Abstract
Elastic phase transitions of crystals and phase transitions whose order parameter couples linearly to elastic degrees of freedom are reviewed with particular focus on instabilities at zero temperature. A characteristic feature of these transitions is the suppression of critical fluctuations by long-range shear forces. As a consequence, at an elastic crystal symmetry-breaking quantum phase transition the phonon velocity vanishes only along certain crystallographic directions giving rise to critical phonon thermodynamics described by a stable Gaussian fixed point. At an isostructural solid-solid quantum critical end point, on the other hand, the complete suppression of critical fluctuations results in true mean-field critical behavior without a diverging correlation length. Whenever an order parameter couples bilinearly to the strain tensor, the critical properties are eventually governed by critical crystal elasticity. This is, for example, the case for quantum critical metamagnetism but also for the classical critical Mott end point at finite T. We discuss and compare the solid-solid end points expected close to the Mott transition in V2O3 and κ-(BEDT-TTF)2 X.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Grüneisen, Annalen der Physik, 331 393 (1908)
In Ref. [1] Grüneisen introduced the parameter γ = −(V/T)(∂T/∂V)S = α/(C VκT) that describes the relative change of temperature upon adiabatically changing the volume, where C V = T(∂S/∂T)V and the isothermal compressibility κT = −(1/V)(∂V/∂p)T
L. Zhu, M. Garst, A. Rosch, Q. Si, Phys. Rev. Lett. 91, 066404 (2003)
M. Garst, A. Rosch, Phys. Rev. B 72, 205129 (2005)
R. Küchler et al., Phys. Rev. Lett. 91, 66405 (2003)
R. Küchler, et al., Phys. Rev. Lett. 93, 96402 (2004)
R. Küchler, et al., Phys. Rev. Lett. 96, 256403 (2006)
T. Lorenz, et al., J. Magn. Mag. Mat. 316, 291 (2007)
B. Wolf, et al., PNAS 108, 6862 (2011)
Y. Tokiwa, E.D. Bauer, P. Gegenwart, Phys. Rev. Lett. 109, 116402 (2012)
Y. Tokiwa, E.D. Bauer, P. Gegenwart, Phys. Rev. Lett. 111 (2013)
Y. Tokiwa, M. Garst, P. Gegenwart, S.L. Budko, P.C. Canfield, Phys. Rev. Lett. 111, 116401 (2013)
Y. Tokiwa, J.J. Ishikawa, S. Nakatsuji, P. Gegenwart, Nat. Mater. 13, 356 (2014)
H. Ryll, et al., Phys. Rev. B 89, 144416 (2014)
H. v. Löhneysen, A. Rosch, M. Vojta, P. Wölfle, Rev. Mod. Phys. 79, 1015 (2007)
P. Gegenwart, Q. Si, F. Steglich, Nat. Phys. 4, 186 (2008)
P. Gegenwart et al., J. Low Temp. Phys. 161, 117 (2010)
O.K. Rice, J. Chem. Phys. 22, 1535 (1954)
C. Domb, J. Chem. Phys. 25, 783 (1956)
A.P. Levanyuk, A.A. Sobyanin, JETP Lett. 11, 371 (1970)
J. Villain, Solid State Comm. 8, 295 (1970)
A.I. Larkin, S.A. Pikin, JETP 29, 891 (1969)
J. Sak, Phys. Rev. B 10, 3957 (1974)
F.J. Wegner, J. Phys. C.: Solid State Phys. 7, 2109 (1974)
D.J. Bergman, B.I. Halperin, Phys. Rev. B 13, 2145 (1976)
S. Aubry, R. Pick, J. Phys. (Paris) 32, 657 (1971)
R.A. Cowley, Phys. Rev. B 13, 4877 (1976)
R. Folk, H. Iro, F. Schwabl, Z. Phys. B 25, 69 (1976)
R. Folk, H. Iro, F. Schwabl, Phys. Rev. B 20, 1229 (1979)
F. Schwabl, “Modern Trends in the Theory of Condensed Matter” (Springer Berlin Heidelberg) 115, 432 (1980)
F. Schwabl, U.C. Täuber, Phil. Trans. R. Soc. Lond. A 354, 2847 (1996)
J.T. Chalker, Physics Letters A 80, 40 (1980)
M. Zacharias, I. Paul, M. Garst (unpublished)
M. Zacharias, L. Bartosch, M. Garst, Phys. Rev. Lett. 109, 176401 (2012)
M. Zacharias, Mott transition and quantum critical metamagnetism on compressible lattices, Ph.D. thesis, Universität zu Köln, 2013
