Quantum transport in quasi-periodic lattice systems in presence of B\"uttiker probes

TL;DR

This paper investigates how B"uttiker probes affect quantum transport in quasi-periodic Aubry-André-Harper systems, revealing power-law conductance scaling and diffusive behavior, with implications for thermoelectric efficiency.

Contribution

It introduces a B"uttiker probe approach to study environment effects on transport in quasi-periodic systems, highlighting power-law scaling and thermoelectric performance analysis.

Findings

Conductance scales as γ^4 at small probe coupling

Transport becomes diffusive at strong probe coupling

Thermoelectric efficiency bounds are validated

Abstract

Quasi-periodic lattice systems offer diverse transport properties. In this work, we investigate the environment induced effects on transport properties for quasi-periodic systems, namely the one-dimensional Aubry-Andr\'e-Harper (AAH) lattice chain and its generalized version (GAAH) by considering the B\"uttiker probe approach. We first consider voltage probe situation and study the electrical conductance properties in the linear response regime. At zero temperature, we observe enhancement in conductance at all the no-transport regimes, located both inside and outside of the band of the original system, for small probe coupling strength $\gamma$ with a power-law scaling $\gamma^4$. Whereas, for large probe coupling strengths, the conductance at all Fermi energies is the same and decays as a power-law with scaling $1/\gamma^4$. This particular scaling survives even in the finite-temperature limit. Interestingly, this scaling result is different from the one recently predicted following the local Lindblad master equation approach. The transport eventually becomes diffusive for all energy ranges and in all regimes of the original model for a sufficiently strong coupling with the probes. We further extend our study and consider voltage-temperature probes to analyze the thermoelectric performance of the chain in terms of the figure of merit. We also demonstrate the validity of two recently obtained bounds on thermoelectric efficiency that are tighter than the seminal Carnot bound and express the same in terms of the Onsager's transport coefficients.