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Magnetic and other unconventional electronic orders are discussed for heavy electrons. In addition to the ordinary Kondo lattice, we consider non-Kramers systems taking the two-channel Kondo lattice, and another lattice that consists of a singlet–triplet f2 configuration. The latter gives a scalar order with staggered sublattices of crystalline-electric-field (CEF) and Kondo singlets, which accounts for the observed order in PrFe4P12. In the two-channel Kondo lattice, an odd-frequency pairing is realized that becomes degenerate at half-filling with a diagonal composite order involving both localized and conduction electrons. The degeneracy is interpreted in terms of a hidden SO(5) symmetry. For the ordinary Kondo lattice with exchange interaction J, we take insulating ground states as reference. The metallic states are approached by infinitesimal doping of carriers either from the Kondo insulator or from the antiferromagnetic insulator. By adding intersite exchange we find that location of the band extremum of the heavy band depends on the value of J. The change of J gives topological change of the Fermi surface, which corresponds to a generalized version of the Lifshitz transition, and occurs separately from the quantum critical point of the antiferromagnetic order.
References
- 1 Y. Kuramoto, in Theory of Heavy Fermions and Valence Fluctuations, ed. T. Kasuya and T. Saso (Springer, Heidelberg, 1985) p. 152. Crossref, Google Scholar
- 2 For a review, see, A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996). 10.1103/RevModPhys.68.13 Crossref, Google Scholar
- 3 A. N. Rubtsov and A. I. Lichtenstein, JETP Lett. 80, 61 (2004). 10.1134/1.1800216 Crossref, Google Scholar
- 4 J. Otsuki, H. Kusunose, P. Werner, and Y. Kuramoto, J. Phys. Soc. Jpn. 76, 114707 (2007). 10.1143/JPSJ.76.114707 Link, Google Scholar
- 5 For a review, see, E. Gull, A. J. Millis, A. I. Lichtenstein, A. N. Rubtsov, M. Troyer, and P. Werner, Rev. Mod. Phys. 83, 349 (2011). 10.1103/RevModPhys.83.349 Crossref, Google Scholar
- 6 K. G. Wilson, Rev. Mod. Phys. 47, 773 (1975). 10.1103/RevModPhys.47.773 Crossref, Google Scholar
- 7 R. Bulla, T. A. Costi, and T. Pruschke, Rev. Mod. Phys. 80, 395 (2008). 10.1103/RevModPhys.80.395 Crossref, Google Scholar
- 8 P. Gegenwart, Q. Si, and F. Steglich, Nat. Phys. 4, 186 (2008). 10.1038/nphys892 Crossref, Google Scholar
- 9 H. v. Löhneysen, A. Rosch, M. Vojta, and P. Wölfle, Rev. Mod. Phys. 79, 1015 (2007). 10.1103/RevModPhys.79.1015 Crossref, Google Scholar
- 10 J. Otsuki, H. Kusunose, and Y. Kuramoto, Phys. Rev. Lett. 102, 017202 (2009). 10.1103/PhysRevLett.102.017202 Crossref, Google Scholar
- 11 S. Hoshino, J. Otsuki, and Y. Kuramoto, J. Phys. Soc. Jpn. 79, 074720 (2010). 10.1143/JPSJ.79.074720 Link, Google Scholar
- 12 Y. Kuramoto, S. Hoshino, and J. Otsuki, J. Phys. Soc. Jpn. 80, SA018 (2011). 10.1143/JPSJS.80SA.SA018 Link, Google Scholar
- 13 D. L. Cox, Phys. Rev. Lett. 59, 1240 (1987). 10.1103/PhysRevLett.59.1240 Crossref, Google Scholar
- 14 For a review, see, D. L. Cox and A. Zawadowski, Adv. Phys. 47, 599 (1998). 10.1080/000187398243500 Crossref, Google Scholar
- 15 S. Hoshino, J. Otsuki, and Y. Kuramoto, Phys. Rev. Lett. 107, 247202 (2011). 10.1103/PhysRevLett.107.247202 Crossref, Google Scholar
