Spin-orbit interaction in quantum dots in the presence of exchange correlations
arXiv:cond-mat/0602552 · doi:10.1103/PhysRevB.74.165333
Abstract
We discuss the problem of spin-orbit interaction in a 2D chaotic or diffusive quantum dot in the presence of exchange correlations. Spin-orbit scattering breaks spin rotation invariance, and in the crossover regime between different symmetries of the spin-orbit coupling, the problem has no closed solution. A conventional choice of a many-particle basis in a numerical diagonalization is the set of Slater determinants built from the single-particle eigenstates of the one-body Hamiltonian (including the spin-orbit terms). We develop a different approach based on the use of a good-spin many-particle basis that is composed of the eigenstates of the universal Hamiltonian in the absence of spin-orbit scattering. We introduce a complete labelling of this good-spin basis and use angular momentum algebra to calculate in closed form the matrix elements of the spin-orbit interaction in this basis. Spin properties, such as the ground-state spin distribution and the spin excitation function, are easily calculated in this basis.
arXiv comment14 pages, 3 figures
References in corpus (22)
- Random Matrix Theories in Quantum Physics: Common Concepts
- The Statistical Theory of Quantum Dots
- Quantum Effects in Coulomb Blockade
- Spectroscopy of discrete energy levels in ultrasmall metallic grains
- Spin-orbit coupling effects on quantum transport in lateral semiconductor dots
- Statistics of Coulomb Blockade Peak Spacings
- Spin-Orbit Coupling, Antilocalization, and Parallel Magnetic Fields in Quantum Dots
- Fluctuations of Conductance Peak Spacings in the Coulomb Blockade Regime: Role of Electron-Electron Interaction
- Statistics of conductance oscillations of a quantum dot in the Coulomb-blockade regime
- Signatures of spin pairing in a quantum dot in the Coulomb blockade regime
- Changing the Electronic Spectrum of a Quantum Dot by Adding Electrons
- Effects of spin and exchange interaction on the Coulomb-blockade peak statistics in quantum dots
- Ground-State Magnetization for Interacting Fermions in a Disordered Potential : Kinetic Energy, Exchange Interaction and Off-Diagonal Fluctuations
- Exchange and the Coulomb blockade: Peak height statistics in quantum dots
- Quantum Dots with Disorder and Interactions: A Solvable Large-g Limit
- Electron correlations in metal nanoparticles with spin-orbit scattering
- Disordered mesoscopic systems with interactions: induced two-body ensembles and the Hartree-Fock approach
- A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade
- Linear conductance in Coulomb-blockade quantum dots in the presence of interactions and spin
- Fluctuations of g-factors in metal nanoparticles: Effects of electron-electron interaction and spin-orbit scattering
- Interplay between the mesoscopic Stoner and Kondo effects in quantum dots
- Random Matrix Crossovers and Quantum Critical Crossovers for Interacting Electrons in Quantum Dots
Cited by in corpus (17)
- Spin-orbit coupling and anisotropic exchange in two-electron double quantum dots
- Spin and Charge Correlations in Quantum Dots: An Exact Solution
- Mesoscopic competition of superconductivity and ferromagnetism: conductance peak statistics in metallic grains
- Effect of a Zeeman field on the superconductor-ferromagnet transition in metallic grains
- An Exact Solution for Spin and Charge Correlations in Quantum Dots: The Effect of Level Fluctuations and Zeeman Splitting
- Mesoscopic Stoner instability in metallic nanoparticles revealed by shot noise
- Localization-Delocalization Transitions in Bosonic Random Matrix Ensembles
- Mesoscopic Stoner instability in open quantum dots: suppression of Coleman-Weinberg mechanism by electron tunneling
- Spin fluctuations in quantum dots
- Interacting Quantum Dot Coupled to a Kondo Spin: A Universal Hamiltonian Study
- The coexistence of superconductivity and ferromagnetism in nano-scale metallic grains
- Statistics of Spin Fluctuations in Quantum Dots with Ising Exchange
- Large spin-orbit effects in small quantum dots
- U(1) and SU(2) quantum dissipative systems: The Caldeira-Leggett vs. the Amegaokar-Eckern-Schön approaches
- The strong-coupling limit of a Kondo spin coupled to a mesoscopic quantum dot: effective Hamiltonian in the presence of exchange correlations
- Tunneling density of states in quantum dots with anisotropic exchange
- Mesoscopic interplay of superconductivity and ferromagnetism in ultra-small metallic grains