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

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 ǫ m = V cos (παm νx x ) cos (παm νy y ) at lattice sites (m x , m y ), with πα being a rational number, and ν x and ν 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 (ν x , ν 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.

Dynamics of two interacting electrons in Anderson-Hubbard chains with long-range correlated disorder: Effect of a static electric field

“…This is a clean signature of Bloch oscillations which are associated with the emergence of ex-tended states in this strongly correlated regime. 16,39 When the Hubbard coupling is finite, both centroid and velocity display amplitude-modulated envelopes and multifrequency patterns. In Fig.…”

Vibrational modes in a two-dimensional aperiodic harmonic lattice

“…The one-electron Schrödinger equation in a 2D square lattice with an aperiodic site potential was solved numerically. It was numerically demonstrated that a phase of extended states emerges in the center of the band giving support to a macroscopic conductivity in the thermodynamic limit [17].…”

“…It was shown that the localized or extended nature of their eigenstates is related to general characteristics of the aperiodic on-site distributions [12][13][14][15][16]. The effect of aperiodicity on the electronic dynamics in 2D lattices was studied in [17]. The one-electron Schrödinger equation in a 2D square lattice with an aperiodic site potential was solved numerically.…”

Resonant tunnelling in a Fibonacci bilayer graphene superlattice

“…An ideal conventional quasi‐periodic superlattice shows a highly fragmented and fractal‐like electronic spectrum with repeated self‐similar patterns, different from that of a periodic superlattice. In the former case (quasi‐periodic), many theoretical studies 20–25 regarding resonant tunnelling properties have been reported using Fibonacci sequences. It is therefore very interesting and worthwhile to know how the ballistic property of chiral Dirac fermions changes due to the inclusion of artificial quasi‐periodicity in graphene superlattices.…”