Theory of valley-orbit coupling in a Si/SiGe quantum dot

TL;DR

This paper investigates how valley-orbit coupling affects electron states in Si/SiGe quantum dots, emphasizing the impact of interface tilt and magnetic fields on energy spectra and qubit coherence.

Contribution

It provides a comprehensive analysis combining numerical and analytical methods to understand valley-orbit interactions considering realistic geometries and interface tilts.

Findings

Valley splitting depends on orbital quantum numbers in the absence of tilt.

Interface tilt induces valley-orbit coupling, complicating valley splitting.

Ground state gap varies with magnetic field, tilt angle, and orbital quantum number.

Abstract

Electron states are studied for quantum dots in a strained Si quantum well, taking into account both valley and orbital physics. Realistic geometries are considered, including circular and elliptical dot shapes, parallel and perpendicular magnetic fields, and (most importantly for valley coupling) the small local tilt of the quantum well interface away from the crystallographic axes. In absence of a tilt, valley splitting occurs only between pairs of states with the same orbital quantum numbers. However, tilting is ubiquitous in conventional silicon heterostructures, leading to valley-orbit coupling. In this context, "valley splitting" is no longer a well defined concept, and the quantity of merit for qubit applications becomes the ground state gap. For typical dots used as qubits, a rich energy spectrum emerges, as a function of magnetic field, tilt angle, and orbital quantum number. Numerical and analytical solutions are obtained for the ground state gap and for the mixing fraction between the ground and excited states. This mixing can lead to valley scattering, decoherence, and leakage for Si spin qubits.