Abstract
Quantum phase transitions in metals are often accompanied by violations of Fermi liquid behavior in the quantum critical regime. Particularly fascinating are transitions beyond the Landau-Ginzburg-Wilson concept of a local order parameter. The breakdown of the Kondo effect in heavy-fermion metals constitutes a prime example of such a transition. Here, the strongly correlated f electrons become localized and disappear from the Fermi surface, implying that the transition is equivalent to an orbital-selective Mott transition, as has been discussed for multi-band transition-metal oxides. In this article, available theoretical descriptions for orbital-selective Mott transitions will be reviewed, with an emphasis on conceptual aspects like the distinction between different low-temperature phases and the structure of the global phase diagram. Selected results for quantum critical properties will be listed as well. Finally, a brief overview is given on experiments which have been interpreted in terms of orbital-selective Mott physics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Baym, C. Pethick, Landau Fermi-Liquid Theory (Wiley, New York, 1991)
H. v. Löhneysen, A. Rosch, M. Vojta, P. Wölfle, Rev. Mod. Phys. 79, 1015 (2007)
S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999)
J.A. Hertz, Phys. Rev. B 14, 1165 (1976)
A.J. Millis, Phys. Rev. B 48, 7183 (1993)
T. Moriya, Spin Fluctuations in Itinerant Electron Magnetism (Springer, Berlin, 1985)
T. Moriya, T. Takimoto, J. Phys. Soc. Jpn. 64, 960 (1995)
T. Vojta, D. Belitz, R. Narayanan, T.R. Kirkpatrick, Z. Phys. B 103, 451 (1997)
D. Belitz, T.R. Kirkpatrick, J. Rollbühler, Phys. Rev. Lett. 94, 247205 (2005)
A. Abanov, A.V. Chubukov, Phys. Rev. Lett. 93, 255702 (2004)
M.A. Metlitski, S. Sachdev, preprint, arXiv:1005.1288
P. Gegenwart, Q. Si, F. Steglich, Nature Phys. 4, 186 (2008)
A. Schröder, G. Aeppli, E. Bucher, R. Ramazashvili, P. Coleman, Phys. Rev. Lett. 80, 5623 (1998)
A. Schröder, G. Aeppli, R. Coldea, M. Adams, O. Stockert, H. v. Löhneysen, E. Bucher, R. Ramazashvili, P. Coleman, Nature (London) 407, 351 (2000)
P. Coleman, C. Pépin, Q. Si, R. Ramazashvili, J. Phys., Condens. Matter 13, R723 (2001)
Q. Si, S. Rabello, K. Ingersent, J.L. Smith, Nature (London) 413, 804 (2001)
Q. Si, S. Rabello, K. Ingersent, J.L. Smith, Phys. Rev. B 68, 115103 (2003)
T. Senthil, S. Sachdev, M. Vojta, Phys. Rev. Lett. 69, 216403 (2003)
T. Senthil, M. Vojta, S. Sachdev, Phys. Rev. B 69, 035111 (2004)
V. Anisimov, I. Nekrasov, D. Kondakov, T. Rice, M. Sigrist, Eur. Phys. J. B 25, 191 (2002)
S. Nakatsuji, Y. Maeno, Phys. Rev. Lett. 84, 2666 (2000)
T. Senthil, Phys. Rev. B 78, 035103 (2008)
S. Doniach, Physica B 91, 231 (1977)
M. Oshikawa, Phys. Rev. Lett. 84, 3370 (2000)
S.J. Yamamoto, Q. Si, Phys. Rev. Lett. 99, 016401 (2007)
