Some Consequences Of Special Relativity In Condensed Matter Physics

The upper critical field far exceeding the Pauli limit in superconductors and the quantum spin Hall effect in topological insulators,which are related to the relativistic effects of electron spin,originating from Dirac equation,are the hot topics in condensed matter physics.However,these materials that show novel physics phenomenon usually have the character an anisotropic effective mass.Therefore,the influence of strongly anisotropic structure cannot be ignored.As a useful attempt,the paper studies the related phenomena from the anisotropic Dirac equation.Firstly,we extend the Dirac equation in vacuum to that of an electron or hole in an orthorhombically anisotropic system,which satisfies the covariance of Lorenz transformation.The appropriate Foldy-Wouthuysen transformations are extended to expand the Hamiltonian about the non-relativistic limit to fourth order in the inverse of the particle’s Einstein rest energy,and accurate expressions for the Zeeman energy,Thomas term(revealing the origin of spin-orbit coupling effect)are provided.The Zeeman interaction is found to depend strongly upon the effective mass anisotropy,vanishing for one-dimensional propagation,and for twodimensional.conduction,only the normal component of its spin interacts with external electric and magnetic fields.Secondly,we study self-consistently the upper critical field of s-wave,dx2-y2-wave with orthorhombically anisotropic electronic effective masses and Zeeman energy,based on the Schrodinger equation got from the anisotropic Dirac equation.The upper critical field for s pairing symmetry is largest in the direction of the lowest effective mass.However,for dx2-y2-wave superconductors with an isotropic planar effective mass,the in-plane upper critical field exhibits a four-fold azimuthal pattern,the maxima of which are along the crystal axes just below the transition temperature but rotate by π/4 about the z axis as the temperature is lowered to 0.Similary,the upper critical field in plane with weak planar effective mass anisotropy,exhibits a two-fold pattern just below the critical temperature,the pattern of which also rotates by π/4 as the temperature is lowered to 0.Finally,we study the often-neglected effects of the magnetic vector potential in Thomas term with an electron or hole travelling in a Corbino disk normally surrounding a solenoid.In the disk,an applied radial electric field and an azimuthal magnetic vector potential generated by the central solenoid combine to generate a quantized angular spin current in the Corbino disk.This is a new way to generate quantum spin current in materials and like the quantum spin Hall effect.