Electrical Conductivity of Interacting Fermions. II. Effects of Normal Scattering Processes in the Presence of Umklapp Scattering Processes

Maebashi, Hideaki; Fukuyama, Hidetoshi

doi:10.1143/jpsj.67.242

Cited by 43 publications

(56 citation statements)

References 13 publications

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“…The fact that T 2 term in the resistivity is absent for an isotropic FS does not mean that it is necessarily present for an anisotropic FS. In fact, the T 2 term is also absent for a simply-connected and convex but otherwise arbitrary FS in 2D [10][11][12][13]16]. Before considering the general case, however, let us study the simplest example of such a FS, i. e., a 2D circular FS with quadratic spectrum.…”

Section: Approximate Integrability: Convex and Simplymentioning

confidence: 99%

“…That momentum relaxation occurs differently in 2D as compared to 3D was pointed by Gurzhi, Kopeliovich, and Rutkevich, first for the electron-phonon [9] and then for the ee [10,11] interactions. Maebashi and Fukuyama [12,13] analyzed an interplay between normal and Umklapp collisions for an anisotropic 2D FS and found that the normal collisions do not give rise to a T 2 term as long as the FS is convex. Rosch and Howell [14] and Rosch [15] showed that a similar nullification happens for the ω 2 term in the optical conductivity in a disorder-free 2D system.…”

Section: Introductionmentioning

confidence: 99%

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Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids

Pal¹,

Yudson²,

Maslov³

2012

Lith. J. Phys.

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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 T 2 behavior. The T 2 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 T 2 term can result only from a combined -but distinct from quantum-interference corrections -effect of the electron-impurity and ee interactions. Whether the T 2 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 T 2 term is absent for any quadratic (but not necessarily isotropic) spectrum both in 2D and 3D. The T 2 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 T 2 term is nullified by the conservation law, the first non-zero term behaves as T 4 . 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+83 ). 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.

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Section: Approximate Integrability: Convex and Simplymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids

Pal¹,

Yudson²,

Maslov³

2012

Lith. J. Phys.

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“…This imaginary quantity is related to the imaginary part of selfenergy, and only by treating the correction from this term in a manner that preserves the conservation laws we can obtain the correct result for the resistivity arising from electron-electron interactions [42,43], i.e. the resistivity vanishes without Umklapp processes.…”

Section: General Expression For Electrical Conductivitiesmentioning

confidence: 99%

“…As discussed by Yamada and Yosida [42,43], C U is divergent and resistivity vanishes if we consider only electron-electron interactions and do not take Umklapp processes into account.…”

Section: General Expression For Electrical Conductivitiesmentioning

confidence: 99%

Theory of Hall Effect and Electrical Transport in High-T_cCuprates: Effects of Antiferromagnetic Spin Fluctuations

Kanki

Kontani

1999

J. Phys. Soc. Jpn.

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In the normal state of high-Tc cuprates, the Hall coefficient shows remarkable temperature dependence, and its absolute value is enhanced in comparison with that value simply estimated on the basis of band structure. It has been recognized that this temperature dependence of the Hall coefficient is due to highly anisotropic quasiparticle damping rate on the Fermi surface. In this paper we further take account of the vertex correction to the current vertex arising from quasiparticle interactions. Then the transport current is transformed to a large extent from the quasiparticle velocity, and is no longer proportional to the latter. As a consequence some pieces of the Fermi surface outside of the antiferromagnetic Brillouin zone make negative contribution to the Hall conductivity, even if the curvature of the Fermi surface is hole-like. The Hall coefficient is much larger at low temperatures than the estimate made without the vertex correction. Temperature dependence of the antiferromagnetic spin correlation length is also crucial to cause remarkable temperature dependence of the Hall coefficient. In our treatment the Hall coefficient of the electron-doped cuprates can be negative despite hole-like curvature of the Fermi surface.

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“…The renormalized classical regime where a pseudogap appears has also been considered but focussing only on the hot spots 32 or neglecting the AL contribution 33 . There are also analytical results for the conductivity with vertex corrections using Fermi liquid theory 34,35 .…”

Section: -8mentioning

confidence: 99%

Optical and dc conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point including vertex corrections

et al. 2011

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The conductivity of the two-dimensional Hubbard model is particularly relevant for hightemperature superconductors. Vertex corrections are expected to be important because of strongly momentum dependent self-energies. To attack this problem, one must also take into account the Mermin-Wagner theorem, the Pauli principle and crucial sum rules in order to reach nonperturbative regimes. Here, we use the Two-Particle Self-Consistent approach that satisfies these constraints. This approach is reliable from weak to intermediate coupling. A functional derivative approach ensures that vertex corrections are included in a way that satisfies the f sum-rule. The two types of vertex corrections that we find are the antiferromagnetic analogs of the Maki-Thompson and Aslamasov-Larkin contributions of superconducting fluctuations to the conductivity but, contrary to the latter, they include non-perturbative effects. The resulting analytical expressions must be evaluated numerically. The calculations are impossible unless a number of advanced numerical algorithms are used. These algorithms make extensive use of fast Fourier transforms, cubic splines and asymptotic forms. A maximum entropy approach is specially developed for analytical continuation of our results. These algorithms are explained in detail in appendices. The numerical results are for nearest neighbor hoppings. In the pseudogap regime induced by two-dimensional antiferromagnetic fluctuations, the effect of vertex corrections is dramatic. Without vertex corrections the resistivity increases as we enter the pseudogap regime. Adding vertex corrections leads to a drop in resistivity, as observed in some high temperature superconductors. At high temperature, the resistivity saturates at the Ioffe-Regel limit. At the quantum critical point and beyond, the resistivity displays both linear and quadratic temperature dependence and there is a correlation between the linear term and the superconducting transition temperature. A hump is observed in the mid-infrared range of the optical conductivity in the presence of antiferromagnetic fluctuations.

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Electrical Conductivity of Interacting Fermions. II. Effects of Normal Scattering Processes in the Presence of Umklapp Scattering Processes

Cited by 43 publications

References 13 publications

Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids

Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids

Theory of Hall Effect and Electrical Transport in High-T_cCuprates: Effects of Antiferromagnetic Spin Fluctuations

Optical and dc conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point including vertex corrections

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Electrical Conductivity of Interacting Fermions. II. Effects of Normal Scattering Processes in the Presence of Umklapp Scattering Processes

Cited by 43 publications

References 13 publications

Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids

Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids

Theory of Hall Effect and Electrical Transport in High-TcCuprates: Effects of Antiferromagnetic Spin Fluctuations

Optical and dc conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point including vertex corrections

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Theory of Hall Effect and Electrical Transport in High-T_cCuprates: Effects of Antiferromagnetic Spin Fluctuations