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We study the magnetoelectric coupling at the surface of a topological insulator. We are in particular interested in the surface current induced by a static Zeeman/exchange field. This surface current can be related to the orbital magnetization of the system. For an insulator with zero Chern number, the orbital magnetization is independent of the details at the boundary. With the appearance of surface states in the topological insulator, it is not immediately obvious if the response is not affected by the conditions at the surface. We investigate this question using exact diagonalization to a lattice model. By applying a time-reversal symmetry-breaking term near the boundary, no matter if the surface states are gapped out, we still find no change in the surface current. This arises from cancelations between Pauli and Van-Vleck contributions between surface and bulk scattering states. We also show that the surface current response is independent of the chemical potential when it is within the bulk gap. Our results are consistent with the claim that orbital magnetization is a bulk property.

Starting from a model Hamiltonian for the normal state of the topological insulator Bi2Se3, we construct a pseudospin basis for the single-particle wavefunctions. Considering weak superconducting pairing near the Fermi surface, we express the recently proposed superconducting order parameters for Cu doped Bi2Se3 in this basis. For the odd parity states, the d-vectors specifying the order parameter can have unusual momentum dependence for certain parameter regimes. Some peculiar results in the literature for surface states are discussed in light of the forms of these d(k)'s. Properties of the even parity states are also illuminated using this pseudospin basis. Results from this single-band description are compared with those from the full two-band model., Comment: 13 pages,1 figure

We study the finite-size and boundary effects on a p-wave superconductor in a mesoscopic rectangular sample using Ginzburg-Landau (GL) and quasi-classical (QC) Green's function theory. Except for a square sample with parameters far away from the isotropic weak-coupling limit, the ground state near the critical temperature always prefers a time-reversal symmetric state, where the order parameter can be represented by a real vector. For large aspect ratio, this vector is parallel to the long side of the rectangle. Within a critical aspect ratio, it has instead a vortex-like structure, vanishing at the sample center., Comment: Revised version published in Physical Review B

We study the finite-size and boundary effects on a time-reversal-symmetry breaking p-wave superconducting state in a mesoscopic disc geometry using Ginzburg-Landau theory. We show that, for a large parameter range, the system exhibits multiple phase transitions. The superconducting transition from the normal state can also be reentrant as a function of external magnetic field., Comment: Revised version published in Physical Review B

We discuss the topology of the wavefunctions of two-dimensional time-reversal symmetric superconductors. We consider (a) the planar state, (b) a system with broken up-down reflection symmetry, and (c) a system with general spin-orbit interaction. We show explicitly how the relative sign of the order parameter on the two Fermi surfaces affects this topology, and clarify the meaning of the $Z_2$ classification for these topological states., Comment: only the Introduction has been modified from v1

We study current fluctuations in a phase coherent Y-shaped conductor connected to external leads and voltage probes. The voltage probes are taken to have finite impedances and thus can cause voltage fluctuations in the circuit. Applying the Keldysh formulation and a saddle point approximation appropriate for slow fluctuations, we examine at zero temperature the feedback effects on the current fluctuations due to the fluctuating voltages. We consider mesoscopic Y-shaped conductors made of tunnel junctions and of diffusive wires. Unlike two-terminal conductors, we find that for the Y-shaped conductors the current moments in the presence of external impedances cannot be obtained from simple rescaling of the bare moments already in the second moments. As a direct consequence, we find that the cross correlation between the output terminals can become positive due to the impedances in the circuit. We provide formulas for the range of parameters that can cause positive cross correlations., Comment: Figures 2(b)(c) left out due to file size constraints (which, however, can be requested from authors). Submitted to Phys. Rev. B

We show that, for a quantum point contact between two superconductors of different gap magnitudes, Andreev bound states do not exist for certain phase differences and gap ratios. Continuum states may dominate the transport, and the supercurrent noise is qualitatively different from the case of equal gaps., Comment: to appear in PRB

In this paper I study the energy resolved supercurrent of a junction consisting of a dirty normal metal between two superconductors. I also consider a cross geometry with two additional arms connecting the above mentioned junction with two normal reservoirs at equal and opposite voltages. The dependence of the supercurrent between the two superconductors on the applied voltages is studied., Comment: revtex, 7 pages, 8 figures. accepted by Phys. Rev. B