G.R. Stewart, Rev. Mod. Phys. 73, 797 (2001)
G.R. Stewart, Rev. Mod. Phys. 78, 743 (2006)
Q. Si, Physica B 378–380, 23 (2006)
M. Vojta, Phys. Rev. B 78, 125109 (2008)
T. Senthil, S. Sachdev, M. Vojta, Physica B 359–361, 9 (2005)
T. Senthil, L. Balents, S. Sachdev, A. Vishwanath, M.P.A. Fisher, Phys. Rev. B 70, 144407 (2004)
S. Friedemann, T. Westerkamp, M. Brando, N. Oeschler, S. Wirth, P. Gegenwart, C. Krellner, C. Geibel, F. Steglich, Nat. Phys. 5, 465 (2009)
M. Vojta, Philos. Mag. 86, 1807 (2006)
D.R. Grempel, Q. Si, Phys. Rev. Lett. 91, 026401 (2003)
M.T. Glossop, K. Ingersent, Phys. Rev. Lett. 99, 227203 (2007)
J.-X. Zhu, S. Kirchner, R. Bulla, Q. Si, Phys. Rev. Lett. 99, 227204 (2007)
P. Sun, G. Kotliar, Phys. Rev. B 71, 245104 (2005)
S. Burdin, D.R. Grempel, A. Georges, Phys. Rev. B 66, 045111 (2002)
A.C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, 1997)
C. Pépin, Phys. Rev. Lett. 98, 206401 (2007)
E. Fradkin, S.H. Shenker, Phys. Rev. D 19, 3682 (1979)
N. Nagaosa, P.A. Lee, Phys. Rev. B 61, 9166 (2000)
I. Paul, C. Pépin, M.R. Norman, Phys. Rev. Lett. 98, 026402 (2007)
A. Hackl, M. Vojta, Phys. Rev. B 77, 134439 (2008)
C. Pépin, Phys. Rev. Lett. 94, 066402 (2005)
K.-S. Kim, Phys. Rev. B 71, 205101 (2005)
K.-S. Kim, C. Jia, Phys. Rev. Lett. 104, 156403 (2010)
L.C. Martin, F.F. Assaad, Phys. Rev. Lett. 101, 066404 (2008)
L.C. Martin, M. Bercx, F.F. Assaad, preprint, arXiv:1007.0010
N. Lanata, P. Barone, M. Fabrizio, Phys. Rev. B 78, 155127 (2008)
H. Watanabe, M. Ogata, Phys. Rev. Lett. 99, 136401 (2007)
L. De Leo, M. Civelli, G. Kotliar, Phys. Rev. B 77, 075107 (2008)
L. De Leo, M. Civelli, G. Kotliar, Phys. Rev. Lett. 101, 256404 (2008)
L. de Medici, A. Georges, G. Kotliar, S. Biermann, Phys. Rev. Lett. 95, 066402 (2005)
A. Koga, N. Kawakami, T.M. Rice, M. Sigrist, Phys. Rev. Lett. 92, 216402 (2004)
S. Biermann, L. de Medici, A. Georges, Phys. Rev. Lett. 95, 206401 (2005)
A. Liebsch, Phys. Rev. Lett. 95, 116402 (2005)
C. Knecht, N. Blümer, P.G.J. van Dongen, Phys. Rev. B 72, 081103(R) (2005)
R. Arita, K. Held, Phys. Rev. B 72, 201102(R) (2005)
P. Werner, A.J. Millis, Phys. Rev. Lett. 99, 126405 (2007)
T.A. Costi, A. Liebsch, Phys. Rev. Lett. 99, 236404 (2007)
L. de Medici, S.R. Hassan, M. Capone, X. Dai, Phys. Rev. Lett. 102, 126401 (2009)
A. Rüegg, M. Indergand, S. Pilgram, M. Sigrist, Eur. Phys. J. B 48, 55 (2005)
P. Coleman, N. Andrei, J. Phys., Condens. Matter 1, 4057 (1989)
T. Senthil, M. Vojta, Phys. Rev. B 71, 121102(R) (2005)
See e.g.: S. Sachdev, Nat. Phys. 4, 173 (2008)
P.A. Lee, Rep. Prog. Phys. 71, 012501 (2008)
R. Moessner, S.L. Sondhi, Phys. Rev. Lett. 86, 1881 (2001)
G. Misguich, C. Lhuillier, B. Bernu, C. Waldtmann, Phys. Rev. B 60, 1064 (1999)
T. Holstein, R. Norton, P. Pincus, Phys. Rev. B 8, 2649 (1973)
M.Yu. Reizer, Phys. Rev. B 40, 11571 (1989)
