Majorana Fermion Induced Non-local Current Correlations in Spin-orbit Coupled Superconducting Wires

Recent observation of zero bias conductance peaks in semiconductor wire/superconductor heterostructures has generated great interest, and there is a hot debate on whether the observation is associated with Majorana fermions (MFs). Here we study the local and crossed Andreev reflections in a junction of two normal leads and a sandwiched superconductor-semiconductor wire with two spatially separated but strongly coupled MF end states. The conductance and Fano factors of such a device are sharply different from the topologically trivial case even in the presence of disorder, and can hence be used to identify MFs unambiguously.Comment: 7+ pages, 10 figure

Giant mesoscopic spin Hall effect on surface of topological insulator

We study mesoscopic spin Hall effect on the surface of topological insulator with a step-function potential. The giant spin polarization induced by a transverse electric current is derived analytically by using McMillan method in the ballistic transport limit, which oscillates across the potential boundary with no confinement from the potential barrier due to the Klein paradox, and should be observable in spin resolved scanning tunneling microscope.Comment: 5 pages, 3 figure

Negative entanglement measure for bipartite separable mixed states

We define a negative entanglement measure for separable states which shows that how much entanglement one should compensate the unentangled state at least for changing it into an entangled state. For two-qubit systems and some special classes of states in higher-dimensional systems, the explicit formula and the lower bounds for the negative entanglement measure have been presented, and it always vanishes for bipartite separable pure states. The negative entanglement measure can be used as a useful quantity to describe the entanglement dynamics and the quantum phase transition. In the transverse Ising model, the first derivatives of negative entanglement measure diverge on approaching the critical value of the quantum phase transition, although these two-site reduced density matrices have no entanglement at all. In the 1D Bose-Hubbard model, the NEM as a function of $t/U$ changes from zero to negative on approaching the critical point of quantum phase transition.Comment: 6 pages, 3 figure

Half Metallic Bilayer Graphene

Charge neutral bilayer graphene has a gapped ground state as transport experiments demonstrate. One of the plausible such ground states is layered antiferromagnetic spin density wave (LAF) state, where the spins in top and bottom layers have same magnitude with opposite directions. We propose that lightly charged bilayer graphene in an electric field perpendicular to the graphene plane may be a half metal as a consequence of the inversion and particle-hole symmetry broken in the LAF state. We show this explicitly by using a mean field theory on a 2-layer Hubbard model for the bilayer graphene.Comment: 4+ pages, 4 figure