Theory of tunneling conductance of graphene NIS junctions

We calculate the tunneling conductance of a graphene normal metal-insulator-superconductor (NIS) junction with a barrier of thickness $d$ and with an arbitrary voltage $V_0$ applied across the barrier region. We demonstrate that the tunneling conductance of such a NIS junction is an oscillatory function of both $d$ and $V_0$. We also show that the periodicity and amplitude of such oscillations deviate from their universal values in the thin barrier limit as obtained in earlier work [Phys. Rev. Lett. {\bf 97}, 217001 (2006)] and become a function of the applied voltage $V_0$. Our results reproduces the earlier results on tunneling conductance of such junctions in the thin [Phys. Rev. Lett. {\bf 97}, 217001 (2006)] and zero [Phys. Rev. Lett. {\bf 97}, 067007 (2006)] barrier limits as special limiting cases. We discuss experimental relevance of our results.Comment: Revised versio

Josephson effect in graphene SBS junctions

We study Josephson effect in graphene superconductor- barrier- superconductor junctions with short and wide barriers of thickness $d$ and width $L$, which can be created by applying a gate voltage $V_0$ across the barrier region. We show that Josephson current in such graphene junctions, in complete contrast to their conventional counterparts, is an oscillatory function of both the barrier width $d$ and the applied gate voltage $V_0$. We also demonstrate that in the thin barrier limit, where $V_0 \to \infty$ and $d \to 0$ keeping $V_0 d$ finite, such an oscillatory behavior can be understood in terms of transmission resonance of Dirac-Bogoliubov-de Gennes quasiparticles in superconducting graphene. We discuss experimental relevance of our work.Comment: 7 Pg., 6 Figs, extended version submitted to PR

Spin-Hall effect in triplet chiral superconductors and graphene

We study spin-Hall effects in time-reversal symmetry (TRS) broken systems such as triplet chiral superconductors and TRS preserved ones such as graphene. For chiral triplet superconductors, we show that the edge states carry a quantized spin-Hall current in response to an applied Zeeman magnetic field $B$ along the ${\bf d}$ vector \cite{leggett1}, whereas the edge spin-current for ${\bf B} \perp {\bf d}$ is screened by the condensate. We also derive the bulk spin-Hall current for chiral triplet superconductors for arbitrary relative orientation of ${\bf B}$ and ${\bf d}$ and discuss its relation with the edge spin-current. For TRS invariant system graphene, we show that the bulk effective action, unlike its TRS broken counterparts, does not support a SU(2) Hopf term but allows a crossed Hopf term in the presence of an external electromagnetic field, which yields a quantized bulk spin-Hall current in response to an electric field. We also present an analytical solution of the edge problem for armchair edges of graphene and contrast the properties of these edge states with their time reversal symmetry broken counterparts in chiral superconductors. We propose possible experiments to test our results.Comment: v2; minor changes, additional ref

Theory of tunneling conductance of graphene normal metal-insulator-superconductor junctions

We calculate the tunneling conductance of a graphene normal metal-insulator-superconductor (NIS) junction with a barrier of thickness d and with an arbitrary voltage $V_0$ applied across the barrier region. We demonstrate that the tunneling conductance of such a NIS junction is an oscillatory function of both d and $V_0$. We also show that the periodicity and amplitude of such oscillations deviate from their universal values in the thin barrier limit as obtained in an earlier work [S. Bhattacharjee and K. Sengupta, Phys. Rev. Lett. 97, 217001 (2006)] and become a function of the applied voltage $V_0$. Our results reproduce the earlier results on tunneling conductance of such junctions in the thin [S. Bhattacharjee and K. Sengupta, Phys. Rev. Lett. 97, 217001 (2006)] and zero [C. W. J. Beenakker, Phys. Rev. Lett. 97, 067007 (2006)] barrier limits as special limiting cases. We discuss the experimental relevance of our results