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Quasi-classical Physics Within Quantum Criticality in HF Compounds

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Theory of Heavy-Fermion Compounds

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 182))

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Abstract

In this chapter, we explore how the fermion condensation paves the road for quasi-classical physics in HF compounds. This means simply that systems with FC admit partly the quasi-classical description of their thermodynamic and transport properties. This, in turn, simplifies a lot not only of their description but permits to gain more insights both in the puzzling NFL physics of HF compounds and of the physics of FC itself. The quasi-classical physics starts to be applicable near FCQPT, at which FC generates flat bands and quantum criticality, and makes the density of electron states in strongly correlated metals diverge. As we shall see, due to the formation of flat bands the strongly correlated metals exhibit the classical properties of elemental ones like copper, silver, aluminum, etc., for the strongly correlated metals demonstrate the quasi-classical behavior at low temperatures.

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References

  1. A.I. Petit, P.L. Dulong, Annales de Chimie ed de Physique 10, 395 (1819)

    Google Scholar 

  2. L. Boltzmann, Wiener Berichte 74, 553 (1877)

    Google Scholar 

  3. P. Debye, Annalen der Physik 39, 789 (1912). (Leipzig).

    Google Scholar 

  4. L.D. Landau, Zh Eksp, Teor. Fiz. 30, 1058 (1956)

    Google Scholar 

  5. D.S. Greywall, Phys. Rev. B 41, 1842 (1990)

    Article  ADS  Google Scholar 

  6. M. Neumann, J. Nyéki, B. Cowan, J. Saunders, Science 317, 1356 (2007)

    Article  ADS  Google Scholar 

  7. V.A. Khodel, J.W. Clark, V.R. Shaginyan, M.V. Zverev, JETP Lett. 92, 585 (2010)

    Article  Google Scholar 

  8. C. Bäuerle, Y.M. Bunkov, A. Chen, S. Fisher, H. Godfrin, J. Low Temp. 110, 333 (1998)

    Article  ADS  Google Scholar 

  9. C. Bäuerle, Y.M. Bunkov, A.S. Chen, S.N. Fisher, H. Godfrin, J. Low Temp. 110, 345 (1998)

    Article  ADS  Google Scholar 

  10. M. Morishita, K. Ishida, K. Yawata, H. Nagatani, H. Fukuyama, J. Low Temp. 110, 351 (1998)

    Article  ADS  Google Scholar 

  11. M. Morishita, H. Nagatani, H. Fukuyama, J. Low Temp. 113, 299 (1998)

    Article  ADS  Google Scholar 

  12. A. Casey, H. Patel, J. Cowan, B.P. Saunders, Phys. Rev. Lett. 90, 115301 (2003)

    Article  ADS  Google Scholar 

  13. A. Golov, F. Pobell, Europhys. Lett. 38, 353 (1997)

    Article  ADS  Google Scholar 

  14. V.R. Shaginyan, A.Z. Msezane, K.G. Popov, V.A. Stephanovich, Phys. Rev. Lett. 100, 096406 (2008)

    Article  ADS  Google Scholar 

  15. I.M. Khalatnikov, An Introduction to the Theory of Superfluidity (Benjamin, New York, 1965)

    Google Scholar 

  16. A.A. Abrikosov, I.M. Halatnikov, Soviet Phys. Uspekhi 1, 68 (1958)

