Ground-state properties of electron-electron biwire systems

TL;DR

This study investigates the ground-state properties of parallel electron biwires using variational Monte Carlo, revealing how interwire interactions influence electronic correlations, energy, and Tomonaga-Luttinger liquid behavior across different separations.

Contribution

It provides a detailed analysis of electron correlations and Tomonaga-Luttinger liquid parameters in biwire systems, highlighting the evolution from two separate wires to a single combined wire as separation decreases.

Findings

Interaction energy scales as ln(d) for small d and as d^{-2} for large d.

Interwire correlations increase while intrawire correlations decrease as wires approach.

The Tomonaga-Luttinger liquid behavior persists with a calculable interaction parameter K_ρ.

Abstract

The correlation between electrons in different quantum wires is expected to affect the electronic properties of quantum electron-electron biwire systems. Here, we use the variational Monte Carlo method to study the ground-state properties of parallel, infinitely thin electron-electron biwires for several electron densities ($r_\text{s}$) and interwire separations ($d$). Specifically, the ground-state energy, the correlation energy, the interaction energy, the pair-correlation function (PCF), the static structure factor (SSF), and the momentum distribution (MD) function are calculated. We find that the interaction energy increases as $\ln(d)$ for $d\to 0$ and it decreases as $d^{-2}$ when $d\to \infty$. The PCF shows oscillatory behavior at all densities considered here. As two parallel wires approach each other, interwire correlations increase while intrawire correlations decrease as evidenced by the behavior of the PCF, SSF, and MD. The system evolves from two monowires of density parameter $r_\text{s}$ to a single monowire of density parameter $r_\text{s}/2$ as $d$ is reduced from infinity to zero. The MD reveals Tomonaga-Luttinger (TL) liquid behavior with a power-law nature near $k_\text{F}$ even in the presence of an extra interwire interaction between the electrons in biwire systems. It is observed that when $d$ is reduced the MD decreases for $k<k_\text{F}$ and increases for $k>k_\text{F}$, similar to its behavior with increasing $r_\text{s}$. The TL liquid exponent is extracted by fitting the MD data near $k_\text{F}$, from which the TL liquid interaction parameter $K_{\rho}$ is calculated. The value of the TL parameter is found to be in agreement with that of a single wire for large separation between the two wires.