Directed current in the Holstein system

We propose a mechanism to rectify charge transport in the semiclassical Holstein model. It is shown that localized initial conditions associated with a polaron solution, in conjunction with static electron on-site potential not having inversion symmetry, constitute minimal prerequisites for the emergence of a directed current in the underlying periodic lattice system. In particular, we demonstrate that for unbiased spatially localized initial conditions (constituted by kicked static polaron states), violation of parity prevents the existence of pairs of counterpropagating trajectories, thus allowing for a directed current despite the time reversibility of the equations of motion. Nevertheless, propagating polaron solutions associated with sets of unbiased localized initial conditions which eventually leave the region of localized initial conditions do not exhibit time reversibility. Since the initial conditions belonging to the corresponding counterpropagating, current-compensating polaron solutions are not contained in the set, this gives rise to the emergence of a current. Occurrence of long-range coherent charge transport is demonstrated.

Figure 1

Profile of the stationary electron occupation probability displayed for a lattice segment around the central site $n_0=0$. The parameter values are given by $\alpha =1.25$ and ${\omega }_0^2=2$. Solid line: the symmetrical on-site potential with $a=U_0=0$. Dashed line: the asymmetrical on-site potential with $a=0$ and $U_0=0.035$.

Figure 2

Spatiotemporal evolution of the electron occupation probability $\left|c_n\right|{}^2$ for a lattice comprising $N=105$ sites and periodic boundary conditions imposed. The parameter values are given by $\alpha =1.25$, ${\omega }_0^2=2$, $\tau =25$, $a=0$, and $U_0=0.035$. Upper (lower) panel $\lambda <0$ ($\lambda >0$).

Figure 3

Temporal behavior of the mean current density $\langle J(t)\rangle$ for an ensemble of $1000$ initial conditions distributed according to Eq. (28) with $E_{\mathrm{kin}}=0.1$. The parameter values are given by $\alpha =1.25$, ${\omega }_0^2=2$, $\tau =25$, $a=0$, and $U_0=0.035$.