., Magnetic properties: ferromagnetism in the hexaborides, Nature, 402, 251 (1999)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.