B.L. Altshuler, L.B. Ioffe, A.J. Millis, Phys. Rev. B 50, 14048 (1994)
C.P. Nave, P.A. Lee, Phys. Rev. B 76, 235124 (2007)
A. Hackl, R. Thomale, in preparation
S. Sachdev, J. Ye, Phys. Rev. Lett. 70, 3339 (1993)
T. Senthil, preprint, arXiv:cond-mat/0604240
T. Senthil, Phys. Rev. B 78, 045109 (2008)
L. Dell’Anna, W. Metzner, Phys. Rev. B 73, 045127 (2006)
I. Paul, C. Pépin, M.R. Norman, Phys. Rev. B 78, 035109 (2008)
L. Zhu, M. Garst, A. Rosch, Q. Si, Phys. Rev. Lett. 91, 066404 (2003)
K.-S. Kim, A. Benlagra, C. Pépin, Phys. Rev. Lett. 101, 246403 (2008)
A. Rosch, Phys. Rev. B 62, 4945 (2000)
L.B. Ioffe, A. Larkin, Phys. Rev. B 39, 8988 (1989)
P.A. Lee, N. Nagaosa, Phys. Rev. B 46, 5621 (1989)
K.-S. Kim, C. Pépin, Phys. Rev. Lett. 102, 156404 (2009)
P. Coleman, J.B. Marston, A.J. Schofield, Phys. Rev. B 72, 245111 (2005)
I. Paul, M. Civelli, Phys. Rev. B 81, 161102(R) (2010)
H. v. Löhneysen, J. Phys., Condens. Matter 8, 9689 (1996)
H. v. Löhneysen, A. Neubert, T. Pietrus, A. Schröder, O. Stockert, U. Tutsch, M. Loewenhaupt, A. Rosch, P. Wölfle, Eur. Phys. J. B 5, 447 (1998)
H. v. Löhneysen, S. Mock, A. Neubert, T. Pietrus, A. Rosch, A. Schröder, O. Stockert, U. Tutsch, J. Magn. Magn. Mater. 177–181, 12 (1998)
O. Stockert, H. v. Löhneysen, A. Rosch, N. Pyka, M. Loewenhaupt, Phys. Rev. Lett. 80, 5627 (1998)
H. Wilhelm, S. Raymond, D. Jaccard, O. Stockert, H. v. Löhneysen, A. Rosch, J. Phys., Condens. Matter 13, L329 (2001)
O. Trovarelli, C. Geibel, S. Mederle, C. Langhammer, F.M. Grosche, P. Gegenwart, M. Lang, G. Sparn, F. Steglich, Phys. Rev. Lett. 85, 626 (2000)
P. Gegenwart, J. Custers, C. Geibel, K. Neumaier, T. Tayama, K. Tenya, O. Trovarelli, F. Steglich, Phys. Rev. Lett. 89, 056402 (2002)
S. Paschen, T. Lühmann, S. Wirth, P. Gegenwart, O. Trovarelli, C. Geibel, F. Steglich, P. Coleman, Q. Si, Nature (London) 432, 881 (2004)
S. Friedemann, PhD thesis, MPI-CPfS Dresden, 2009
P. Gegenwart, T. Westerkamp, C. Krellner, Y. Tokiwa, S. Paschen, C. Geibel, F. Steglich, E. Abrahams, Q. Si, Science 315, 969 (2006) (2007)
J. Custers, P. Gegenwart, C. Geibel, F. Steglich, P. Coleman, S. Paschen, Phys. Rev. Lett. 104, 186402 (2010)
R. Küchler, 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)
T. Park, F. Ronning, H.Q. Yuan, M.B. Salamon, R. Movshovich, J.L. Sarrao, J.D. Thompson, Nature (London) 440, 65 (2006)
T. Park, M.J. Graf, L. Boulaevskii, J.L. Sarrao, J.D. Thompson, Proc. Natl. Acad. Sci. USA 105, 6825 (2008)
G. Knebel, D. Aoki, J.P. Brison, J. Flouquet, J. Phys. Soc. Jpn. 77, 114704 (2008)
H. Shishido, R. Settai, H. Harima, Y. Onuki, J. Phys. Soc. Jpn. 74, 1103 (2005)
S.K. Goh, J. Paglione, M. Sutherland, E.C.T. O’Farrell, C. Bergemann, T.A. Sayles, M.B. Maple, Phys. Rev. Lett. 101, 056402 (2008)
