Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2008-09-19
Phys. Lett. A 372, 6694 (2008)
Physics
Condensed Matter
Disordered Systems and Neural Networks
16 pages, to appear in Phys. Lett. A
Scientific paper
10.1016/j.physleta.2008.09.019
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.
de Moura A. B. F. F.
Dominguez-Adame Francisco
Lyra Marcelo L.
Malyshev Victor A.
Viana Leonardo P.
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