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.
Categories: cond-mat.dis-nn cond-mat.mes-hall