The two-impurity Kondo model with spin-orbit interactions

TL;DR

This paper investigates how spin-orbit interactions influence the two-impurity Kondo model in two dimensions, affecting quantum criticality and entanglement, with implications for quantum computing in semiconductor devices.

Contribution

It generalizes previous results on spin-orbit effects in the TIKM and explores their impact on quantum critical points and entanglement in quantum dot systems.

Findings

Spin-orbit interactions can produce a line of critical points with the same scaling as the TIKM.

Spin-orbit coupling can control entanglement between RKKY-coupled spins in quantum dots.

Gate-controlled spin-orbit interactions can switch entanglement states in semiconductor heterostructures.

Abstract

We study the two-impurity Kondo model (TIKM) in two dimensions with spin-orbit coupled conduction electrons. In the first part of the paper we analyze how spin-orbit interactions of Rashba as well as Dresselhaus type influence the Kondo and RKKY interactions in the TIKM, generalizing results obtained by H. Imamura {\em et al.} (2004) and J. Malecki (2007). Using our findings we then explore the effect from spin-orbit interactions on the non-Fermi liquid quantum critical transition between the RKKY-singlet and Kondo-screened RKKY-triplet states. We argue that spin-orbit interactions under certain conditions produce a line of critical points exhibiting the same leading scaling behavior as that of the ordinary TIKM. In the second part of the paper we shift focus and turn to the question of how spin-orbit interactions affect the entanglement between two localized RKKY-coupled spins in the parameter regime where the competition from the direct Kondo interaction can be neglected. Using data for a device with two spinful quantum dots patterned in a gated InAs heterostructure we show that a gate-controlled spin-orbit interaction may drive a maximally entangled state to one with vanishing entanglement, or vice versa (as measured by the concurrence). This has important implications for proposals using RKKY interactions for nonlocal control of qubit entanglement in semiconductor heterostructures.