arXiv subjects

Edvin G. Idrisov

Publications and source records attributed to Edvin G. Idrisov.

17 recordsLinked to original sources

arXiv2026

Fabry-Pérot interferometry with stochastic anyonic sources

We investigate the interference of Laughlin quasiparticles (QPs) in the fractional quantum Hall regime that are stochastically injected into a Fabry--Pérot interferometer. We find that the effective Aharonov--Bohm (AB) phase accumulated along the interferometer loop acquires an additional contribution of $\sin(2πλ)/2$ per QP present on it, where $πλ$ is the QP exchange phase. This contribution originates from time-domain braiding processes associated with injected QPs passing the interferometer quantum point contacts. In the limit of symmetric QP injection, the tunneling current noise exhibits AB oscillations as a function of the total injected current, providing access to the exchange phase $πλ$. In the regime of large total injection, we identify a universal Fano factor that displays power-law scaling and a characteristic phase shift reflecting time-domain QP braiding at the interferometer QPCs. These results are relevant for accessing anyonic exchange statistics in mesoscopic interferometers.

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arXiv2024

Charge-conserving equilibration of quantum Hall edge states

We address the experimentally relevant situation, where a non-equilibrium state is created at the edge of a quantum Hall system by injecting charge current into a chiral edge state with the help of a quantum point contact, quantum dots, or mesoscopic Ohmic contact. We show that the commonly accepted picture of the full equilibration of a non-equilibrium state at finite distances longer than a characteristic length scale contradicts to the charge conservation requirement. We use a phenomenological transmission line model to account for the local equilibration process and the charge and energy conserving dynamics of the collective mode. By solving this model in the limit of long distances $L$ from the injection point, we demonstrate that the correction of the electron distribution function to its eventual equilibrium form scales down slowly as $1/\sqrt{L}$.

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arXiv2023

Hydrodynamic Navier-Stokes equations in two-dimensional systems with Rashba spin-orbit coupling

We study a two-dimensional (2D) electron system with a linear spectrum in the presence of Rashba spin-orbit (RSO) coupling in the hydrodynamic regime. We derive a semiclassical Boltzmann equation with a collision integral due to Coulomb interactions in the basis of the eigenstates of the system with RSO coupling. Using the local equilibrium distribution functions, we obtain a generalized hydrodynamic Navier-Stokes equation for electronic systems with RSO coupling. In particular, we discuss the influence of the spin-orbit coupling on the viscosity and the enthalpy of the system and present some of its observable effects in hydrodynamic transport.

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arXiv2022

Overlap of parafermionic zero modes at a finite distance

Parafermion bound states (PBSs) are generalizations of Majorana bound states (MBSs) and have been predicted to exist as zero-energy eigenstates in proximitized fractional quantum Hall edge states. Similarly to MBSs, a finite distance between the PBS can split the ground state degeneracy. However, parafermionic modes have a richer exchange statistics than MBSs, so several interaction terms are allowed by the underlying $\mathbb{Z}_{2n}$ symmetry, rendering the effective Hamiltonian governing a pair of PBSs at a finite distance nontrivial. Here, we use a combination of analytical techniques (semiclassical instanton approximation) and numerical techniques (quantum Monte Carlo simulations) to determine the effective coupling Hamiltonian. For this purpose, we go beyond the dilute one-instanton gas approximation and show how finite-size effects can give rise to higher-order parafermion interactions. We find excellent agreement between the analytical results and Monte Carlo simulations. We estimate that these finite-size corrections should be observable in some of the recently proposed experiments to observe PBSs in strongly correlated systems.

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arXiv2022

Coulomb drag of viscous electron fluids: drag viscosity and negative drag conductivity

We show that Coulomb drag in hydrodynamic bilayer systems leads to additional viscosity terms in the hydrodynamic equations, i.e., the drag and drag-Hall viscosities, besides the well-known kinematic and Hall viscosities. These new viscosity terms arise from a change of the stress tensor due to the interlayer Coulomb interactions. All four viscosity terms are tunable by varying the applied magnetic field and the electron densities in the two layers. At certain ratios between the electron densities in the two layers, the drag viscosity dramatically changes the longitudinal transport resulting in a negative drag conductivity.

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arXiv2022

Thermal drag effect in quantum Hall circuits

We study the thermal drag between two mesoscopic quantum Hall (QH) circuits. Each circuit consists of Ohmic contact perfectly coupled to quantum Hall edge states. The drag is caused by strong capacitive coupling between Ohmic contacts. The non-equilibirum conditions and the electron-electron interaction are taken into account by using the non-equilibrium bosonization technique. The thermal drag current in the passive circuit, the noise power of the corresponding heat current, and the Fano factor are calculated and analyzed.

