Variational study of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mn /></mml:math>quantum Hall ferromagnet in the presence of spin-orbit interaction

Schliemann, John; Egues, J. Carlos; Loss, Daniel

doi:10.1103/physrevb.67.085302

Cited by 68 publications

(54 citation statements)

References 46 publications

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“…Here, ε 0 is the band offset, δ = (1 − 1/2 gm * ) ω c , and g is the electron g-factor [49,50]. The upper and lower Rashba-split branches qualitatively correspond to the inner and outer Rashba 'cones', respectively.…”

Section: Ll Dispersion: Rashba Regimementioning

confidence: 99%

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Momentum-resolved STM studies of Rashba-split surface states on the topological semimetal Sb

Soumyanarayanan

Hoffman

2015

Journal of Electron Spectroscopy and Related Phenomena

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Topological materials host protected surface states with locked spin and momentum degrees of freedom. The helical Dirac character of the surface states, of tremendous scientific interest, stems from the interplay of the bulk band structure and surface Rashba spin-orbit interaction. The semimetal Sb offers a pristine platform to examine the Rashba origins of the Dirac-like topological surface states. Here we present an overview of our momentum-resolved scanning tunneling spectroscopy studies of Sb, over an extended (300 meV) energy range, revealing several features characteristic of the emergence of the Dirac-like surface states from a conventional Rashba-type parabolic dispersion. Our work provides a conceptual framework to create and investigate tunable Rashba states with topological properties.

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Section: Ll Dispersion: Rashba Regimementioning

confidence: 99%

“…the LLs, indexed by n, are first separated by the cyclotron energy, ω c , with ω c = eB/m * . An additional term, dependent on the Rashba parameter v 0 , further splits each LL (n > 0) according to [49][50][51]:…”

Section: Ll Dispersion: Rashba Regimementioning

confidence: 99%

Momentum-resolved STM studies of Rashba-split surface states on the topological semimetal Sb

Soumyanarayanan

Hoffman

2015

Journal of Electron Spectroscopy and Related Phenomena

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“…Similar systems have been studied before in the presence of Landau level quantization, using either variational (Hartree-Fock) methods 17 , second order perturbation 18,19 or by obtaining the energy spectrum in terms of perturbation series 20 . However, we are unaware of any analytical solution for both Rashba and Dresselhaus that goes beyond second order perturbation for multiple levels, i.e., not just treating the two lowest orbital levels as in Ref.…”

Section: Introductionmentioning

confidence: 99%

Energy spectra for quantum wires and two-dimensional electron gases in magnetic fields with Rashba and Dresselhaus spin-orbit interactions

2010

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We introduce an analytical approximation scheme to diagonalize parabolically confined two dimensional electron systems with both the Rashba and Dresselhaus spin-orbit interactions. The starting point of our perturbative expansion is a zeroth-order Hamiltonian for an electron confined in a quantum wire with an effective spin-orbit induced magnetic field along the wire, obtained by properly rotating the usual spin-orbit Hamiltonian. We find that the spin-orbit-related transverse coupling terms can be recast into two parts W and V , which couple crossing and non-crossing adjacent transverse modes, respectively. Interestingly, the zeroth-order Hamiltonian together with W can be solved exactly, as it maps onto the Jaynes-Cummings model of quantum optics. We treat the V coupling by performing a Schrieffer-Wolff transformation. This allows us to obtain an effective Hamiltonian to third order in the coupling strength kRℓ of V , which can be straightforwardly diagonalized via an additional unitary transformation. We also apply our approach to other types of effective parabolic confinement, e.g., 2D electrons in a perpendicular magnetic field. To demonstrate the usefulness of our approximate eigensolutions, we obtain analytical expressions for the n th Landau-level gn-factors in the presence of both Rashba and Dresselhaus couplings. For small values of the bulk g-factors, we find that spin-orbit effects cancel out entirely for particular values of the spin-orbit couplings. By solving simple transcendental equations we also obtain the band minima of a Rashba-coupled quantum wire as a function of an external magnetic field. These can be used to describe Shubnikov-de Haas oscillations. This procedure makes it easier to extract the strength of the spin-orbit interaction in these systems via proper fitting of the data.

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“…The specific laser setup used in Ref. [2] -that gives rise to an "Abelian" spin-orbit coupling (sometimes referred to as the "persistent-spin-helix symmetry point," [15][16][17][18][19][20][21] where the Rashba and Dresselhaus couplings are equal to each other) -was later analyzed in detail by Ho and collaborators in Ref. [22].…”

Section: Introductionmentioning

confidence: 99%

Vortices in spin-orbit-coupled Bose-Einstein condensates

et al. 2011

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Realistic methods to create vortices in spin-orbit-coupled Bose-Einstein condensates are discussed. It is shown that, contrary to common intuition, rotation of the trap containing a spin-orbit condensate does not lead to an equilibrium state with static vortex structures, but gives rise instead to non-equilibrium behavior described by an intrinsically time-dependent Hamiltonian. We propose here the following alternative methods to induce thermodynamically stable static vortex configurations: (1) to rotate both the lasers and the anisotropic trap; and (2) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. Effective Hamiltonians for spin-orbit condensates under such perturbations are derived for most currently known realistic laser schemes that induce synthetic spin-orbit couplings. The Gross-Pitaevskii equation is solved for several experimentally relevant regimes. The new interesting effects include spatial separation of left-and right-moving spin-orbit condensates, the appearance of unusual vortex arrangements, and parity effects in vortex nucleation where the topological excitations are predicted to appear in pairs. All these phenomena are shown to be highly non-universal and depend strongly on a specific laser scheme and system parameters.

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Variational study of theν=1quantum Hall ferromagnet in the presence of spin-orbit interaction

Cited by 68 publications

References 46 publications

Momentum-resolved STM studies of Rashba-split surface states on the topological semimetal Sb

Momentum-resolved STM studies of Rashba-split surface states on the topological semimetal Sb

Energy spectra for quantum wires and two-dimensional electron gases in magnetic fields with Rashba and Dresselhaus spin-orbit interactions

Vortices in spin-orbit-coupled Bose-Einstein condensates

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