[PDF]     http://dx.doi.org/10.3952/lithjphys.52207

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 52, 142164 (2012)

H.K. Pala, V.I. Yudsonb, and D.L. Maslova
aDepartment of Physics, University of Florida, Gainesville, FL 32611-8440, USA
E-mail: maslov@phys.ufl.edu
bInstitute for Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region, 142190, Russia

Received 13 April 2012; accepted 7 June 2012

While it is well-known that the electron-electron (ee) interaction cannot affect the resistivity of a Galilean-invariant Fermi liquid (FL), the reverse statement is not necessarily true: the resistivity of a non-Galilean-invariant FL does not necessarily follow a T2 behavior. The T2 behavior is guaranteed only if Umklapp processes are allowed; however, if the Fermi surface (FS) is small or the electron-electron interaction is of a very long range, Umklapps are suppressed. In this case, a T2 term can result only from a combined – but distinct from quantum-interference corrections – effect of the electron-impurity and ee interactions. Whether the T2 term is present depends on (i) dimensionality [two dimensions (2D) vs three dimensions (3D)], (ii) topology (simply- vs multiply-connected), and (iii) shape (convex vs concave) of the FS. In particular, the T2 term is absent for any quadratic (but not necessarily isotropic) spectrum both in 2D and 3D. The T2 term is also absent for a convex and simply-connected but otherwise arbitrarily anisotropic FS in 2D. The origin of this nullification is approximate integrability of the electron motion on a 2D FS, where the energy and momentum conservation laws do not allow for current relaxation to leading – second – order in T/EF (EF is the Fermi energy). If the T2 term is nullified by the conservation law, the first non-zero term behaves as T4. The same applies to a quantum-critical metal in the vicinity of a Pomeranchuk instability, with a proviso that the leading (first non-zero) term in the resistivity scales as T(D+2)/3 (T(D+8)/3 ). We discuss a number of situations when integrability is weakly broken, e. g., by inter-plane hopping in a quasi-2D metal or by warping of the FS as in the surface states of topological insulators of the Bi2Te3 family. The paper is intended to be self-contained and pedagogical; review of the existing results is included along with the original ones wherever deemed necessary for completeness.
Keywords: normal-state electron transport, Fermi-liquid theory, quantum phase transitions
PACS: 71.10.Ay, 71.10.Hf, 73.20.-r

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