L.D. Landau, E.M. Lifshitz, Theory of Elasticity (Butterworth-Heinemann, 1986)
M. Born, K. Huang, Dynamical theory of crystal lattices (Clarendon Press, 1962)
F. Anfuso, et al., Phys. Rev. B 77, 235113 (2008)
M. Dzero, M.R. Norman, I. Paul, C. Pépin, J. Schmalian, Phys. Rev. Lett. 97, 185701 (2006)
M. Dzero, M.R. Norman, I. Paul, C. Pépin, J. Schmalian, Phys. Rev. Lett. 104, 119901 (2010)
A. Hackl, M. Vojta, Phys. Rev. B 77, 134439 (2008)
A.J. Millis, A.J. Schofield, G.G. Lonzarich, S.A. Grigera, Phys. Rev. Lett. 88, 217204 (2002)
M. Zacharias, M. Garst, Phys. Rev. B 87, 075119 (2013)
E. Courtens, R. Gammon, S. Alexander, Phys. Rev. Lett. 43, 1026 (1979)
E.G. Poniatovskii, Sov. Phys. Dokl. 3, 498 [Dokl. Akad. Nauk. SSR 120, 1021 (1958)]
J.M. Lawrence, M.C. Croft, R.D. Parks, Phys. Rev. Lett. 35, 289 (1975)
M.C. Croft, R.D. Parks, in Valence Instabilities and Related Narrow Band Phenomena, edited by R.D. Parks (Plenum, New York, 1977), p. 455
E.P. Wohlfarth, P. Rhodes, Philos. Mag. 7, 1817 (1962)
S.A. Grigera, R.S. Perry, A.J. Schofield, M. Chiao, S.R. Julian, G.G. Lonzarich, S.I. Ikeda, Y. Maeno, A.J. Millis, A.P. Mackenzie, Science 294, 329 (2001)
F. Weickert, M. Brando, F. Steglich, P. Gegenwart, M. Garst, Phys. Rev. B 81, 134438 (2010)
P. Gegenwart, F. Weickert, M. Garst, R.S. Perry, Y. Maeno, Phys. Rev. Lett. 96, 136402 (2006)
R.A. Cowley, Phys. Rev. Lett. 36, 744 (1976)
M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998)
C. Castellani, C. Di Castro, D. Feinberg, J. Ranninger, Phys. Rev. Lett. 43, 1957 (1979)
G. Kotliar, E. Lange, M.J. Rozenberg, Phys. Rev. Lett. 84, 5180 (2000)
A. Jayaraman, D.B. McWhan, J.P. Remeika, P.D. Dernier, Phys. Rev. B 2, 3751 (1970)
D. Fournier, M. Poirier, M. Castonguay, K.D. Truong, Phys. Rev. Lett. 90, 127002 (2003)
P. Limelette, A. Georges, D. Jérome, P. Wzietek, P. Metcalf, J.M. Honig, Science 302, 89 (2003)
F. Kagawa, K. Miyagawa, K. Kanoda, Nature 436, 534 (2005)
F. Kagawa, K. Miyagawa, K. Kanoda, Nature Phys. 5, 880 (2009)
S. Lefebvre, P. Wzietek, S. Brown, C. Bourbonnais, D. Jérome, C. Mézière, M. Fourmigué, P. Batail, Phys. Rev. Lett. 85, 5420 (2000)
P. Limelette, P. Wzietek, S. Florens, A. Georges, T.A. Costi, C. Pasquier, D. Jérome, C. Mézière, P. Batail, Phys. Rev. Lett. 91, 016401 (2003) t
N. Toyota, M. Lang, J. Müller, Low-dimensional molecular metals (Springer, Berlin, 2007)
S. Papanikolaou, R.M. Fernandes, E. Fradkin, P.W. Phillips, J. Schmalian, R. Sknepnek, Phys. Rev. Lett. 100, 026408 (2008)
M. de Souza, A. Brühl, C. Strack, B. Wolf, D. Schweitzer, M. Lang, Phys. Rev. Lett. 99, 037003 (2007)
L. Bartosch, M. de Souza, M. Lang, Phys. Rev. Lett. 104, 245701 (2010)
M. Imada, Phys. Rev. B 72, 075113 (2005)
M. Imada, T. Misawa, Y. Yamaji, J. Phys.: Cond. Mat. 22, 164206 (2010)
M. Sentef, P. Werner, E. Gull, A.P. Kampf, Phys. Rev. B 84, 165133 (2011)
P. Sémon, A.-M.S. Tremblay, Phys. Rev. B 85, 201101 (2012)
L.D. Landau, E.M. Lifshitz, Stat. Phys. (Butterworth-Heinemann, 1975)
D. Nichols, R. Sladek, H. Harrison, Phys. Rev. B 24, 3025 (1981)
P. Fonseca, A. Zamolodchikov, J. Stat. Phys. 110, 527 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zacharias, M., Rosch, A. & Garst, M. Critical elasticity at zero and finite temperature. Eur. Phys. J. Spec. Top. 224, 1021–1040 (2015). https://doi.org/10.1140/epjst/e2015-02444-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2015-02444-5