Influences of a topological defect on the spin Hall effect

Abstract

We study the influence of topological defects on the spin current as well as the spin Hall effect. We find that the nontrivial deformation of the space time due to topological defects can generate a spin-dependent current which then induces an imbalanced accumulation of spin states on the edges of the sample. The corresponding spin Hall conductivity has also been calculated for the topological defect of a cosmic string. Compared to the ordinary value, a correction which is linear with mass density of the cosmic string appears. Our approach to the dynamics of non relativistic spinor in the presence of a topological defect is based on the Foldy-Wouthuysen transformation. The spin current is obtained by using the extended Drude model which is independent of the scattering mechanism.

Effect of a cosmic string on spin dynamics

“…This indicates that the crystal symmetry and geometry give an observable change in the conductivity in the case of the asymmetric semiconductor. From (70) one can easily note that the dependence of the spin conductivity on cosmic string parameters is of the order of ζG c 2 , which exactly matches with the spin conductivity mentioned in [19]. The effect of the cosmic string parameters and the symmetry related parameters of the crystal on the defect induced Hall electric field and spin current in the case of noncubic parameters is clear from the presence of the η, ζ, and κ i terms.…”

“…From (1), we can write the deformed Dirac equation of an electron in the cosmic string background as [19] H ¼ βmc 2 þ cðα:πÞ þ qVðrÞ þα:Γ þ cðα:Ω:πÞ þ Γ 0 ;…”

“…Neglecting the rest energy term the Pauli-Schrödinger equation in the presence of a cosmic string can be readily obtained as [19] …”

Scattering and bound states for the Hulthén potential in a cosmic string background

“…As a result, the potential couples to the charge and a great number of physical phenomena can be studied through the Dirac equation (1). For instance, it is used to study the relativistic quantum motion of charged spin-0 and spin-1/2 particles in the presence of a uniform magnetic field and scalar potentials [5], to study the influence of topological defects on the spin current as well as the spin Hall effect [6] and to investigate the role of the cosmic string on spin current and Hall electric field [7]. On the other hand, contrary to the coupling (5), the scalar coupling (6) acts equally on particles and antiparticles.…”

Probing noncommutativities of phase space by using persistent charged current and its asymmetry

“…Nevertheless, noncommutative property can also appear in a real quantum system [6,7]. Because the noncommutative extension is fundamental, all the ordinary quantum physics are deformed with corrections parametrized by the constant θ μν , for instance, the breaking of rotational symmetry [8,9], distortion of energy levels of the atoms [10][11][12], corrections on the spin-orbital interactions [13][14][15][16][17][18][19][20], and the quantum speed of relativistic charged particles [21][22][23][24][25] and fluid dynamics [26,27]. Most importantly, the spatial component of the noncommutative parameter (θ μν ), θ ij , behaves like a permanent magnetic dipole moment and gives a contribution ϵ ijk θ ij B k to the energy of system.…”