Igor Valery Yurkevich

We study a multichannel quasi-one-dimensional system in the framework of the Tomonaga–Luttinger liquid model. Relevant backscattering perturbations create gaps in the corresponding fields, thereby changing the properties of the system. We model these gapped fields by introducing masses of bosonic fields and sending them to infinity to find the correlator of two fields describing the original channels. The exact solution for the corresponding Green function in the low-frequency limit allows us to use the Kubo formula to calculate the dc conductance of the system, which explains all seminal experimental results.

Quasi-one-dimensional systems with multiple conduction channels are essential for describing a range of physical phenomena. In this paper, we analyse transport in wires where electrons are subject to arbitrary number of strong multi-particle backscattering terms. We present an exact calculation of the system’s scattering matrix and derive a formula for the two-terminal conductance. We find the conductance is reduced from its ideal value by a term corresponding to the projection of current fields onto the subspace of integer-valued vectors characterising the gapped channels created by the perturbations. Applying this result, we establish the minimal model required to reproduce the recently observed, yet unexplained, fractional conductance plateaus with even denominators.

Quasi-one-dimensional systems with multiple conduction channels are essential for describing a range of physical phenomena. In this paper, we analyse transport in wires where electrons are subject to arbitrary number of strong multi-particle backscattering terms. We present an exact calculation of the system's scattering matrix and derive a formula for the two-terminal conductance. We find the conductance is reduced from its ideal value by a term corresponding to the projection of current fields onto the subspace of integer-valued vectors characterising the gapped channels created by the perturbations. Applying this result, we establish the minimal model required to reproduce the recently observed, yet unexplained, fractional conductance plateaus with even denominators.

We consider how the absence of thermalization affects the classical Coulomb blockade regime in quantum dots. By solving the quantum kinetic equation in the experimentally accessible regime when the dot has two relevant occupation states, we calculate the current–voltage characteristics for arbitrary coupling to the leads. If the couplings are strongly asymmetric, the Coulomb staircase is practically reduced to the first step, which is independent of the charging energy, when the Fermi energy is comparatively small, while the standard thermalized results are recovered in the opposite case. When the couplings are of the same order, the absence of thermalization has a new, striking signature—a robust additional peak in the differential conductance.

We study the interplay between quasiperiodic disorder and superconductivity in a one-dimensional tight-binding model with the quasiperiodic modulation of on-site energies that follow the Fibonacci rule, and all the eigenstates are multifractal. As a signature of multifractality, we observe the power-law dependence of the correlation between different single-particle eigenstates as a function of their energy difference. We numerically compute the mean-field superconducting transition temperature for every realization of a Fibonacci chain of a given size and find the distribution of critical temperatures, analyze their statistics, and estimate the mean value and variance of critical temperatures for various regimes of the attractive coupling strength and quasiperiodic disorder. We find an enhancement of the critical temperature compared to the analytical results that are based on strong assumptions of the absence of correlations and self-averaging of multiple characteristics of the system, which are not justified for the Fibonacci chain. For the very weak coupling regime, we observe a crossover where the self-averaging of the critical temperature breaks down completely and strong sample-to-sample fluctuations emerge.

In recent experiments on conductance of one-dimensional (1D) channels in ultra-clean samples, a diverse set of plateaus were found at fractions of the quantum of conductance in zero magnetic field. We consider a discrete model of strongly interacting electrons in a clean 1D system where the current between weak tunneling contacts is carried by fractionally charged solutions. While in the spinless case conductance remains unaffected by the interaction, as is typical for the strongly interacting clean 1D systems, we demonstrate that in the spinful case the peak conductance takes fractional values that depend on the filling factor of the 1D channel.

We investigate nonequilibrium transport properties of a quantum dot in the Coulomb blockade regime under the condition of negligible inelastic scattering during the dwelling time of the electrons in the dot. Using the quantum kinetic equation we show that the absence of thermalization leads to a double step in the distribution function of electrons on the dot, provided that it is symmetrically coupled to the leads. This drastically changes nonlinear transport through the dot resulting in an additional (compared to the thermalized case) jump in the conductance at voltages close to the charging energy, which could serve as an experimental manifestation of the absence of thermalization.

We investigate the Coulomb blockade in quantum dots asymmetrically coupled to the leads for an arbitrary voltage bias focusing on the regime where electrons do not thermalise during their dwell time in the dot. By solving the quantum kinetic equation, we show that the current–voltage characteristics are crucially dependent on the ratio of the Fermi energy to charging energy on the dot. In the standard regime when the Fermi energy is large, there is a Coulomb staircase which is practically the same as in the thermalised regime. In the opposite case of the large charging energy, we identify a new regime in which only one step is left in the staircase, and we anticipate experimental confirmation of this finding.

A strongly interacting 1D system with many channels is studied. When single‐electron interchannel backscattering processes become relevant, new fields are defined. Some fields are frozen (gapped) by these relevant perturbations, whereas others remain free. A mathematical procedure to separate gapped and conducting channels is proposed. The problem for a two‐channel system with particular relevant perturbation is then solved exactly for arbitrary intra‐ and interchannel interactions, and effective Luttinger parameter and velocity for the free field are found. The parameters of the free field are independent of the interactions between right‐ and left‐moving electrons in the same channel and between electrons moving in the same direction in different channels. Finally, if the interchannel interactions are weak, the free field becomes noninteracting (effective Luttinger parameter ) independently of how strong intrachannel interactions are.