Skip to main content
    • Aa
    • Aa
  • Print publication year: 2015
  • Online publication date: December 2015

18 - Mixed valence, fluctuations, and topology

Recommend this book

Email your librarian or administrator to recommend adding this book to your organisation's collection.

Introduction to Many-Body Physics
  • Online ISBN: 9781139020916
  • Book DOI:
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
[1] P. Coleman, New approach to the mixed-valence problem, Phys. Rev. B, vol. 29, p. 3035, 1984.
[2] S. E. Barnes, New method for the Anderson model, J. Phys. F, vol. 6, p. 1375, 1976.
[3] N. Read and D. M. Newns, A new functional integral formalism for the degenerate Anderson model, J. Phys. C, vol. 29, p. L105, 1983.
[4] A. J. Millis and P. A. Lee, Large-orbital-degeneracy expansion for the lattice Anderson model, Phys. Rev. B, vol. 35, no. 7, p. 3394, 1987.
[5] M. C. Gutzwiller, Effect of correlation on the ferromagnetism of transition metals, Phys. Rev. Lett., vol. 10, no. 5, p. 159, 1963. The Hubbard model was written down independently by Gutzwiller in equation (11) of this paper.
[6] F. D. M. Haldane, Scaling theory of the asymmetric Anderson model, Phys. Rev. Lett., vol. 40, p. 416, 1978.
[7] P. W. Anderson, Infrared catastrophe in Fermi gases with local scattering potentials, Phys. Rev. Lett., vol. 18, p. 1049, 1967.
[8] S. Elitzur, Impossibility of spontaneously breaking local symmetries, Phys. Rev. D, vol. 12, p. 3978, 1975.
[9] P. Coleman, Large-N as a classical limit (1/N ˜ ħ) of mixed valence, J. Magn. Magn. Mater., vol. 47–48, p. 323, 1985.
[10] P. Coleman and N. Andrei, Kondo-stabilized spin liquids and heavy-fermion superconductivity, J. Phys.: Condens. Matter., vol. 1, p. 4057, 1989.
[11] N. Read, Role of infrared divergences in the 1/N expansion of the U =8Anderson model, J. Phys. C: Solid State Phys., vol. 18, no. 13, p. 2651, 1985.
[12] E. Witten, Chiral symmetry, the 1/N expansion and the SU(N) Thirring model, Nucl. Phys. B, vol. 145, p. 110, 1978.
[13] P. Coleman and N. Andrei, Diagonalisation of the generalised Anderson model, J. Phys. C: Solid State Phys., vol. 19, no. 17, p. 3211, 1986.
[14] P. Nozières and C. De Dominicis, Singularities in the X-ray absorption and emission of metals III. one-body theory exact solution, Phys. Rev., vol. 178, no. 3, p. 1097, 1969.
[15] P. Coleman, J. B. Marston, and A. J. Schofield, Transport anomalies in a simplified model for a heavy electron quantum critical point, Phys. Rev. B, vol. 72, p. 245111, 2005.
[16] T. Senthil, M. Vojta, and S. Sachdev, Fractionalized Fermi liquids, Phys. Rev. Lett., vol. 90, p. 216403, 2003.
[17] P. Coleman, J. B. Marston, and A. J. Schofield, Transport anomalies in a simplified model for a heavy-electron quantum critical point, Phys. Rev., vol. 72, p. 245111, 2005.
[18] P. W. Anderson, The resonating valence bond state in La2CuO4 and superconductivity, Science, vol. 235, p. 1196, 1987.
[19] L. B. Ioffe and A. I. Larkin, Gapless fermions and gauge fields in dielectrics, Phys. Rev. B, vol. 39, p. 8988, 1989.
[20] J. W. Allen, B. Batlogg, and P. Wachter, Large low-temperature Hall effect and resistivity in mixed-valent SmB6, Phys. Rev. B, vol. 20, p. 4807, 1979.
[21] J. E. Moore, The birth of topological insulators, Nature, vol. 464, no. 7286, p. 194, 2010.
[22] R. B. Laughlin, Quantized Hall conductivity in two-dimensions, Phys. Rev. B, vol. 23, no. 10, p. 5632, 1981.
[23] D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. Den Nijs, Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett., vol. 49, no. 6, p. 405, 1982.
[24] F. D. M. Haldane, Model for a quantum Hall effect without Landau levels condensed matter realization of the parity anomaly, Phys. rev. lett., vol. 61, no. 18, p. 2015, 1988.
[25] C. L. Kane and E. J. Mélé, Z2 topological order and the quantum spin Hall effect, Phys. Rev. Lett., vol. 95, p. 146802, 2005.
[26] B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science, vol. 314, no. 5806, p. 1757, 2006.
