Interface roughness, valley-orbit coupling, and valley manipulation in quantum dots

Abstract

We present a systematic study of interface roughness and its effect on coherent dynamical processes in quantum dots. The potential due to a sharp, flat interface lifts the degeneracy of the lowest energy valleys and yields a set of valley eigenstates. Interface roughness is characterized by fluctuations in the location of the interface and in the magnitude of the potential step. Variations in the position of the interface, which are expected to occur on the length scale of the lattice constant, reduce the magnitude of the valley-orbit coupling. Variations in the size of the interface potential step alter the magnitude of the valley-orbit coupling and induce transitions between different valley eigenstates in dynamics involving two (or more) dots. Such transitions can be studied experimentally by manipulating the bias between two dots and can be detected by charge sensing. However, if the random variable characterizing the position of the interface is correlated over distances of the order of a quantum dot, which is unlikely but possible, the phase of the valley-orbit coupling may be different in adjacent dots. In this case tunneling between like and opposite valley eigenstates is in effect a random variable and cannot be controlled. We suggest a resonant tunneling experiment that can identify the matrix elements for tunneling between like and opposite valley eigenstates. arXiv:1006.5448v2 [cond-mat.mes-hall]

Signatures of the valley Kondo effect in Si/SiGe quantum dots

“…The appearance and persistence of the center peak with B > 0 is a key prediction of the theory of the valley Kondo effect and arises physically from an interference of valley conserving and valley non-conserving processes. This suggests that valley index is not always conserved during tunneling, a subject of some debate, 12,13,15,[22][23][24][25][26][27] and in accord with recent effective mass calculations of the effects of atomic step disorder at the quantum well interface. 17 Secondly, given a non-zero ∆, the QD electrons must occupy an excited state rather than the ground state viewed in terms of single-particle levels.…”

Coherent electrical rotations of valley states in Si quantum dots using the phase of the valley-orbit coupling

“…The assumptions underlying this formulation of the problem have been discussed at length in Ref. 91.…”

“…If, in addition, the interface is sharp along the growth direction and flat perpendicular to it, or if interface roughness is correlated over distances much shorter than the size of the QD, the valley eigenstates |D ± are identical in both dots. 91 Under such circumstances interdot tunneling occurs only between the same valley eigenstates (+ to + and − to −), while interdot tunneling between valley eigenstates (+ to − and − to +) is suppressed. In this section we discuss the modification of the phase of the valley-orbit coupling due to a top-gate, and demonstrate that tuning the top-gate electric field to be different on the L and R dots enables a small amount of interdot tunneling between different valley eigenstates which can be effective in the neighborhood of a level anticrossing.…”

“…Experimentally,t andt −+ can be identified using resonant tunneling, 94 as described in detail in Ref. 91. We discuss next a series of numerical estimates for the valley-orbit coupling, the effect of an electric field on it, and the interdot tunneling parametert −+ .…”

“…80 For two electrons in a single QD the ground state moves down as a function of magnetic field, 79 and in a double QD (DQD) different valley eigenstates may be identified via resonant tunneling. 91 Since the two valleys are separated by a wave vector of the size of the Brillouin zone, manipulation of the valley degree of freedom is a difficult task. No scheme has been experimentally demonstrated to date for achieving rotations of valley eigenstates in a 2DEG or in a single QD.…”