Quantum transport in quasi-periodic lattice systems in presence of Büttiker probes

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-André-Harper (AAH) lattice chain and its generalized version (GAAH) by considering the Büttiker 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 γ with a power-law scaling γ 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/γ 4 . This particular scaling survives even in the finitetemperature 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.

Long-Range Charge Transport in Homogeneous and Alternating-Rigidity Chains

“…Beyond studies of short (1-10 units) molecular junctions, there have been fundamental applications of the LBP method to understand scaling relations in transport. This includes simulations of carriers' transport in periodic and quasi-periodic lattices under dissipation 42,43 , and the coherent (ballistic) to Ohmic (diffusive) crossover in charge 44,45 and phonon transport 46,47 .…”