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

Dimitrije Stepanenko, Mark Rudner, Bertrand I. Halperin, and Daniel Loss
Phys. Rev. B 85, 075416 – Published 16 February 2012

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 an 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.

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  • Received 8 December 2011

DOI:https://doi.org/10.1103/PhysRevB.85.075416

©2012 American Physical Society

Authors & Affiliations

Dimitrije Stepanenko1, Mark Rudner2, Bertrand I. Halperin2, and Daniel Loss1

  • 1Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
  • 2Department of Physics, Harvard University, 17 Oxford St., Cambridge, Massachusetts 02138, USA

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Issue

Vol. 85, Iss. 7 — 15 February 2012

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