Mesoscopic rings with Spin-Orbit interactions

Abstract

A didactic description of charge and spin equilibrium currents on mesoscopic rings in the presence of Spin-Orbit interaction is presented. Emphasis is made on the non trivial construction of the correct Hamiltonian in polar coordinates, the calculation of eigenvalues and eigenfunctions and the symmetries of the ground state properties. Spin currents are derived following an intuitive definition and then a more thorough derivation is built upon the canonical Lagrangian formulation that emphasizes the SU(2) gauge structure of the transport problem of spin 1/2 fermions in spin-orbit active media. The quantization conditions that follow from the constraint of single-valued Pauli spinors are also discussed. The targeted students are those of a graduate Condensed Matter Physics course.

References in corpus (14)

• Aharonov-Bohm effect and broken valley-degeneracy in graphene rings
• Persistent current in ballistic mesoscopic rings with Rashba spin-orbit coupling
• Quantum rings as electron spin beam splitters
• Non-Abelian gauge field theory of the spin-orbit interaction and a perfect spin filter
• Proposal for a Mesoscopic Optical Berry-Phase Interferometer
• Pumping in a mesoscopic ring with Ahronov-Casher effect
• Magnetoconductance properties of rectangular arrays of spintronic quantum rings
• Quantum rings with time dependent spin-orbit coupling: Rabi oscillations, spintronic Schrodinger-cat states, and conductance properties
• Gauge symmetry breaking and topological quantization for the Pauli Hamiltonian
• Quantum Rings with Rashba spin orbit coupling: a path integral approach
• Orbital magnetic phase and pure persistent spin current in spin-orbit coupling mesoscopic rings
• Sagnac Rotational Phase Shifts in a Mesoscopic Electron Interferometer with Spin-Orbit Interactions
• Semiconductor Spintronics: Progress and Challenges
• Gauge field theory approach to spin transport in a 2D electron gas

Cited by in corpus (24)

• Continuum model for chiral induced spin selectivity in helical molecules
• Bound states and persistent currents in topological insulator rings
• Persistent charge and spin currents in the long wavelength regime for graphene rings
• Generation of geometrical phases and persistent spin currents in 1-dimensional rings by Lorentz-violating terms
• Light-induced spin polarizations in quantum rings
• Weak (anti)localization in tubular semiconductor nanowires with spin-orbit coupling
• Classical Yang-Mills theory in condensed matter physics
• Quantum oscillation and wave packet revival in conical graphene structure
• Thermodynamics of a quantum ring modified by Lorentz violation
• Magnetic field effects on a nanowire with inhomogeneous Rashba spin-orbit coupling: Spin properties at equilibrium
• Majorana-like localized spin density without bound states in topologically trivial spin-orbit coupled nanowires
• Persistent spin textures and currents in wurtzite nanowire-based quantum structures
• Analytical solution of narrow quantum rings with general Rashba and Dresselhaus spin-orbit couplings
• Topological insulator ring with magnetic impurities
• Rashba spin-orbit interaction enhanced by graphene in-plane deformations
• Charge and spin polarized currents in mesoscopic rings with Rashba spin-orbit interactions coupled to an electron reservoir
• Effect of magnetic field on the electronic properties of an $\alpha$-$T_3$ ring
• Achiral dipoles on a ferromagnet can affect its magnetization direction
• Spin current generation and control in carbon nanotubes by combining rotation and magnetic field
• Exact unitary transformation for Rashba rings in magnetic and electric fields
• Pure Gauge Spin-Orbit Couplings
• Bound state and persistent currents in the presence of torsion and Rashba spin-orbit coupling
• Spin relaxation in Rashba rings
• Spin-orbit coupled transport in a curved quantum wire