Exchange coupling in semiconductor nanostructures: Validity and limitations of the Heitler-London approach

Abstract

The exchange coupling of the spins of two electrons in double well potentials in a semiconductor background is calculated within the Heitler-London (HL) approximation. Atomic and quantum dot types of confining potentials are considered, and a systematic analysis for the source of inaccuracies in the HL approach is presented. For the strongly confining coulombic atomic potentials in the H2 molecule, the most dramatic failure occurs at very large interatomic distances, where HL predicts a triplet ground state, both in 3D and in 2D, coming from the absence of electron-electron correlation effects in this approach. For a 2D double well potential, failures are identified at relatively smaller interdot distances, and may be attributed to the less confining nature of the potential, leading to larger overlap and consequently an inadequate representation of the two-particle states written, within HL, in terms of the ground state orbital at each isolated well. We find that in the double dot case, the range of validity of HL is improved (restricted) in a related 3D (1D) model, and that results always tend to become more reliable as the interdot distance increases. Our calculated exchange coupling is of relevance to the exchange gate quantum computer architectures in semiconductors.

6 pages, 3 figures. As accepted in Physical Review B

References in corpus (4)

• Triplet-Singlet Spin Relaxation via Nuclei in a Double Quantum Dot
• Charge-qubit operation of an isolated double quantum dot
• The Exchange Gate in Solid State Spin Quantum Computation: The Applicability of the Heisenberg Model
• Two-electron lateral quantum-dot molecules in a magnetic field

Cited by in corpus (16)

• Silicon Quantum Electronics
• Semiconductor Spin Qubits
• Exchange coupling in silicon quantum dots: Theoretical considerations for quantum computation
• Strong coupling of spin qubits to a transmission line resonator
• External field control of donor electron exchange at the Si/SiO2 interface
• Implications of Simultaneous Requirements for Low Noise Exchange Gates in Double Quantum Dots
• Failure of standard approximations of the exchange coupling in nanostructures
• Spin-orbit mediated anisotropic spin interaction in interacting electron systems
• Reliability of the Heitler-London approach for the exchange coupling between electrons in semiconductor nanostructures
• Influence of confining potentials on the exchange coupling in double quantum dots
• Size effects in the exchange coupling between two electrons in quantum wire quantum dots
• Exchange between deep donors in semiconductors: a quantum defect approach
• Spin-orbit enabled quantum transport channels in a two-hole double quantum dot
• Ab initio modelling of quantum dot qubits: Coupling, gate dynamics and robustness versus charge noise
• Dressed basis sets for the modeling of exchange interactions in double quantum dots
• Comparison of methods for computing the exchange energy in laterally coupled quantum dots