Impurity-directed transport within a finite disordered lattice

Abstract

We consider a finite, disordered 1D quantum lattice with a side-attached impurity. We study theoretically the transport of a single electron from the impurity into the lattice, at zero temperature. The transport is dominated by Anderson localization and, in general, the electron motion has a random character due to the lattice disorder. However, we show that by adjusting the impurity energy the electron can attain quasi-periodic motions, oscillating between the impurity and a small region of the lattice. This region corresponds to the center of a localized state in the lattice with an energy matched by that of the impurity. By precisely tuning the impurity energy, the electron can be set to oscillate between the impurity and a region far from the impurity, even distances larger than the Anderson localization length. The electron oscillations result from the interference of hybrized states, which have some resemblance to Pendry's necklace states [J. B. Pendry, J. Phys. C: Solid State Phys. 20, 733-742 (1987)]. The dependence of the electron motion on the impurity energy gives a potential mechanism for selectively routing an electron towards different regions of a 1D disordered lattice. * for the electron. Necklace states also exist in optical systems [22,23]. These states form a sub-band that can induce resonant transport similar to the energy band of an ordered lattice. Resonances of finite disordered systems coupled to infinite reservoirs have been theoretically studied in [24,25].Extrapolating from these previous studies, here we consider finite disordered lattices (or quantum wires) with a side-attached impurity ("T-junction"). The impurity can be realized using a quantum dot, which constitutes a nano-control device. The properties of the dot can be altered through a gate potential allowing an experimentalist control over electron transport. Varying the gate potential on the dot can be used to probe the spectrum and localization properties of the lattice. As we will show, we can indeed use an impurity to direct transport within a disordered lattice. In our theoretical study we will consider the case of zero temperature. Therefore the transport we will discuss is different from variable-range hopping [26,27], which occurs at non-zero temperature. We will discuss possible extension of our work to the case of nonzero temperature in section VIII. Note that our lattice is finite, but large enough so that boundary effects only play a minor role.Experimentally, effective 1-D systems can be synthesized by a variety of techniques [28,29], including lattice geometries that incorporate a side-attached quantum dot [30,31]. Randomized site potentials in a finite lattice might be obtained, for example, by varying segment lengths (i.e., growth times) in GaAs/GaP superlattices assembled by laser-assisted catalytic growth [15,29]. An arXiv:1511.08758v2 [cond-mat.mes-hall]

Effect of disorder on transport properties in a tight-binding model for lead halide perovskites

“…and the index i labels the different sites in the lattice and therefore runs over all the sites in the lattice [28][29][30][31]. Roughly speaking, the IPR for a state gives the inverse of the spatial extent (or volume) of the state.…”

Impurity coupled to a lattice with disorder

“…The occupation of an impurity state for a single realization of the disorder was studied in Ref. 46. We consider here the return probability averaged over a large number N of disorder realizations.…”