[27] R. Roy, Z2 classification of quantum spin Hall systems; an approach using timereversal invariance Phys. Rev. B, vol. 79, p. 195321, 2009.
[28] L. Fu, C. L. Kane, and E. J.Mélé, Topological insulators in three dimensions, Phys. Rev. Lett., vol. 98, p. 106803, 2007.
[29] J. E. Moore and L. Balents, Topological invariants of time-reversal-invariant band structures, Phys. Rev. B, vol. 75, p. 121306(R), 2007.
[30] G.E. Volovik, Fermion zero modes at the boundary of superfluid 3He-B, JETP Lett., vol. 90, no. 5, p. 398, 2009.
[31] G.E. Volovik, Topological invariant for superfluid 3He-B and quantum phase transitions, JETP Lett., vol. 90, no. 8, p. 587, 2009.
[32] M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi and S.-C. Zhan, Quantum spin Hall insulator state in HgTe quantum wells, Science, vol. 318, p. 766, 2007.
[33] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, A topological Dirac insulator in a quantum spin Hall phase, Nature, vol. 452, no. 7190, p. 970, 2008.
[34] L. Fu and C. L. Kane, Topological insulators with inversion symmetry, Phys. Rev. B, vol. 76, no. 4, p. 45302, 2007.
[35] M. Dzero, K. Sun, V. Galitski, and P. Coleman, Topological Kondo insulators, Phys. Rev. Lett., vol. 104, p. 106408, 2010.
[36] J. C. Cooley, M. C. Aronson, A. Lacerda, Z. Fisk, P. C. Canfield, and R. P. Guertin, High magnetic fields and the correlation gap in SmB6, Phys. Rev. B, vol. 52, p. 7322, 1995.
[37] M. Dzero, K. Sun, P. Coleman, and V. Galitski, Theory of topological Kondo insulators, Phys. Rev. B, vol. 85, p. 045130, 2012.
[38] S. Wolgast, Ç. Kurdak, K. Sun, J.W. Allen, D.-J. Kim, and Z. Fisk, Low-temperature surface conduction in the Kondo insulator SmB6, Phys. Rev. B, vol. 88, p. 180405, 2013.
[39] D. J. S. Thomas, T. Grant, J. Botimer, Z. Fisk, and J. Xia, Surface Hall effect and nonlocal transport in SmB6: evidence for surface conduction, Sci. Rep., vol. 3, p. 3150, 2014.
[40] N. Xu, P. K. Biswas, J. H. Dil, et al. Direct observation of the spin texture in SmB6 as evidence of the topological Kondo insulator, Nat. Commun., vol. 5, p. 1, 2014.
[41] V. Alexandrov, P. Coleman, and O. Erten, Surface Kondo breakdown and the light surface states in topological Kondo insulators, Phys. Rev. Lett., vol. 114, p. 177202, 2015.
[42] W. Shockley, On the surface states associated with a periodic potential, Phys. Rev., vol. 56, p. 317, 1939.
[43] A. Yu. Kitaev, Unpaired Majorana fermions in quantum wires, Phys.-Usp (Supplement), vol. 44, no. 10S, p. 131, 2001.
[44] V. Alexandrov and P. Coleman, End states in a 1-D topological Kondo insulator, Phys. Rev. B, vol. 90, p. 115147, 2014.
[45] V. Alexandrov, M. Dzero, and P. Coleman, Cubic topological Kondo insulators, Phys. Rev. Lett., vol. 111, p. 226403, 2013.
[46] M. B. Maple and D. Wohlleben, Nonmagnetic 4f shell in the high-pressure phase of SmS, Phys. Rev. Lett., vol. 27, no. 8, p. 511, 1971.
[47] T. Takimoto, SmB6: a promising candidate for a topological insulator, J. Phys. Soc. Jpn., vol. 80, no. 12, p. 123710, 2011.
[48] M. Neupane, N. Alidoust, S. Y. Xu, and T. Kondo, Surface electronic structure of the topological Kondo-insulator candidate correlated electron system SmB6, Nat. Commun., 4:2991 DOI:0.1038/ncomms3991, 2013.
[49] N. Xu, X. Shi, P. K. Biswas, et al., Surface and bulk electronic structure of the strongly correlated system SmB6 and implications for a topological Kondo insulator, Phys. Rev. B, vol. 88, p. 121102, 2013.
[50] M. Sigrist and K. Ueda, Unconventional superconductivity, Rev. Mod. Phys., vol. 63, p. 239, 1991.
[51] N. Mathur, F. M. Grosche, S. R. Julian, I. R. Walker, D. M. Freye, and R. K. W. Haselwimmer, and G. G. Lonzarich, Magnetically mediated superconductivity in heavy-fermion compounds, Nature, vol. 394, p. 39, 1998.
