Singlet-triplet splitting in double quantum dots due to spin orbit and hyperfine interactions

TL;DR

This paper investigates the effects of spin orbit and hyperfine interactions on the energy spectrum of a two-electron double quantum dot, deriving a formula for level splitting relevant for experimental parameter extraction.

Contribution

It develops a perturbative two-level Hamiltonian model near the singlet-triplet avoided crossing, incorporating spin orbit and hyperfine effects in double quantum dots.

Findings

Derived an explicit formula for singlet-triplet level splitting.

Identified parameter regimes where spin orbit and hyperfine interactions are comparable.

Provided insights for experimental extraction of spin orbit parameters.

Abstract

We analyze the low-energy spectrum of a two-electron double quantum dot under a potential bias in the presence of an external magnetic field. We focus on the regime of spin blockade, taking into account the spin orbit interaction and hyperfine coupling of electron and nuclear spins. Starting from a model for two interacting electrons in a double dot, we derive a perturbative, effective two-level Hamiltonian in the vicinity of an avoided crossing between singlet and triplet levels, which are coupled by the spin-orbit and hyperfine interactions. We evaluate the level splitting at the anticrossing, and show that it depends on a variety of parameters including the spin orbit coupling strength, the orientation of the external magnetic field relative to an internal spin-orbit axis, the potential detuning of the dots, and the difference between hyperfine fields in the two dots. We provide a formula for the splitting in terms of the spin orbit length, the hyperfine fields in the two dots, and the double dot parameters such as tunnel coupling and Coulomb energy. This formula should prove useful for extracting spin orbit parameters from transport or charge sensing experiments in such systems. We identify a parameter regime where the spin orbit and hyperfine terms can become of comparable strength, and discuss how this regime might be reached.