Transport properties of graphene - superconductor junction has been studied extensively to understand the interplay of the relativistic Dirac quasiparticles and superconductivity. Though shot noise measurements in graphene has been performed to reali
ze many theoretical predictions, both at zero magnetic field as well as quantum Hall (QH) regime, its junction with superconductor remain unexplored. Here, we have carried out the shot noise measurements in an edge contacted bilayer graphene - Niobium superconductor junction at zero magnetic field as well as QH regime. At the Dirac point we have observed a Fano factor ~ 1/3 above the superconducting gap and a transition to an enhanced Fano factor ~ 0.5 below the superconducting gap. By changing the carrier density we have found a continuous reduction of Fano factor for both types of carriers, however the enhancement of Fano factor within the superconducting gap by a factor of ~ 1.5 is always preserved. The enhancement of shot noise is also observed in the QH regime, where the current is carried by the edge state, below the critical magnetic field and within the superconducting gap. These observations clearly demonstrate the enhanced charge transport at the graphene-superconductor interface.
Each end of a Kitaev chain in topological phase hosts a Majorana fermion. Zero bias conductance peak is an evidence of Majorana fermion when the two Majorana fermions are decoupled. These two Majorana fermions are separated in space and this nonlocal
aspect can be probed when the two are coupled. Crossed Andreev reflection is the evidence of the nonlocality of Majorana fermions. Nonlocality of Majorana fermions has been proposed to be probed by noise measurements since simple conductance measurements cannot probe it due to the almost cancellation of currents from electron tunneling and crossed Andreev reflection. Kitaev ladders on the other hand host subgap Andreev states which can be used to control the relative currents due to crossed Andreev reflection and electron tunneling. We propose to employ Kitaev ladder in series with Kitaev chain and show that the transconductance in this setup can be used as a probe of nonlocality of Majorana fermions by enhancing crossed Andreev reflection over electron tunneling.
A quantum dot weakly coupled to two normal metal leads exhibits resonant transmission when one of the dot energy levels lies within the applied bias window. But when the quantum dot is sidecoupled to the transport channel, transmission in the channel
is suppressed when a dot energy lies in the bias window. A steady current can also be driven in a transport channel by connecting it to superconducting reservoirs and applying a Josephson phase difference instead of a voltage bias. An interesting question is to investigate the transport across quantum dot connected to two superconductors maintained at a superconducting phase difference. To incorporate the geometry where quantum dot is sidecoupled, we consider a quantum dot with two sites connected to the superconductors in two geometrical configurations: (A) the one where both the sites are in the transport channel and (B) the other where only one site is in the transport channel and the second site sidecoupled. We find that both the configurations show resonant transmission for Josephson current and give qualitatively same result when the onsite energies of the two sites in the dot are equal. The two configurations exhibit distinct Josephson current characteristics when the onsite energies of the two sites are equal in magnitude and opposite in sign. We understand the obtained results. The systems studied are within the reach of current experiments.
Andreev reflection in graphene is special since it can be of two types- retro or specular. Specular Andreev reflection (SAR) dominates when the position of the Fermi energy in graphene is comparable to or smaller than the superconducting gap. Bilayer
graphene (BLG) is an ideal candidate to observe the crossover from retro to specular since the Fermi energy broadening near the Dirac point is much weaker compared to monolayer graphene. Recently, the observation of signatures of SAR in BLG have been reported experimentally by looking at the enhancement of conductance at finite bias near the Dirac point. However, the signatures were not very pronounced possibly due to the participation of normal quasi-particles at bias energies close to the superconducting gap. Here, we propose a scheme to observe the features of enhanced SAR even at zero bias at a normal metal (NM)-superconductor (SC) junction on BLG. Our scheme involves applying a Zeeman field to the NM side of the NM-SC junction on BLG (making the NM ferromagnetic), which energetically separates the Dirac points for up-spin and down-spin. We calculate the conductance as a function of chemical potential and bias within the superconducting gap and show that well-defined regions of specular- and retro-type Andreev reflection exist. We compare the results with and without superconductivity. We also investigate the possibility of the formation of a p-n junction at the interface between the NM and SC due to a work function mismatch.