N.K. Sato, N. Aso, K. Miyake, R. Shiina, P. Thalmeier, G. Varelogiannis, C. Geibel, F. Steglich, P. Fulde, T. Komatsubara, Nature 410, 340 (2001)
G. Zwicknagl, A.N. Yaresko, P. Fulde, Phys. Rev. B 65, 081103 (2002)
G. Zwicknagl, P. Fulde, J. Phys., Condens. Matter 15, S1911 (2003)
G. Zwicknagl, A.N. Yaresko, P. Fulde, Phys. Rev. B 68, 062508 (2003)
D.V. Efremov, N. Hasselmann, E. Runge, P. Fulde, G. Zwicknagl, Phys. Rev. B 69, 115114 (2004)
D.-A. Le, S. Burdin, G. Zwicklnagl, P. Fulde, to be published
A. Liebsch, H. Ishida, Phys. Rev. Lett. 98, 216403 (2007)
M. Neupane, P. Richard, Z.-H. Pan, Y.-M. Xu, R. Jin, D. Mandrus, X. Dai, Z. Fang, Z. Wang, H. Ding, Phys. Rev. Lett. 103, 097001 (2009)
D.S. Greywall, Phys. Rev. B 41, 1842 (1990)
M. Siqueira et al., Phys. Rev. Lett. 78, 2600 (1997)
M. Neumann et al., Science 317, 1356 (2007)
M. Roger, Phys. Rev. Lett. 64, 297 (1990)
A. Casey, H. Patel, J. Nyeki, B.P. Cowan, J. Saunders, Phys. Rev. Lett. 90, 115301 (2003)
A. Benlagra, C. Pépin, Phys. Rev. Lett. 100, 176401 (2008)
A. Rancon-Schweiger, A. Benlagra, C. Pépin, preprint, arXiv:1005.1905
For reviews see: E.W. Carlson, V.J. Emery, S.A. Kivelson, D. Orgad, in The Physics of Conventional and Unconventional Superconductors, ed. by K.H. Bennemann, J.B. Ketterson (Springer, Berlin, 2003)
P.A. Lee, N. Nagaosa, X.-G. Wen, Rev. Mod. Phys. 78, 17 (2006)
K. Haule, G. Kotliar, Phys. Rev. B 76, 092503 (2007)
N.S. Vidhyadhiraja, A. Macridin, C. Sen, M. Jarrell, M. Ma, preprint, arXiv:0809.1477
S. Sakai, Y. Motome, M. Imada, Phys. Rev. Lett. 102, 056404 (2009)
P. Werner, E. Gull, O. Parcollet, A.J. Millis, Phys. Rev. B 80, 045120 (2009)
M. Ferrero, P.S. Cornaglia, L. De Leo, O. Parcollet, G. Kotliar, A. Georges, Phys. Rev. B 80, 064501 (2009)
Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, J. Am. Chem. Soc. 130, 3296 (2008)
M. Rotter, M. Tegel, D. Johrendt, Phys. Rev. Lett. 101, 107006 (2008)
Q. Si, E. Abrahams, Phys. Rev. Lett. 101, 076401 (2008)
J. Wu, P. Phillips, A.H. Castro Neto, Phys. Rev. Lett. 101, 126401 (2008)
S.-P. Kou, T. Li, Z.-Y. Weng, EPL 88, 17010 (2009)
A. Hackl, M. Vojta, New J. Phys. 11, 055064 (2009)
I. Mazin, private communication
L. de Medici, S.R. Hassan, M. Capone, J. Supercond. Nov. Magn. 22, 535 (2009)
H. Ishida, A. Liebsch, Phys. Rev. B 81, 054513 (2010)
A. Liebsch, H. Ishida, preprint, arXiv:1004.2851
K. Haule, G. Kotliar, preprint, arXiv:1007.2867
L. Craco, M.S. Laad, S. Leoni, preprint, arXiv:0910.3828
J.-X. Zhu, R. Yu, H. Wang, L.L. Zhao, M.D. Jones, J. Dai, E. Abrahams, E. Morosan, M. Fang, Q. Si, Phys. Rev. Lett. 104, 216405 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Vojta, M. Orbital-Selective Mott Transitions: Heavy Fermions and Beyond. J Low Temp Phys 161, 203–232 (2010). https://doi.org/10.1007/s10909-010-0206-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10909-010-0206-3