Bias driven coherent carrier dynamics in a two-dimensional aperiodic potential

TL;DR

This study investigates how aperiodic potentials influence electron dynamics in a 2D lattice, revealing extended states, anisotropic Bloch oscillations, and potential conductivity in weakly aperiodic regimes.

Contribution

It introduces a tunable aperiodic potential model and demonstrates the emergence of extended states and anisotropic Bloch oscillations using exact diagonalization.

Findings

Extended states appear at zero field in weakly aperiodic regimes.

Bloch oscillations exhibit a double peak structure indicating anisotropy.

Oscillation frequencies align with semi-classical predictions.

Abstract

We study the dynamics of an electron wave-packet in a two-dimensional square lattice with an aperiodic site potential in the presence of an external uniform electric field. The aperiodicity is described by $\epsilon_{\bf m} = V\cos{(\pi\alpha m_x^{\nu_x})}\cos{(\pi\alpha m_y^{\nu_y})}$ at lattice sites $(m_x, m_y)$, with $\pi \alpha$ being a rational number, and $\nu_x$ and $\nu_y$ tunable parameters, controlling the aperiodicity. Using an exact diagonalization procedure and a finite-size scaling analysis, we show that in the weakly aperiodic regime ($\nu_x,\nu_y < 1$), a phase of extended states emerges in the center of the band at zero field giving support to a macroscopic conductivity in the thermodynamic limit. Turning on the field gives rise to Bloch oscillations of the electron wave-packet. The spectral density of these oscillations may display a double peak structure signaling the spatial anisotropy of the potential landscape. The frequency of the oscillations can be understood using a semi-classical approach.