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

de Moura, F. A. B. F.; Viana, L. P.; Lyra, M. L.; Malyshev, V. A.; Dominguez-Adame, F.

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

Authors

de Moura, F. A. B. F.

Description

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 $ε_{\bf m} = V\cos{(παm_x^{ν_x})}\cos{(παm_y^{ν_y})}$ 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.
16 pages, to appear in Phys. Lett. A