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arXiv:2310.14454 · Physical review. B./Physical review. B

Tunneling between two systems of interacting chiral fermions

D. B. Karki, К. А. Матвеев

Published Apr 12, 2024• 0 citations
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Abstract

We develop a theory of tunneling between two systems of spinless chiral fermions. This setup can be realized at the edge of a quantum Hall bilayer structure. We find that the differential conductance of such a device in the absence of interactions has an infinitely sharp peak as a function of applied voltage. Interaction between fermions results in broadening of the conductance peak. We focus on the regime of strong interactions, in which the shape of the peak manifests well defined features associated with the elementary excitations of the system.

DOI
10.1103/physrevb.109.155415

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We develop a theory of tunneling between two systems of spinless chiral fermions. This setup can be realized at the edge of a quantum Hall bilayer structure. We find that the differential conductance of such a device in the absence of interactions has an infinitely sharp peak as a function of applied voltage. Interaction between fermions results in broadening of the conductance peak. We focus on the regime of strong interactions, in which the shape of the peak manifests well defined features associated with the elementary excitations of the system.
The resonant tunneling through a double-barrier structure in a one-dimensional system of interacting spinless fermions is studied. The conductance is calculated as a function of gate voltage and temperature. It is shown that even in Luttinger liquids the line shape of resonances is almost the same as that of the noninteracting Fermi liquid provided that the temperature is not too low. The temperature dependence, on the other hand, is drastically changed by the interaction, and the height of the conductance peak is a nonmonotonic function of temperature for weak repulsive interaction.
Interactions in one-dimensional (1D) electron systems are expected to cause a dynamical separation of electronic spin and charge degrees of freedom. A promising system for experimental observation of this non-Fermi-liquid effect consists of two quantum wires coupled via tunneling through an extended uniform barrier. Here we consider the minimal model of an interacting 1D electron system exhibiting spin-charge separation, and calculate the differential tunneling conductance as well as the density-density response function. Both quantities exhibit distinct strong features arising from spin-charge separation. Our analysis of these features within the minimal model neglects interactions between electrons of opposite chirality, and therefore applies directly to chiral 1D electron systems realized, e.g., at the edge of integer quantum Hall systems. Physical insight gained from our results is useful for interpreting current experiment in quantum wires, as our main conclusions still apply with nonchiral interactions present. In particular, we discuss the effect of charging due to applied voltages, and the possibility to observe spin-charge separation in a time-resolved experiment.
We generalize the fermionic renormalization group method to describe analytically transport through a double barrier structure in a one-dimensional system. Focusing on the case of weakly interacting electrons, we investigate thoroughly the dependence of the conductance on the strength and the shape of the double barrier for arbitrary temperature T. Our approach allows us to systematically analyze the contributions to renormalized scattering amplitudes from different characteristic scales absent in the case of a single impurity, without restricting the consideration to the model of a single resonant level. Both a sequential resonant tunneling for high T and a resonant transmission for T smaller than the resonance width are studied within the unified treatment of transport through strong barriers. For weak barriers, we show that two different regimes are possible. Moderately weak impurities may get strong due to a renormalization by interacting electrons, so that transport is described in terms of theory for initially strong barriers. The renormalization of very weak impurities does not yield any peak in the transmission probability; however, remarkably, the interaction gives rise to a sharp peak in the conductance, provided asymmetry is not too high.
In this work we investigate the phenomena associated with the new thresholds in the spectrum of excitations arising when different one-dimensional strongly interacting systems are voltage biased and weakly coupled by tunneling. We develop the perturbation theory with respect to tunneling and derive an asymptotic behavior of physical quantities close to threshold energies. We reproduce earlier results for the electron relaxation at the edge of an integer quantum Hall system and for the nonequilibrium Fermi edge singularity phenomenon. In contrast to previous works, our analysis does not rely on the free-fermionic character of local tunneling; therefore, we are able to extend our theory to a wider class of systems, without well-defined electron excitations, such as spinless Luttinger liquids and chiral quantum Hall edge states at fractional filling factors.
We study edge dynamics in the presence of interlayer tunneling, parallel magnetic field, and various types of disorder for two infinite sequences of quantum Hall states in symmetric bilayers. These sequences begin with the 110 and 331 Halperin states and include their fractional descendants at lower filling factors; the former is easily realized experimentally while the latter is a candidate for the experimentally observed quantum Hall state at a total filling factor of 1/2 in bilayers. We discuss the experimentally interesting observables that involve just one chiral edge of the sample and the correlation functions needed for computing them. We present several methods for obtaining exact results in the presence of interactions and disorder that rely on the chiral character of the system. Of particular interest are our results on the 331 state, which suggest that a time-resolved measurement at the edge can be used to discriminate between the 331 and Pfaffian scenarios for the observed quantum Hall state at filling factor 1/2 in realistic double-layer systems.