arXiv subjects

Tatia Kiliptari

Publications and source records attributed to Tatia Kiliptari.

3 recordsLinked to original sources

arXiv2026

Conserving relaxation-time approximation for electron-electron collisions

We develop a conserving relaxation-time approximation (cRTA) based on an explicit energy-resolved projection onto the full space of collision invariants. Our cRTA retains the energy dependence of the nonequilibrium quasiparticle distribution, allowing one to describe transport quantities sensitive to states near, but not exactly on, the Fermi surface (FS). We apply the method to several charge-transport problems in both Galilean-invariant and non-Galilean-invariant Fermi liquids. In particular, the cRTA reproduces the low- and high-temperature limits of the dc conductivity of a non-Galilean-invariant Fermi liquid with disorder, the hydrodynamic and collisionless limits of the finite-wavevector longitudinal conductivity of a clean Galilean-invariant Fermi liquid, and the asymptotic scaling forms of the optical conductivity of a clean non-Galilean-invariant Fermi liquid beyond the semiclassical limit. For several observables, the agreement with exact solutions is quantitative at the percent level. These results demonstrate that the cRTA provides a simple and accurate framework for describing transport beyond the FS projection.

cond-mat.str-el↗

arXiv2026

Conductivity of a Non-Galilean--Invariant Fermi Liquid: Exact Solution of the Kinetic Equation

We obtain an exact expression for the conductivity of a disordered, non-Galilean-invariant Fermi liquid by solving the kinetic equation with both screened Coulomb and $z=3$ Pomeranchuk critical interactions. While consistent with previous asymptotic results, our solution shows that electron-electron interactions enter the conductivity solely via the quasiparticle scattering time, $τ_\mathrm{ee}$. Accordingly, the crossovers between the collisionless and hydrodynamic regimes occur when $1/τ_\mathrm{ee}$ becomes comparable to the larger of the impurity scattering rate and the probe frequency, $Ω$. In addition, the exact solution yields the optical response in the hydrodynamic regime, $Ω\ll 1/τ_\mathrm{ee}$, which is inaccessible within perturbation theory. Near a $z=3$ Pomeranchuk quantum critical point, consistency between the kinetic-equation and Kubo approaches requires proper inclusion of mass renormalization within the Eliashberg approximation, which also ensures that the crossover between the collisionless and hydrodynamic regimes in the optical conductivity occurs at the Planckian scale $Ω\sim T$.

cond-mat.str-el↗

arXiv2025

Magnetoconductivity due to electron-electron interaction in a non-Galilean-invariant Fermi liquid

The $T^2$-scaling of resistivity with temperature is often viewed as a classic hallmark of a Fermi-liquid (FL) behavior in metals. However, if umklapp scattering is suppressed, this scaling is not universally guaranteed to occur. In this case, the resistivity behavior is influenced by several factors, such as dimensionality (two vs. three), topology (simply- vs. multiply-connected Fermi surfaces), and (in two dimensions) the shape (convex vs. concave) of the Fermi surface (FS). Specifically for an isotropic spectrum, as well as for a two-dimensional (2D) convex FS, the $T^2$ term is absent, and the first non-zero contribution scales as $T^4\ln T$ in 2D and as $T^4$ in 3D. In this paper, we study the $T$-dependence of the resistivity, arising from electron-electron interactions, in the presence of a weak magnetic field. We show that, for an isotropic FS in any dimensions and for a convex 2D FS, the $T^2$ term is also absent in both Hall and diagonal components of the magnetoconductivity, which instead scale as $BT^4\ln T$ and $B^2T^4\ln T$, respectively, in 2D and as $BT^4$ and $B^2T^4$ in 3D. The FL-like scaling, i.e., $BT^2$ and $B^2T^2$ of the Hall and diagonal conductivities is recovered for a concave FS in 2D. Furthermore, we show that, for an isotropic spectrum, magnetoresistance is absent even in the presence of electron-electron interactions. Additionally, we examine the high-temperature limit, when electron-electron scattering prevails over electron-impurity one, and show that all the components of the conductivity tensor saturate in this limit at values that are determined by impurity scattering but, in general, differ from the corresponding values at $T=0$.

cond-mat.str-el↗