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 ${\epsilon }_{\mathbf{m}}=V\cos (\pi \alpha m_x^{{\nu }_x})\cos (\pi \alpha m_y^{{\nu }_y})$ 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.

16 pages, to appear in Phys. Lett. A