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arXiv2022

Current cross-correlations in a quantum Hall collider at filling factor two

We use the non-equilibrium bosonization technique to study the effects of Coulomb interactions in mesoscopic electron colliders based on quantum Hall (QH) edge states at filing factor $ν= 2$. The current cross-correlations and Fano factor, which carry the information about the exclusion statistics, are calculated. It is shown that both these quantities have a non-analytical dependence on the source transparency, which scales as $\log(1/T_s)$ at small $T_s \ll 1$. This is the consequence of electron-electron interactions in the outgoing non-equilibrium states of the collider.

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arXiv2021

Towards the theory of types III and IV non-Hermitian Weyl fermions

We develop the non-Hermitian Hamiltonian formalism to describe Weyl fermions of type III and IV. The spectrum of Hamiltonian has an unusual type of anisotropy. Namely, the hermiticity of Hamiltonian strongly depends on the direction in momentum space: for some directions the spectrum is real, in contrast for other directions it becomes complex. This fact leads to non-trivial adiabatic evolution and fractional Chern number. Additionally, we demonstrate that the non-Hermitian Hamiltonian can be regarded as a one-particle problem in context of topological band theory.

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arXiv2020

Electron hydrodynamics of anomalous Hall materials

We study two-dimensional electron systems in the hydrodynamic regime. We show that a geometrical Berry curvature modifies the effective Navier-Stokes equation for viscous electron flow in topological materials. For small electric fields, the Hall current becomes negligible compared to the viscous longitudinal current. In this regime, we highlight an unconventional Poiseuille flow with an asymmetric profile and a deviation of the maximum of the current from the center of the system. In a two-dimensional infinite geometry, the Berry curvature leads to current whirlpools and an asymmetry of potential profile. This phenomenon can be probed by measuring the asymmetric non-local resistance profile.

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arXiv2020

Current correlations of Cooper-pair tunneling into a quantum Hall system

We study Cooper pair transport through a quantum point contact between a superconductor and a quantum Hall edge state at integer and fractional filling factors. We calculate the tunnelling current and its finite-frequency noise to the leading order in the tunneling amplitude for dc and ac bias voltage in the limit of low temperatures. At zero temperature and in case of tunnelling into a single edge channel both the conductance and differential shot noise vanish as a result of Pauli exclusion principle. In contrast, in the presence of two edge channels, this Pauli blockade is softened and a non-zero conductance and shot noise are revealed.

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arXiv2020

Parafermion braiding in fractional quantum Hall edge states with finite chemical potential

Parafermions are non-Abelian anyons which generalize Majorana fermions and hold great promise for topological quantum computation. We study the braiding of $\mathbb{Z}_{2n}$ parafermions which have been predicted to emerge as bound states in fractional quantum Hall systems at filling factor $ν= 1/n$ ($n$ odd). Using a combination of bosonization and refermionization, we calculate the energy splitting as a function of distance and chemical potential for a pair of parafermions separated by a gapped region. Braiding of parafermions in quantum Hall edge states can be implemented by repeated fusion and nucleation of parafermion pairs. We simulate the conventional braiding protocol of parafermions numerically, taking into account the finite separation and finite chemical potential. We show that a nonzero chemical potential poses challenges for the adiabaticity of the braiding process because it leads to accidental crossings in the spectrum. To remedy this, we propose an improved braiding protocol which avoids those degeneracies.

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arXiv2019

Entropy production in one-dimensional quantum fluids

We study nonequilibrium thermodynamic properties of a driven one-dimensional quantum fluid by combining nonlinear Luttinger liquid theory with the quantum kinetic equation. In particular, we derive an entropy production consistent with the laws of thermodynamics for a system subject to an arbitrary perturbation varying slowly in space and time. Working in a basis of weakly interacting fermionic quasiparticles, we show that the leading contribution to the entropy production results from three-particle collisions, and we derive its scaling law at low temperatures.

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arXiv2019

Quantum ammeter

We present the theoretical model of the "quantum ammeter", a device that is able to measure the full counting statistics of an electron current at quantum time scales. It consists of an Ohmic contact, perfectly coupled to chiral quantum Hall channels, and of a quantum dot attached to one of the outgoing channels. At energies small compared to its charging energy, the Ohmic contact fractionalizes each incoming electron and redistributes it between outgoing channels. By monitoring the resonant tunneling current through the quantum dot, one gets an access to the moment generator of the current in one of the incoming channels at time scales comparable to its correlation time.

