Pauli equation for a charged spin particle on a curved surface in an electric and magnetic field

Abstract

We derive the Pauli equation for a charged spin particle confined to move on a spatially curved surface S in an electromagnetic field. Using the thin-layer quantization scheme to constrain the particle on S, and in the transformed spinor representations, we obtain the well-known geometric potential Vg and the presence of e −iϕ , which can generate additive spin connection geometric potentials by the curvilinear coordinate derivatives, and we find that the two fundamental evidences in the literature [Giulio Ferrari and Giampaolo Cuoghi, Phys. Rev. Lett. 100, 230403 (2008).] are still valid in the present system without source current perpendicular to S. Finally, we apply the surface Pauli equation to spherical, cylindrical, and toroidal surfaces, in which we obtain expectantly the geometric potentials and new spin connection geometric potentials, and find that only the normal Pauli matrix appears in these equations.

Pseudo-magnetic-field and effective spin-orbit interaction for a spin-1/2 particle confined to a curved surface

“…. In other words, the presence of the spin degree of freedom can influence the geometric effects of the curved surface [33]. Besides, the termh 2R 8m has no contribution to the scalar potential as Ricci scalar vanishes in the thin-layer procedure.…”

“…In the language of quantum field theory, it can also be viewed as a non-Abelian gauge field generated by local Lorentz transformations [31]. In the 2D curved space, the motion of a fermion should embody the effect of this gauge field [32].Several studies have considered the contribution of the spin connection to the dynamics on curved surfaces [33][34][35], however, the explicit effective SOI Hamiltonian from curvature has not be given. In addition, it has been found that the SOI from electric fields can also be reformulated in terms of non-Abelian gauge fields [36][37][38][39].…”

Position-dependent mass effects in the electronic transport of two-dimensional quantum systems: Applications to nanotubes

“…Geometry can also induce a reminiscent of the Hall effect [5]. Related important investigations can also be found in the literature, for instance: the quantum Hall effect near conical singularities [6] and investigations taking into account the Pauli equation for a charged spin particle on a curved surface with externally applied fields [7,8]. Recent developments can also be found in [9,10,11,12,13,14,15,16,17].…”

A Curved Noninteracting 2D Electron Gas with Anisotropic Mass

“…An application in this case can be viewed in [9], where important features concerned to the quantum Hall states on surfaces with conical singularities has been presented. The version for Pauli equation for a charged spin particle on a curved surface in an electric and magnetic field has been addressed in [10]. An application which followed this reference can be viewed in [11].…”