- 16 S. Hoshino, J. Otsuki, and Y. Kuramoto, J. Phys. Soc. Jpn. 82, 044707 (2013). 10.7566/JPSJ.82.044707 Link, Google Scholar
- 17 S. Hoshino and Y. Kuramoto, arXiv:1309.5719; Google ScholarS. Hoshino and Y. Kuramoto, to be published in Phys. Rev. Lett. (2014). Google Scholar
- 18 J. W. Rasul and P. Schlottmann, Phys. Rev. Lett. 62, 1701 (1989). 10.1103/PhysRevLett.62.1701 Crossref, Google Scholar
- 19 I. Affleck and W. W. Ludwig, Phys. Rev. Lett. 68, 1046 (1992). 10.1103/PhysRevLett.68.1046 Crossref, Google Scholar
- 20 H. Tanida, H. Suzuki, S. Takagi, H. Onodera, and K. Tanigaki, J. Phys. Soc. Jpn. 75, 073705 (2006). 10.1143/JPSJ.75.073705 Link, Google Scholar
- 21 A. Yatskar, W. P. Beyermann, R. Movshovich, and P. C. Canfield, Phys. Rev. Lett. 77, 3637 (1996). 10.1103/PhysRevLett.77.3637 Crossref, Google Scholar
- 22 T. Onimaru, T. Sakakibara, A. Harita, T. Tayama, D. Aoki, and Y. Onuki, J. Phys. Soc. Jpn. 73, 2377 (2004). 10.1143/JPSJ.73.2377 Link, Google Scholar
- 23 A. Sakai and S. Nakatsuji, J. Phys. Soc. Jpn. 80, 063701 (2011). 10.1143/JPSJ.80.063701 Link, Google Scholar
- 24 Ph. Nozières and A. Blandin, J. Phys. (Paris) 41, 193 (1980). 10.1051/jphys:01980004103019300 Crossref, Google Scholar
- 25 H. R. Ott, H. Rudigier, Z. Fisk, and J. I. Smith, Phys. Rev. Lett. 50, 1595 (1983). 10.1103/PhysRevLett.50.1595 Crossref, Google Scholar
- 26 M. S. Torikachvili, J. W. Chen, Y. Dalichaouch, R. P. Guertin, M. W. McElfresh, C. Rossel, M. B. Maple, and G. P. Meisner, Phys. Rev. B 36, 8660 (1987). 10.1103/PhysRevB.36.8660 Crossref, Google Scholar
- 27 L. Hao, K. Iwasa, M. Nakajima, D. Kawana, K. Kuwahara, M. Kohgi, H. Sugawara, T. D. Matsuda, Y. Aoki, and H. Sato, Acta Phys. Pol. B 34, 1113 (2003). Google Scholar
- 28 T. D. Matsuda, S. R. Saha, T. Namiki, H. Sugawara, Y. Aoki, and H. Sato, J. Phys. Soc. Jpn. 71 [Suppl.], 246 (2002). 10.1143/JPSJS.71S.246 Link, Google Scholar
- 29 T. Tayama, Y. Isobe, T. Sakakibara, H. Sugawara, Y. Aoki, and H. Sato, J. Phys. Soc. Jpn. 76, 083702 (2007). 10.1143/JPSJ.76.083702 Link, Google Scholar
- 30 H. Hidaka, I. Ando, H. Kotegawa, T. C. Kobayashi, H. Harima, M. Kobayashi, H. Sugawara, and H. Sato, Phys. Rev. B 71, 073102 (2005). 10.1103/PhysRevB.71.073102 Crossref, Google Scholar
- 31 M. Jarrell, H. Pang, D. L. Cox, and K. H. Luk, Phys. Rev. Lett. 77, 1612 (1996). 10.1103/PhysRevLett.77.1612 Crossref, Google Scholar
- 32 I. Affleck, A. W. W. Ludwig, H.-B. Pang, and D. L. Cox, Phys. Rev. B 45, 7918 (1992). 10.1103/PhysRevB.45.7918 Crossref, Google Scholar
- 33 J. A. Mydosh and P. M. Oppeneer, Rev. Mod. Phys. 83, 1301 (2011). 10.1103/RevModPhys.83.1301 Crossref, Google Scholar
- 34 P. Coleman, E. Miranda, and A. Tsvelik, Phys. Rev. B 49, 8955 (1994). 10.1103/PhysRevB.49.8955 Crossref, Google Scholar
- 35 F. Mancini and A. Avella, Adv. Phys. 53, 537 (2004). 10.1080/00018730412331303722 Crossref, Google Scholar
- 36 V. L. Berezinskii, Pis’ma Z. Eksp. Teor. Fiz. 20, 628 (1974) [JETP Lett. 20 (1974) 287]. Google Scholar
- 37 V. J. Emery and S. Kivelson, Phys. Rev. B 46, 10812 (1992). 10.1103/PhysRevB.46.10812 Crossref, Google Scholar
- 38 A. Balatsky and E. Abrahams, Phys. Rev. B 45, 13125 (1992). 10.1103/PhysRevB.45.13125 Crossref, Google Scholar
- 39 V. J. Emery and S. A. Kivelson, Phys. Rev. Lett. 71, 3701 (1993). 10.1103/PhysRevLett.71.3701 Crossref, Google Scholar