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arXiv2019

Finite frequency noise in chiral Luttinger liquid coupled to phonons

We study transport between Quantum Hall (QH) edge states at filling factor $ν= 1$ in the presence of electron-acoustic-phonon coupling. Performing a Bogoliubov-Valatin (BV) trasformation the low-energy spectrum of interacting electron-phonon system is presented. The electron-phonon interaction splits the spectrum into charged and neutral "downstream" and neutral "upstream" modes with different velocities. In the regimes of dc and periodic ac biases the tunelling current and non-equilibrium finite frequency non-symmetrized noise are calculated perturbatively in tunneling coupling of quantum point contact (QPC). We show that the presence of electron-phonon interaction strongly modifies noise and current relations compared to free-fermion case.

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arXiv2017

Dephasing in Mach-Zehnder interferometer by an Ohmic contact

We study dephasing in an electronic Mach-Zehnder (MZ) interferometer based on quantum Hall (QH) edge states by a micromiter-sized Ohmic contact embedded in one of its arms. We find that at the filling factor $ν=1$, as well as in the case where an Ohmic contact is connected to an MZ interfeoremter by a quantum point contact (QPC) that transmits only one electron channel, the phase coherence may not be fully suppressed. Namely, if the voltage bias $Δμ$ and the temperature $T$ are small compared to the charging energy of the Ohmic contact $E_C$, the free fermion picture is manifested, and the visibility saturates at its maximum value. At large biases, $Δμ\gg E_C$, the visibility decays in a power-law manner.

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arXiv2017

Thermal decay of the Coulomb blockade oscillations

We study transport properties and the charge quantization phenomenon in a small metallic island connected to the leads through two quantum point contacts (QPCs). The linear conductance is calculated perturbatively with respect to weak tunneling and weak backscattering at QPCs as a function of the temperature $T$ and gate voltage. The conductance shows Coulomb blockade (CB) oscillations as a function of the gate voltage that decay with the temperature as a result of thermally activated fluctuations of the charge in the island. The regimes of quantum, $T \ll E_C$, and thermal, $T \gg E_C$, fluctuations are considered, where $E_C$ is the charging energy of an isolated island. Our predictions for CB oscillations in the quantum regime coincide with previous findings in [A. Furusaki and K. A. Matveev, Phys. Rev. B {\bf 52}, 16676 (1995)]. In the thermal regime the visibility of Coulomb blockade oscillations decays with the temperature as $\sqrt{T/E_C}\exp(-π^2T/E_C)$, where the exponential dependence originates from the thermal averaging over the instant charge fluctuations, while the prefactor has a quantum origin. This dependence does not depend on the strength of couplings to the leads. The differential capacitance, calculated in the case of a single tunnel junction, shows the same exponential decay, however the prefactor is linear in the temperature. This difference can be attributed to the non-locality of the quantum effects. Our results agree with the recent experiment [S. Jezouin {\em et al}., Nature {\bf 536}, 58 (2016)] in the whole range of the parameter $T/E_C$.

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arXiv2015

Relaxation of an electron wave packet at the quantum Hall edge at filling factor 2

In this work, we address the recent experiment [S. Tewari et al., arXiv:1503.05057v1], where the suppression of phase coherence of a single-electron wave packet created at the edge of a quantum Hall (QH) system at filling factor 2 has been investigated with the help of an electronic Mach-Zehnder (MZ) interferometer. The authors of the experiment have observed an unexpected behavior of phase coherence, that saturates at high energies instead of vanishing, presumably suggesting the relaxation of a wave packet to the ground state before it arrives to the MZ interferometer. Here, we theoretically investigate this situation using the model of edge states [I. P. Levkivskyi, E. V. Sukhorukov, Phys. Rev. B 78, 045322 (2008)], which accounts for the strong Coulomb interaction between the two electron channels at the edge of a QH system. We conclude that the observed phenomenon cannot be explained within this model for the reason that under an assumption of linearity of the electron spectrum at low energies the system remains integrable in terms of the collective charge excitations, and therefore full relaxation to the ground state is not possible, despite strong interactions. As a result, the degree of the phase coherence decreases with energy of the initial state in a power-law manner. Since this does not happen in the experiment, a new physical phenomenon may take place at the edge of a QH state, which deserves further investigations. We support our findings by calculating the energy distribution and the Wigner function of the outgoing non-equilibrium state of the single-electron wave packet.

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