[52] C. Petrovic, P. G. Pagliuso, M. F. Hundley, R. Movshovich, J. L. Sarrao, J. D. Thompson, Z. Fisk, and P. Monthoux, Heavy-fermion superconductivity in CeCoIn5 at 2.3 K, J. Phys: Condens. Matter, vol. 13, p. L337, 2001.
[53] N. J. Curro, T. Caldwell, E. D. Bauer et al., Unconventional superconductivity in PuCoGa5, Nature, vol. 434, p. 622, 2005.
[54] G. Stewart, Heavy-fermion systems, Rev. Mod. Phys., vol. 73, p. 797, 2001.
[55] G. Stewart, Addendum: Non-Fermi-liquid behavior in d-and f-electron metals, Rev. Mod. Phys., vol. 78, p. 743, 2006.
[56] P. Coleman, C. Pépin, Q. Si, and R. Ramazashvili, How do Fermi liquids get heavy and die?, J. Phys.: Condens. Matter, vol. 13, p. 273, 2001.
[57] C. M. Varma, Z. Nussinov, and W. van Saarlos, Singular Fermi liquids, Phys. Rep., vol. 361, p. 267, 2002.
[58] H. von Löhneysen, A. Rosch, M. Vojta, and P. Wölfle, Fermi-liquid instabilities at magnetic quantum phase transitions, Rev. Mod. Phys., vol. 79, p. 1015, Aug 2007.
[59] J. Custers, P. Gegenwart, H. Wilhelm, The break-up of heavy electrons at a quantum critical point, Nature, vol. 424, p. 524, 2003.
[60] Y. Matsumoto, S. Nakatsuji, K. Kuga, Y. Karaki, and N. Horie, Quantum criticality without tuning in the mixed valence compound ß-YbAlB4, Science, vol. 331, p. 316, 2011.
[61] P. Coleman and N. Andrei, Kondo-stabilised spin liquids and heavy-fermion superconductivity, J. Phys.: Condens. Matter, vol. 1, no. 26, p. 4057, 1989.
[62] R. Flint, M. Dzero, P. Coleman, and M. Dzero, Heavy electrons and the symplectic symmetry of spin, Nat. Phys., vol. 4, no. 8, p. 643, 2008.
[63] R. Flint and P. Coleman, Tandem pairing in heavy-fermion superconductors, Phys. Rev. Lett., vol. 105, p. 246404, 2010.
[64] R. Flint, A. Nevidomskyy, and P. Coleman, Composite pairing in a mixed-valent two-channel Anderson model, Phys. Rev. B, vol. 84, no. 6, p. 064514, 2011.
[65] W. Metzner and D. Vollhardt, Correlated lattice fermions in d = ∞ dimensions, Phys. Rev. Lett., vol. 62, p. 324, 1989.
[66] A. Georges and G. Kotliar, Hubbard model in infinite dimensions, Phys. Rev. B, vol. 45, p. 6479, 1992.
[67] A. Georges, G. Kotliar, W. Krauth, and M. Rozenberg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys., vol. 68, p. 13, 1996.
[68] S. R. White, Strongly correlated electron systems and the density matrix renormalization group, Phys. Rep., vol. 301, p. 187, 1998.
[69] K. A. Hallberg, New trends in density matrix renormalization, Adv. Phys., vol. 55, p. 477, 2006.
[70] T. R. Chien, Z. Z. Wang, and N. P. Ong, Effect of Zn impurities on the normal-state Hall angle in single-crystal YBa2Cu3-xZnx O7-δ, Phys. Rev. Lett., vol. 67, p. 2088, 1991.
[71] J. Paglione, M. A. Tanatar, D. G. Hawthorn, Nonvanishing energy scales at the quantum critical point of CeCoIn5, Phys. Rev. Lett., vol. 97, p. 106606, 2006.
[72] P. W. Anderson, Hall effect in the two-dimensional Luttinger liquid, Phys. Rev. Lett., vol. 67, p. 2092, 1991.
[73] P. Coleman, A. J. Schofield, and A. M. Tsvelik, Phenomenological transport equation for the cuprate metals, Phys. Rev. Lett., vol. 76, p. 1324, 1996.
[74] Y. Nakajima, K. Izawa, Y. Matsuda, Normal-state Hall angle and magnetoresistance in quasi-2D heavy fermion CeCoIn5 near a quantum critical point, J. Phys. Soc. Jpn., vol. 73, p. 5, 2004.
[75] J. M. Drouffe and J. B. Zuber, Strong coupling and mean-field methods in lattice gauge theories, Phys. Rep., vol. 102, p. 1, 1983.