Abstract

For a free particle that moves non-relativistically on a curved surface, there are curvature-induced quantum potentials that significantly influence the surface quantum states. However, the experimental results in topological insulators, whether curved or not, indicate no evidence of such a potential for the relativistic particles constrained on the curved surface. Within the framework of Dirac quantization scheme, we demonstrate a general result that for a Dirac fermion on a two-dimensional curved surface of revolution, no curvature-induced quantum potential is permissible.

Highlights

  • The discovery of topological insulators has initialized a new era of condensed matter physics [1–7]

  • Within the framework of Dirac quantization scheme, we demonstrate a general result that for a Dirac fermion on a two-dimensional curved surface of revolution, no curvatureinduced quantum potential is permissible

  • Our principle is the conventional Dirac quantization scheme in which Fundamental quantum conditions (FQCs) [xi, xj] = 0, [xi, pj] = i δij, and [pi, pj] = 0 suffice, which are defined by the commutation relations between positions xi and momenta pi (i, j, k, l = 1, 2, 3, ..., N ) where N denotes the number of dimensions of the flat space in which the particle moves [40]

Read more

Summary

INTRODUCTION

The discovery of topological insulators has initialized a new era of condensed matter physics [1–7]. By the surface quantum states of the topological insulators, we mean the two-dimensional states for relativistic spin 1/2 particles, usually with zero mass, and is is the Dirac fermions as commonly called. For the constrained particle that moves relativistically, whether there is curvature-induced quantum potential remains an open problem. Let us first see what the usual Fundamental quantum conditions (FQCs) are for a particle that moves in flat space RN In this simplest case, our principle is the conventional Dirac quantization scheme in which FQCs [xi, xj] = 0, [xi, pj] = i δij, and [pi, pj] = 0 suffice, which are defined by the commutation relations between positions xi and momenta pi (i, j, k, l = 1, 2, 3, ..., N ) where N denotes the number of dimensions of the flat space in which the particle moves [40].

A CURVED SURFACE OF REVOLUTION
DISCUSSIONS AND CONCLUSIONS
Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.