    Article  ADS  Google Scholar 

  17. M. Pfitzner, P. Wölfle, Phys. Rev. B 33, 2003 (1986)

    Article  ADS  Google Scholar 

  18. P. Nozières, J. Phys. I France 2, 443 (1992)

    Article  Google Scholar 

  19. M.V. Zverev, M. Baldo, JETP 87, 1129 (1998)

    Article  ADS  Google Scholar 

  20. M.V. Zverev, M. Baldo, J. Phys. Condens. Matter 11, 2059 (1999)

    Article  ADS  Google Scholar 

  21. S.A. Artamonov, Y.G. Pogorelov, V.R. Shaginyan, JETP Lett. 68, 942 (1998)

    Article  ADS  Google Scholar 

  22. V.A. Khodel, J.W. Clark, M.V. Zverev, Phys. Rev. B 78, 075120 (2008)

    Article  ADS  Google Scholar 

  23. V.A. Khodel, V.R. Shaginyan, JETP Lett. 51, 553 (1990)

    ADS  Google Scholar 

  24. G.E. Volovik, JETP Lett. 53, 222 (1991)

    ADS  Google Scholar 

  25. V.A. Khodel, V.R. Shaginyan, V.V. Khodel, Phys. Rep. 249, 1 (1994)

    Article  ADS  Google Scholar 

  26. V.R. Shaginyan, M.Y. Amusia, K.G. Popov, Phys. Usp. 50, 563 (2007)

    Article  ADS  Google Scholar 

  27. V.R. Shaginyan, M.Y. Amusia, A.Z. Msezane, K.G. Popov, Phys. Rep. 492, 31 (2010)

    Article  ADS  Google Scholar 

  28. A.A. Abrikosov, L.P. Gorkov, I.E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1975)

    Google Scholar 

  29. V.A. Khodel, M.V. Zverev, V.M. Yakovenko, Phys. Rev. Lett. 95, 236402 (2005)

    Article  ADS  Google Scholar 

  30. P. Wölfle, E. Abrahams, Phys. Rev. B 84, 041101(R) (2011)

    Article  ADS  Google Scholar 

  31. H. v. Löhneysen, A. Rosch, M. Vojta, P. Wölfle, Rev. Mod. Phys. 79, 1015 (2007).

    Google Scholar 

  32. P. Gegenwart, Q. Si, F. Steglich, Nature Phys. 4, 186 (2008)

    Article  ADS  Google Scholar 

  33. P. Gegenwart, J. Custers, T. Tayama, K. Tenya, C. Geibel, O. Trovarelli, F. Steglich, K. Neumaier, Acta Phys. Pol. 34, 323 (2003)

    Google Scholar 

  34. J. Custers, P. Gegenwart, S. Geibel, F. Steglich, P. Coleman, S. Paschen, Phys. Rev. Lett. 104, 186402 (2010)

    Article  ADS  Google Scholar 

  35. L. Taillefer, Ann. Rev. Cond. Matt. Phys. 1, 51 (2010)

    Article  ADS  Google Scholar 

  36. D. Pines, P. Noziéres, Theory of Quantum Liquids (Benjamin, New York, 1966)

    Google Scholar 

  37. D.M. Maslov, A.V. Chubukov, Phys. Rev. B 81, 045110 (2010)

    Article  ADS  Google Scholar 

  38. S.L. Bud’ko, E. Morosan, P.C. Canfield, Phys. Rev. B 69, 014415 (2004)

    Article  ADS  Google Scholar 

  39. J.W. Clark, V.A. Khodel, M.V. Zverev, Phys. Lett. A 377, 647 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  40. A.S. Alexandrov, N. Mott, Polarons and Bipolarons (World Scientific, Singapore, 1996)

    Book  Google Scholar 

  41. A.S. Alexandrov, P.P. Kornilovitch, Phys. Rev. Lett. 82, 807 (1999)

    Article  ADS  Google Scholar 

  42. E.M. Lifshitz, L.P. Pitaevskii, Physical Kinetics (Pergamon Press, Oxford, 1981)

    Google Scholar 

  43. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1996)