- 40 E. Abrahams, A. Balatsky, J. R. Schrieffer, and P. B. Allen, Phys. Rev. B 47, 513 (1993). 10.1103/PhysRevB.47.513 Crossref, Google Scholar
- 41 M. Jarrell, H. Pang, and D. L. Cox, Phys. Rev. Lett. 78, 1996 (1997). 10.1103/PhysRevLett.78.1996 Crossref, Google Scholar
- 42 F. B. Anders, Eur. Phys. J. B 28, 9 (2002). 10.1140/epjb/e2002-00195-8 Crossref, Google Scholar
- 43 C. N. Yang, Phys. Rev. Lett. 63, 2144 (1989). 10.1103/PhysRevLett.63.2144 Crossref, Google Scholar
- 44 E. Demler, W. Hanke, and S.-C. Zhang, Rev. Mod. Phys. 76, 909 (2004). 10.1103/RevModPhys.76.909 Crossref, Google Scholar
- 45 L. C. Martin, M. Bercx, and F. F. Assaad, Phys. Rev. B 82, 245105 (2010). 10.1103/PhysRevB.82.245105 Crossref, Google Scholar
- 46 S. Hoshino and Y. Kuramoto, Phys. Rev. Lett. 111, 026401 (2013). 10.1103/PhysRevLett.111.026401 Crossref, Google Scholar
- 47 T. Iizuka, T. Mizuno, B. Min, Y. Kwon, and S. Kimura, J. Phys. Soc. Jpn. 81, 043703 (2012). 10.1143/JPSJ.81.043703 Link, Google Scholar
- 48 J. Robert, J.-M. Mignot, G. Andre, T. Nishioka, R. Kobayashi, M. M. H. Tanida, D. Tanaka, and M. Sera, Phys. Rev. B 82, 100404(R) (2010). 10.1103/PhysRevB.82.100404 Crossref, Google Scholar
- 49 D. D. Khalyavin, A. D. Hillier, D. T. Adroja, A. M. Strydom, P. Manuel, L. C. Chapon, P. Peratheepan, K. Knight, P. Deen, C. Ritter, Y. Muro, and T. Takabatake, Phys. Rev. B 82, 100405(R) (2010). 10.1103/PhysRevB.82.100405 Crossref, Google Scholar
- 50 H. Tanida, Y. Nonaka, D. Tanaka, M. Sera, Y. Kawamura, Y. Uwatoko, T. Nishioka, and M. Matsumura, Phys. Rev. B 85, 205208 (2012). 10.1103/PhysRevB.85.205208 Crossref, Google Scholar
- 51 A. Kondo, K. Kindo, K. Kunimori, H. Nohara, H. Tanida, M. Sera, R. Kobayashi, T. Nishioka, and M. Matsumura, J. Phys. Soc. Jpn. 82, 054709 (2013). 10.7566/JPSJ.82.054709 Link, Google Scholar
- 52 R. Kobayashi, Y. Ogane, D. Hirai, T. Nishioka, M. Matsumura, Y. Kawamura, K. Matsubayashi, Y. Uwatoko, H. Tanida, and M. Sera, J. Phys. Soc. Jpn. 82, 093702 (2013). 10.7566/JPSJ.82.093702 Link, Google Scholar
- 53 J. Robert, J. Mignot, S. Petit, P. Steffens, T. Nishioka, R. Kobayashi, M. Matsumura, H. Tanida, D. Tanaka, and M. Sera, Phys. Rev. Lett. 109, 267208 (2012). 10.1103/PhysRevLett.109.267208 Crossref, Google Scholar
- 54 S. Kimura, T. Iizuka, H. Miyazaki, T. Hajiri, M. Matsunami, T. Mori, A. Irizawa, Y. Muro, J. Kajino, and T. Takabatake, Phys. Rev. B 84, 165125 (2011). 10.1103/PhysRevB.84.165125 Crossref, Google Scholar
- 55 H. Watanabe and M. Ogata, Phys. Rev. Lett. 99, 136401 (2007). 10.1103/PhysRevLett.99.136401 Crossref, Google Scholar
- 56 J. A. Hertz, Phys. Rev. B 14, 1165 (1976). 10.1103/PhysRevB.14.1165 Crossref, Google Scholar
- 57 A. J. Millis, Phys. Rev. B 48, 7183 (1993). 10.1103/PhysRevB.48.7183 Crossref, Google Scholar
- 58 T. Moriya and T. Takimoto, J. Phys. Soc. Jpn. 64, 960 (1995). 10.1143/JPSJ.64.960 Link, Google Scholar
- 59 D. V. Vyalikh, S. Danzenbächer, Yu. Kucherenko, K. Kummer, C. Krellner, C. Geibel, M. G. Holder, T. K. Kim, C. Laubschat, M. Shi, L. Patthey, R. Follath, and S. L. Molodtsov, Phys. Rev. Lett. 105, 237601 (2010). 10.1103/PhysRevLett.105.237601 Crossref, Google Scholar
- 60 S.-K. Mo, W. S. Lee, F. Schmitt, Y. L. Chen, D. H. Lu, C. Capan, D. J. Kim, Z. Fisk, C.-Q. Zhang, Z. Hussain, and Z.-X. Shen, Phys. Rev. B 85, 241103(R) (2012). 10.1103/PhysRevB.85.241103 Crossref, Google Scholar