Nonlinear Schr\"odinger Equation for Superconductors

Using the Hartree-Fock-Bogoliubov factorization of the density matrix and the Born-Oppenheimer approximation we show that the motion of the condensate satisfies a nonlinear Schr\"odinger equation in the zero temperature limit. The Galilean invariance of the equation is explicitly manifested. {}From this equation some general properties of a superconductor, such as Josephson effects, the Magnus force, and the Bogoliubov-Anderson mode can be obtained readily.Comment: Latex, 12 page

Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals

We derive a multi-band formulation of the orbital magnetization in a normal periodic insulator (i.e., one in which the Chern invariant, or in 2d the Chern number, vanishes). Following the approach used recently to develop the single-band formalism [T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta, Phys. Rev. Lett. {\bf 95}, 137205 (2005)], we work in the Wannier representation and find that the magnetization is comprised of two contributions, an obvious one associated with the internal circulation of bulk-like Wannier functions in the interior and an unexpected one arising from net currents carried by Wannier functions near the surface. Unlike the single-band case, where each of these contributions is separately gauge-invariant, in the multi-band formulation only the \emph{sum} of both terms is gauge-invariant. Our final expression for the orbital magnetization can be rewritten as a bulk property in terms of Bloch functions, making it simple to implement in modern code packages. The reciprocal-space expression is evaluated for 2d model systems and the results are verified by comparing to the magnetization computed for finite samples cut from the bulk. Finally, while our formal proof is limited to normal insulators, we also present a heuristic extension to Chern insulators (having nonzero Chern invariant) and to metals. The validity of this extension is again tested by comparing to the magnetization of finite samples cut from the bulk for 2d model systems. We find excellent agreement, thus providing strong empirical evidence in favor of the validity of the heuristic formula.Comment: 14 pages, 8 figures. Fixed a typo in appendix

Transverse force on a quantized vortex in a superconductor

The total transverse force acting on a quantized vortex in a type-II superconductor determines the Hall response in the mixed state, yet a consensus as to its correct form is still lacking. In this paper we present an essentially exact expression for this force, valid in the superclean limit, which was obtained by generalizing the recent work by Thouless, Ao, and Niu [D. J. Thouless, P. Ao, and Q. Niu, Phys. Rev. Lett. 76, 3758 (1996)] on the Magnus force in a neutral superfluid. We find the transverse force per unit length to be $f = \rho K \times V$, where $\rho = \rho_{n} + \rho_{s}$ is the sum of the mass densities of the normal and superconducting components, $K$ is a vector parallel to the line vortex with a magnitude equal to the quantized circulation, and $V$ is the vortex velocity.Comment: 4 pages, Revtex, 1 figur

Implications of adiabatic phases for a vortex in a superconductor film

Based on ideas of off-diagonal long range order and two-fluid model, we demonstrate that adiabatic phases for a slow motion of a vortex in a superconductor film give rise naturally to the Magnus force at finite temperatures.Comment: 6 pages, Late

Width-amplitude relation of Bernstein-Greene-Kruskal solitary waves

Inequality width-amplitude relations for three-dimensional Bernstein-Greene-Kruskal solitary waves are derived for magnetized plasmas. Criteria for neglecting effects of nonzero cyclotron radius are obtained. We emphasize that the form of the solitary potential is not tightly constrained, and the amplitude and widths of the potential are constrained by inequalities. The existence of a continuous range of allowed sizes and shapes for these waves makes them easily accessible. We propose that these solitary waves can be spontaneously generated in turbulence or thermal fluctuations. We expect that the high excitation probability of these waves should alter the bulk properties of the plasma medium such as electrical resistivity and thermal conductivity.Comment: 5 pages, 2 figure

Electric polarization in a Chern insulator

We extend the Berry-phase concept of polarization to insulators having a non-zero value of the Chern invariant. The generalization to such Chern insulators requires special care because of the partial occupation of chiral edge states. We show how the integrated bulk current arising from an adiabatic evolution can be related to a difference of bulk polarizations. We also show how the surface charge can be related to the bulk polarization, but only with a knowledge of the wavevector at which the occupancy of the edge state is discontinuous. Furthermore we present numerical calculations on a model Hamiltonian to provide additional support for our analytic arguments.Comment: 4 pages, 3 figures (small corrections

Rectified voltage induced by a microwave field in a confined two-dimensional electron gas with a mesoscopic static vortex

We investigate the effect of a microwave field on a confined two dimensional electron gas which contains an insulating region comparable to the Fermi wavelength. The insulating region causes the electron wave function to vanish in that region. We describe the insulating region as a static vortex. The vortex carries a flux which is determined by vanishing of the charge density of the electronic fluid due to the insulating region. The sign of the vorticity for a hole is opposite to the vorticity for adding additional electrons. The vorticity gives rise to non-commuting kinetic momenta. The two dimensional electron gas is described as fluid with a density which obeys the Fermi-Dirac statistics. The presence of the confinement potential gives rise to vanishing kinetic momenta in the vicinity of the classical turning points. As a result, the Cartesian coordinate do not commute and gives rise to a Hall current which in the presence of a modified Fermi-Surface caused by the microwave field results in a rectified voltage. Using a Bosonized formulation of the two dimensional gas in the presence of insulating regions allows us to compute the rectified current. The proposed theory may explain the experimental results recently reported by J. Zhang et al.Comment: 14 pages, 2 figure

Winding Numbers, Complex Currents, and Non-Hermitian Localization

The nature of extended states in disordered tight binding models with a constant imaginary vector potential is explored. Such models, relevant to vortex physics in superconductors and to population biology, exhibit a delocalization transition and a band of extended states even for a one dimensional ring. Using an analysis of eigenvalue trajectories in the complex plane, we demonstrate that each delocalized state is characterized by an (integer) winding number, and evaluate the associated complex current. Winding numbers in higher dimensions are also discussed.Comment: 4 pages, 2 figure