    Google Scholar 

  44. J.A. Hertz, Phys. Rev. B 14, 1165 (1976)

    Article  ADS  Google Scholar 

  45. A.J. Millis, Phys. Rev. B 48, 7183 (1993)

    Article  ADS  Google Scholar 

  46. A.S. Alexandrov, Physica C 274, 237 (1997)

    Article  ADS  Google Scholar 

  47. R.D. Barnard, Thermoelectricity in Metals and Alloys (Taylor and Francis, London, 1972)

    Google Scholar 

  48. S. Hartmann, N. Oeschler, C. Krellner, C. Geibel, S. Paschen, F. Steglich, Phys. Rev. Lett. 104, 096401 (2010)

    Article  ADS  Google Scholar 

  49. K. Behnia, D. Jaccard, J. Flouquet, J. Phys.: Condens. Matter 16, 5187 (2004)

    ADS  Google Scholar 

  50. V.R. Shaginyan, K.G. Popov, V.A. Khodel, Phys. Rev. B 88, 115103 (2013)

    Article  ADS  Google Scholar 

  51. A.N. Bruin, H. Sakai, R.S. Perry, A.P. Mackenzie, Science 880, 339 (2013)

    Google Scholar 

  52. C.M. Varma, P.B. Littlewood, S. Schmittrink, E. Abrahams, A.E. Ruckenstein, Phys. Rev. Lett. 63, 1996 (1989)

    Article  ADS  Google Scholar 

  53. M.E. Simon, C.M. Varma, Phys. Rev. Lett. 89, 247003 (2002)

    Article  ADS  Google Scholar 

  54. P. Phillips, Phil. Trans. R. Soc. A 369, 1572 (2011)

    Article  ADS  Google Scholar 

  55. P. Phillips, Phil. Trans. R. Soc. A 369, 1574 (2011)

    Article  ADS  Google Scholar 

  56. P. Aynajian, E. Neto, A. Gyenis, R.E. Baumbach, J.D. Thompson, Z. Fisk, E.D. Bauer, A. Yazdani, Nature 486, 201 (2012)

    Google Scholar 

  57. V.R. Shaginyan, A.Z. Msezane, K.G. Popov, J.W. Clark, M.V. Zverev, V.A. Khodel, Phys. Rev. B 86, 085147 (2012)

    Article  ADS  Google Scholar 

  58. D.C. Peets, D.G. Hawthorn, K.M. Shen, Y.J. Kim, D.S. Ellis, H. Zhang, S. Komiya, Y. Ando, G.A. Sawatzky, R. Liang, D.A. Bonn, W.N. Hardy, Phys. Rev. Lett. 103, 087402 (2009)

    Article  ADS  Google Scholar 

  59. M.M.J. French, J.G. Analytis, A. Carrington, L. Balicas, N.E. Hussey, New J. Phys. 11, 055057 (2009)

    Article  ADS  Google Scholar 

  60. J.W. Alldredge, J. Lee, K. McElroy, M. Wang, K. Fujita, Y. Kohsaka, C. Taylor, H. Eisaki, S. Uchida, P.J. Hirschfeld, J.C. Davis, Nature Phys. 4, 319 (2008)

    Google Scholar 

  61. G.E. Volovik, in Quantum Analogues: From Phase Transitions to Black Holes and Cosmology, ed. by W.G. Unruh, R. Schutzhold, Springer Lecture Notes in Physics, 718 (Springer, Orlando, 2007), p. 31.

    Google Scholar 

  62. V.R. Shaginyan, Physics of Atomic Nuclei 74, 1107 (2011)

    Article  ADS  Google Scholar 

  63. V.A. Khodel, J.W. Clark, M.V. Zverev, Physics of Atomic Nuclei 74, 1237 (2011)

    Article  ADS  Google Scholar 

  64. M.V. Zverev, V.A. Khodel, V.R. Shaginyan, M. Baldo, JETP Lett. p. 863 (1997).

    Google Scholar 

  65. M.Y. Amusia, A.Z. Msezane, V.R. Shaginyan, Phys. Lett. A 320, 459 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  66. N. Oeschler, P. Gegenwart, M. Lang, R. Movshovich, J.L. Sarrao, J.D. Thompson, F. Steglich, Phys. Rev. Lett. 91, 076402 (2003)

    Article  ADS  Google Scholar 

  67. J.G. Donath, F. Steglich, E.D. Bauer, J.L. Sarrao, P. Gegenwart, Phys. Rev. Lett 100, 136401 (2008)

    Article  ADS  Google Scholar 

  68. S. Zaum, K. Grube, R. Schäfer, E.D. Bauer, J.D. Thompson, H. v. Löhneysen. Phys. Rev. Lett. 106, 087003 (2011)

    Article  ADS  Google Scholar 

  69. R. Kúchler, N. Oeschler, P. Gegenwart, T. Cichorek, K. Neumaier, O. Tegus, C. Geibel, J.A. Mydosh, F. Steglich, L. Zhu, Q. Si, Phys. Rev. Lett. 91, 066405 (2003)

    Google Scholar 

  70. P. Gegenwart, F. Weickert, M. Garst, R.S. Perry, Y. Maeno, Phys. Rev. Lett. 96, 136402 (2006)

    Article  ADS  Google Scholar 

  71. C. Stingl, R.S. Perry, Y. Maeno, P. Gegenwart, Phys. Rev. Lett. 107, 026404 (2011)

    Article  ADS  Google Scholar 

  72. V.A. Khodel, J.W. Clark, H. Li, M.V. Zverev, Phys. Rev. Lett. 98, 216404 (2007)

    Article  ADS  Google Scholar 

  73. S.A. Grigera, P. Gegenwart, R.A. Borzi, F. Weickert, A.J. Schofield, R.S. Perry, T. Tayama, T. Sakakibara, Y. Maeno, A.G. Green, A.J. Millis, A.P. Mackenzie, Science 306, 1154 (2004)

