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Register a new userUniversality of vertex corrections to the electrical conductivity in models with elastically scattered electrons
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We study quantum coherence of elastically scattered lattice fermions. We calculate vertex corrections to the electrical conductivity of electrons scattered either on thermally equilibrated or statically distributed random impurities. We demonstrate that the sign of the vertex corrections to the Drude conductivity is in both cases negative. Quantum coherence due to elastic back-scatterings always leads to diminution of diffusion.
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Mean-field theory of non-interacting disordered electron systems is widely and successfully used to describe equilibrium properties of alloys in the whole range of disorder strengths. It, however, fails to take into account effects of quantum coherence and localizing back-scattering effects when applied to transport phenomena. We present an approximate scheme extending the mean-field theory for one-electron properties in that it offers a formula for the two-particle vertex and the electrical conductivity non-perturbatively including the leading-order vertex corrections in a way that the approximation remains consistent and the conductivity non-negative in all disorder regimes.
It is well known that conductivity of disordered metals is suppressed in the limit of low frequencies and temperatures by quantum corrections. Although predicted by theory to exist up to much higher energies, such corrections have so far been experimentally proven only for $lesssim$80 meV. Here, by a combination of transport and optical studies, we demonstrate that the quantum corrections are present in strongly disordered conductor MoC up to at least $sim$4 eV, thereby extending the experimental window where such corrections were found by a factor of 50. The knowledge of both, the real and imaginary parts of conductivity, enables us to identify the microscopic parameters of the conduction electron fluid. We find that the conduction electron density of strongly disordered MoC is surprisingly high and we argue that this should be considered a generic property of metals on the verge of disorder-induced localization transition.
We study the thermal conductivity in disordered $s$-wave superconductors. Expanding on previous works for normal metals, we develop a formalism that tackles particle diffusion as well as the weak localization (WL) and weak anti-localization (WAL) effects. Using a Greens functions diagrammatic technique, which takes into account the superconducting nature of the system by working in Nambu space, we identify the systems low-energy modes, the diffuson and the Cooperon. The time scales that characterize the diffusive regime are energy dependent; this is in contrast with the the normal state, where the relevant time scale is the mean free time $tau_e$, independent of energy. The energy dependence introduces a novel energy scale $varepsilon_*$, which in disordered superconductors ($tau_e Deltall 1$, with $Delta$ the gap) is given by $varepsilon_* = sqrt{Delta/tau_e}$. From the diffusive behavior of the low-energy modes, we obtain the WL correction to the thermal conductivity. We give explicitly expressions in two dimensions. We determine the regimes in which the correction depends explicitly on $varepsilon_*$ and propose an optimal regime to verify our results in an experiment.
We study the temperature dependence of the conductivity due to quantum interference processes for a two-dimensional disordered itinerant electron system close to a ferromagnetic quantum critical point. Near the quantum critical point, the cross-over between diffusive and ballistic regimes of quantum interference effects occurs at a temperature $ T^{ast}=1/tau gamma (E_{F}tau)^{2}$, where $gamma $ is the parameter associated with the Landau damping of the spin fluctuations, $tau $ is the impurity scattering time, and $E_{F}$ is the Fermi energy. For a generic choice of parameters, $T^{ast}$ is smaller than the nominal crossover scale $1/tau $. In the ballistic quantum critical regime, the conductivity behaves as $T^{1/3}$.
The electron-electron interaction quantum correction to the conductivity of the gated single quantum well InP/In$_{0.53}$Ga$_{0.47}$As heterostructures is investigated experimentally. The analysis of the temperature and magnetic field dependences of the conductivity tensor allows us to obtain reliably the diffusion part of the interaction correction for different values of spin relaxation rate, $1/tau_s$. The surprising result is that the spin relaxation processes do not suppress the interaction correction in the triplet channel and, thus, do not enhance the correction in magnitude contrary to theoretical expectations even in the case of relatively fast spin relaxation, $1/Ttau_ssimeq (20-25)gg 1$.
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