Theory for electric dipole superconductivity with an application for bilayer excitons

Exciton superfluid is a macroscopic quantum phenomenon in which large quantities of excitons undergo the Bose-Einstein condensation. Recently, exciton superfluid has been widely studied in various bilayer systems. However, experimental measurements only provide indirect evidence for the existence of exciton superfluid. In this article, by viewing the exciton in a bilayer system as an electric dipole, we provide a general theory for the electric dipole superconductivity, and derive the London-type and Ginzburg-Landau-type equations for the electric dipole superconductors. By using these equations, we discover the Meissner-type effect and the electric dipole current Josephson effect. These effects can provide direct evidence for the formation of the exciton superfluid state in bilayer systems and pave new ways to drive an electric dipole current.Comment: 10 pages, 5 figures, 1 Supplementary Informatio

Bogoliubov Hamiltonian as Derivative of Dirac Hamiltonian via Braid Relation

In this paper we discuss a new type of 4-dimensional representation of the braid group. The matrices of braid operations are constructed by q-deformation of Hamiltonians. One is the Dirac Hamiltonian for free electron with mass m, the other, which we find, is related to the Bogoliubov Hamiltonian for quasiparticles in $^3$He-B with the same free energy and mass being m/2. In the process, we choose the free q-deformation parameter as a special value in order to be consistent with the anyon description for fractional quantum Hall effect with $\nu = 1/2$.Comment: 3 pages, 5 figure

Ginzburg-Landau-type theory of non-polarized spin superconductivity

Since the concept of spin superconductor was proposed, all the related studies concentrate on spin-polarized case. Here, we generalize the study to spin-non-polarized case. The free energy of non-polarized spin superconductor is obtained, and the Ginzburg-Landau-type equations are derived by using the variational method. These Ginzburg-Landau-type equations can be reduced to the spin-polarized case when the spin direction is fixed. Moreover, the expressions of super linear and angular spin currents inside the superconductor are derived. We demonstrate that the electric field induced by super spin current is equal to the one induced by equivalent charge obtained from the second Ginzburg-Landau-type equation, which shows self-consistency of our theory. By applying these Ginzburg-Landau-type equations, the effect of electric field on the superconductor is also studied. These results will help us get a better understanding of the spin superconductor and the related topics such as Bose-Einstein condensate of magnons and spin superfluidity.Comment: 9 pages, 5 figure