Magnetic tunnel junctions comprising of an insulator sandwiched between two ferromagnetic films are the simplest spintronic devices. Theoretically, these can be modeled by a metallic Hamiltonian in both the lattice and the continuum with an addition
of Zeeman field. We calculate conductance at arbitrary orientations of the easy axes of the two ferromagnets. When mapped, the lattice and the continuum models show a discrepancy in conductance in the limit of a large Zeeman field. We resolve the discrepancy by modeling the continuum theory in an appropriate way.
Crossed Andreev reflection (cAR) is a scattering process that happens in a quantum transport set-up consisting of two normal metals (NM) attached to a superconductor (SC), where an electron incident from one NM results in a hole emerging in the other
. Typically, an electron tunnelling through the superconductor from one NM to the other (ET) competes with cAR and masks the signature of cAR in the conductance spectrum. We propose a novel scheme to enhance cAR, in which SC part of the NM-SC-NM is side-coupled to another SC having a different SC phase to form a Josephson junction in the transverse direction. At strong enough coupling and adequate phase difference, one can smoothly traverse between highly ET-dominant to highly cAR-dominant transport regimes by tuning chemical potential, due to the appearance of subgap Andreev states that are extended in the longitudinal direction. We also discuss connections to realistic systems.
Though the Fermi surface of surface states of a 3D topological insulator (TI) has zero magnetization, an arbitrary segment of the full Fermi surface has a unique magnetic moment consistent with the type of spin-momentum locking in hand. We propose a
three-terminal set up, which directly couples to the magnetization of a chosen segment of a Fermi surface hence leading to a finite tunnel magnetoresistance (TMR) response of the nonmagnetic TI surface states, when coupled to spin polarized STM probe. This multiterminal TMR not only provides a unique signature of spin-momentum locking for a pristine TI but also provides a direct measure of momentum resolved out of plane polarization of hexagonally warped Fermi surfaces relevant for $Bi_2Te_3$, which could be as comprehensive as spin-resolved ARPES. Implication of this unconventional TMR is also discussed in the broader context of 2D spin-orbit (SO) materials.
We use the bulk Hamiltonian for a three-dimensional topological insulator such as $rm Bi_2 Se_3$ to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the surface Ham
iltonians (which are derived from the bulk Hamiltonian) and numerical methods based on a lattice discretization of the bulk Hamiltonian. We find that the application of a potential along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering across the edge is studied as a function of the edge potential. We show that a magnetic field in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states.
We study transport across a line junction lying between two orthogonal topological insulator surfaces and a superconductor which can have either s-wave (spin-singlet) or p-wave (spin-triplet) pairing symmetry. We present a formalism for studying the
effect of a general time-reversal invariant barrier at the junction and show that such a barrier can be completely described by three arbitrary parameters. We compute the charge and the spin conductance across such a junction and study their behaviors as a function of the bias voltage applied across the junction and the three parameters used to characterize the barrier. We find that the presence of topological insulators and a superconductor leads to both Dirac and Schrodinger-like features in charge and spin conductances. We discuss the effect of bound states on the superconducting side of the barrier on the conductance; in particular, we show that for triplet p-wave superconductors such a junction may be used to determine the spin state of its Cooper pairs. Our study reveals that there is a non-zero spin conductance for some particular spin states of the triplet Cooper pairs; this is an effect of the topological insulators which break the spin rotation symmetry. Finally, we find an unusual satellite peak (in addition to the usual zero bias peak) in the spin conductance for p-wave symmetry of the superconductor order parameter.
We study electronic transport across a helical edge state exposed to a uniform magnetic ({$vec B$}) field over a finite length. We show that this system exhibits Fabry-Perot type resonances in electronic transport. The intrinsic spin anisotropy of th
e helical edge states allows us to tune these resonances by changing the direction of the {$vec B$} field while keeping its magnitude constant. This is in sharp contrast to the case of non-helical one dimensional electron gases with a parabolic dispersion, where similar resonances do appear in individual spin channels ($uparrow$ and $downarrow$) separately which, however, cannot be tuned by merely changing the direction of the {$vec B$} field. These resonances provide a unique way to probe the helical nature of the theory.
