Rectification from band gap oscillation

Abstract

We study a one-dimensional chain of identical atoms with two electronic orbitals and two electrons per atom, subject to an external oscillating pressure that periodically modulates the lattice spacing. This leads to time-dependent intra- and inter-orbital hopping amplitudes. In the tight-binding limit with weak inter-orbital hopping, the system exhibits two electronic bands separated by an oscillating indirect band-gap. By tuning hopping amplitudes and orbital energies, a periodic metal-insulator transition emerges in the half-filled system. When the frequency of this transition matches that of an external alternating electric field, the system undergoes half-wave rectification: it behaves as a conductor during one half-cycle and as an insulator during the other. This dynamic switching enables directional current flow and remains robust under small to intermediate onsite electron-electron interactions.

Figures (6)

• Figure 1: (a) Schematic shows a tight binding chain of atoms with two orbitals $A$ and $B$ on each atom. Electron hops from one atom to its nearest neighbor within same orbitals (intra) and between different orbitals (inter). The lattice spacing oscillates with time $t'$ as the length of the chain is periodically stretched and compressed. (b) Schematic shows the increasing bandwidth of the two bands with decreasing lattice spacing or increasing hopping amplitude in the static case. For simplicity the intra-orbital hopping amplitudes are considered equal in this figure with the assumption that inter-orbital hopping is vanishingly small. Oscillation of $t$ about $t^{*}$, the metal-insulator transition point, gives periodic oscillation of the band-gap, which means the system becomes metallic and insulating periodically at half-filling.
• Figure 2: (a) Figure shows plot of the band-gap $\Delta(t')$ as a function of time $t'$ for $\epsilon_{A}=0.8,\epsilon_{B}=0.2$ and hopping amplitude oscillation of $0.05$ around $t_{AA}^{*}=0.2,t_{BB}^{*}=0.1$. For $\Delta(t')>0$, the system is a band insulator (shaded as red) whereas for $\Delta(t')<0$, the system is a metal (shaded as blue) at half-filling. (b),(c) show the band dispersions at $t'=1$ and $t'=5$ where the system is a band insulator and a metal respectively at half-filling.
• Figure 3: (a)-(b) An external alternating voltage $V(t')=V_{0}\sin(\omega t')$ with $\omega=1$ , i.e., having the same frequency as that of the oscillating pressure subjected on the chain is half-wave rectified due to a periodic metal-insulator transition at half-filling. Here $I(t')$ is the current in the system due to the external electric field.
• Figure 4: Panels $(a)-(c)$ show the oscillation of band-gap $\Delta(t')$ for $U/t_{AA}^{*}=1$ and the band dispersions for $t'=1,5$. There is an oscillation between a band insulator (BI) and an orbital imbalanced ferromagnetic metal (FM) in this case. Panels $(d)-(f)$ show the same for $U/t_{AA}^{*}=6$ where there is a dynamic phase transition between a Mott insulator (MI) and an orbital imbalanced ferromagnetic metal (FM). Panels $(g)-(i)$ also show the same for $U/t_{AA}^{*}=10$ where the system is always a MI but with oscillations in the positive value of the band-gap.
• Figure 5: Panel $(a)$ shows the density difference, $\delta$ between the two orbitals $A$ and $B$ as a function of time, $t'$ for $U/t_{AA}^{*}=0,1,6,10$. Panel $(b)$ shows the orbital magnetization, $m_{\alpha}$ where $\alpha \in A,B$ as a function of time, $t'$ for $U/t_{AA}^{*}=1,6,10$. For $U/t_{AA}^{*}=0$, there is no orbital magnetization.