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We study the dynamics of an electron wave-packet in a two-dimensional squarelattice with an aperiodic site potential in the presence of an external uniformelectric 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 exactdiagonalization procedure and a finite-size scaling analysis, we show that inthe weakly aperiodic regime ($\nu_x,\nu_y < 1$), a phase of extended statesemerges in the center of the band at zero field giving support to a macroscopicconductivity in the thermodynamic limit. Turning on the field gives rise toBloch oscillations of the electron wave-packet. The spectral density of theseoscillations may display a double peak structure signaling the spatialanisotropy of the potential landscape. The frequency of the oscillations can beunderstood using a semi-classical approach.

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