    Google Scholar 

  74. R.A. Borzi, S.A. Grigera, J. Farrell, R.S. Perry, S.J.S. Lister, S.L. Lee, D.A. Tennant, Y. Maeno, A.P. Mackenzie, Science 315, 214 (2007)

    Article  ADS  Google Scholar 

  75. A.W. Rost, R.S. Perry, J.F. Mercure, A.P. Mackenzie, S.A. Grigera, Science 325, 1360 (2009)

    Article  ADS  Google Scholar 

  76. S. Raghu, A. Paramekanti, E.A. Kim, R.A. Borzi, S.A. Grigera, A.P. Mackenzie, S.A. Kivelson, Phys. Rev. B 79, 214402 (2009)

    Article  ADS  Google Scholar 

  77. A.W. Rost, S.A. Grigera, J.A.N. Bruin, R.S. Perry, D. Tian, S. Raghu, S.A. Kivelson, A.P. Mackenzie, Proc. Natl. Acad. Sci. USA 108, 16549 (2011)

    Google Scholar 

  78. B. Binz, M. Sigrist, Europhys. Lett. 65, 816 (2004)

    Article  ADS  Google Scholar 

  79. A.M. Berridge, S.A. Grigera, B.D. Simons, A.G. Green, Phys. Rev. B 81, 054429 (2010)

    Article  ADS  Google Scholar 

  80. A.P. Mackenzie, J.A.N. Bruin, R.A. Borzi, A.W. Rost, S.A. Grigera, Physica C 481, 207 (2012)

    Article  ADS  Google Scholar 

  81. V.A. Khodel, J.W. Clark, V.R. Shaginyan, M.V. Zverev, JETP Lett. 92, 532 (2010)

    Article  ADS  Google Scholar 

  82. V.R. Shaginyan, A.Z. Msezane, K.G. Popov, J.W. Clark, M.V. Zverev, V.A. Khodel, JETP Lett. 96, 397 (2012)

    Article  ADS  Google Scholar 

  83. V.R. Shaginyan, A.Z. Msezane, K.G. Popov, J.W. Clark, M.V. Zverev, V.A. Khodel, Phys. Lett. A 377, 2800 (2013)

    Article  ADS  Google Scholar 

  84. K. Deguchi, S. Matsukawa, N.K. Sato, T. Hattori, K. Ishida, H. Takakura, T. Ishimasa, Nature Materials 11, 1013 (2012)

    ADS  Google Scholar 

  85. V.R. Shaginyan, A.Z. Msezane, K.G. Popov, G.S. Japaridze, V.A. Khodel, Phys. Rev. B 87, 245122 (2013)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Racah Institute of Physics, The Hebrew University, Jerusalem, Israel

    Miron Ya. Amusia

  2. A. F. Ioffe Physical-Technical Institute, St. Petersburg, Russian Federation

    Miron Ya. Amusia

  3. Ural Division Komi Science Center, Russian Academy of Sciences, Syktyvkar, Russia

    Konstantin G. Popov

  4. Petersburg Nuclear Physics Institute, Gatchina, Russia

    Vasily R. Shaginyan

  5. CTSPS, Clark Atlanta University, Atlanta, USA

    Vasily R. Shaginyan

  6. Institute of Physics, Opole University, Opole, Poland

    Vladimir A. Stephanovich

Authors
  1. Miron Ya. Amusia
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  2. Konstantin G. Popov
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  3. Vasily R. Shaginyan
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  4. Vladimir A. Stephanovich
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Correspondence to Miron Ya. Amusia .

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Amusia, M.Y., Popov, K.G., Shaginyan, V.R., Stephanovich, V.A. (2015). Quasi-classical Physics Within Quantum Criticality in HF Compounds. In: Theory of Heavy-Fermion Compounds. Springer Series in Solid-State Sciences, vol 182. Springer, Cham. https://doi.org/10.1007/978-3-319-10825-4_9

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