Out-of-plane equilibrium spin current in a quasi-two-dimensional electron gas under in-plane magnetic field

Abstract

Equilibrium spin-current is calculated in a quasi-two-dimensional electron gas with finite thickness under in-plane magnetic field and in the presence of Rashba-and Dresselhaus spin-orbit interactions. The transverse confinement is modeled by means of a parabolic potential. An orbital effect of the in-plane magnetic field is shown to mix a transverse quantized spin-up state with nearestneighboring spin-down states. The out-off-plane component of the equilibrium spin current appears to be not zero in the presence of an in-plane magnetic field, provided at least two transverse-quantized levels are filled. In the absence of the magnetic field the obtained results coincide with the wellknown results, yielding cubic dependence of the equilibrium spin current on the spin-orbit coupling constants. The persistent spin-current vanishes in the absence of the magnetic field if Rashba-and Dresselhaus spin-orbit coefficients, α and β, are equal each other. In-plane magnetic field destroys this symmetry, and accumulates a finite spin-current as α → β. Magnetic field is shown to change strongly the equilibrium current of the in-plane spin components, and gives new contributions to the cubic-dependent on spin-orbit constants terms. These new terms depend linearly on the spin-orbit constants.

Majorana-like localized spin density without bound states in topologically trivial spin-orbit coupled nanowires

“…For example, for µ = 0 and in the regime ∆ Z E SO , one has J s z = −sgn(α) √ ∆ Z E SO /3π. Equilibrium spin currents have been predicted for other RSOC systems as well [58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73] and, in fact, they can be regarded to as the diamagnetic color currents associated to the non-abelian spin-orbit gauge fields [74]. However, its measurement in actual experiments has not been achieved thus far.…”

Magnetic field effects on a nanowire with inhomogeneous Rashba spin-orbit coupling: Spin properties at equilibrium

“…Secondly, as far as equilibrium properties are concerned, nanowires have been much less analyzed than 2D electron gases (2DEGs) with RSOC. In 2D, for instance, RSOC can lead to a background spin current flow even at equilibrium [31], a surprising effect that opened up an interesting conceptual debate about its observability, with various proposals by several groups [32][33][34][35][36][37][38][39][40][41][42][43][44][45]. In 1D systems, however, such effect is absent [46,47], and this has probably contributed to convey the impression that the equilibrium properties of Rashba nanowires are trivial.…”

Engineering the Electronic and Spintronic Properties of Graphene by Spin-Orbit Coupling and Periodic Vacancies

“…(i) S = 0: In the absence of magnetization, it is known that RSOC itself is sufficient to induce a spin current polarized in x direction and flowing in y direction, and another one that is polarized in y direction and flowing in x direction, as our numerical calculation also confirms [19]. Besides, a helical (spin chiral) edge spin current polarized in z is also produced, whose flowing direction is opposite between the two edges [20,21,22]. The origin of this helical edge spin current can be understood from the figure of the band structure, where we color the eigenstate according to the spin component of the wave function at the left edge (blue and green colors).…”

“…(1, 10), (2,11), (3,12), (7,4), (8,5), (9,6), Type − II : (13,42), (14,43), (15,44), (40,16), (41,17), (18,38), (19,39), (35,20), (36,21), (37,22), (23,32), (24,33), (25,34), (29,26), (30,27), (31,28).…”