Superconducting proximity effect in silicene: Spin-valley-polarized Andreev reflection, nonlocal transport, and supercurrent

Abstract

We theoretically study the superconducting proximity effect in silicene, which features massive Dirac fermions with a tunable mass (band gap), and compute the conductance across a normal|superconductor (N|S) silicene junction, the non-local conductance of an N|S|N junction, and the supercurrent flowing in an S|N|S junction. It is demonstrated that the transport processes consisting of local and non-local Andreev reflection may be efficiently controlled via an external electric field owing to the buckled structure of silicene. In particular, we demonstrate that it is possible to obtain a fully spin-valley polarized crossed Andreev reflection process without any contamination of elastic cotunneling or local Andreev reflection, in stark contrast to ordinary metals. It is also shown that the supercurrent flowing in the S|N|S junction can be fully spin-valley polarized and that it is controllable by an external electric field. PACS numbers:With the advent of graphene [1] and topological insulators [2], the study of Dirac fermions in condensed matter systems [3] has become one of the most active research fields in physics over the last decade. Condensed matter systems with such a 'relativistic' electronic band-structure are intriguing examples of low-energy emergent symmetries (in this case, Lorentz-invariance). This has led to a tremendous amount of interest in terms of possible application value as well as from a fundamental physics viewpoint.One of the most recent advances in this field has been the synthesis of silicene [4] which consists of silicon atoms arranged in a honeycomb pattern with a buckled sublattice structure. As in graphene, the states near the Fermi energy may be described by Dirac theory at two valleys K and K , but an important difference is that the fermions are massive in silicene due to a spin-orbit coupling which is much larger than in graphene. As a result, silicene is under the right circumstances a quantum spin Hall insulator with topologically protected edge states. In fact, it is possible [5] to achieve a rich variety of topological states in silicene due to a unique feature: the buckled structure causes the sublattices to respond differently to an applied electric field, which in turn induces a fermion mass-gap which is tunable. Closing and reopening this gap allows for a transition between different topological phases at a critical field value |E z | = E c as shown in Fig. 1(a).The combination of a superconducting proximity effect with topologically protected edge-states is currently generating a lot of interest due to the possibility of creating Majorana fermions in this manner [2,[6][7][8][9]. However, there exists no study of proximity-induced superconductivity in silicene so far. In this Letter, we investigate precisely this topic and focus on the signature of Andreev reflection process, both locally and non-locally (which is usually dubbed crossed Andreev reflection (CAR)). We find that the possibility to tune both the band-gap via an electric field E z as well as the local Fermi l...

Thermal conductance by Dirac fermions in a normal-insulator-superconductor junction of silicene

“…32. The bulk-boundary correspondence has not been taken into account within our scattering matrix formalism.…”

“…Very recently superconducting proximity effect in silicene has been investigated in Ref. 32 in which the authors have theoretically studied the behavior of electrical conductance in a normal-superconductor (NS) junction of silicene. Up to now, no experiment has been carried out in the context of proximity effect in silicene.…”

Gate-controlled supercurrent reversal in MoS 2 -based Josephson junctions

“…Here, motivated by experimental and some theoretical studies [16][17][18][19][20][21][22], we investigate the Josephson effect through the ML-MoS 2 both at its normal and spin-polarized (magnetic) states. If we induce conventional s-wave superconductivity in ML-MoS 2 via proximity, the Cooper pairs are formed from excitations from different (opposite) valleys and having opposite spins, very similar to the case of graphene [23].…”

Valley- and spin-switch effects in molybdenum disulfide superconducting spin valve

“…3 in terms of the exchange field of the right F region, h R , for three different lengths of the S region, where the pure CAR process (for h R = −h L < 0) is fully changed in the pure CT process (for h R = h L > 0) by changing the configuration of the magnetization directions from AP to P. The length dependence of the CT and CAR conductances will be explained in details in the following paragraphs. We note that the existence of a fully valley-and spin-polarized nonlocal charge current via the pure CAR (CT) process, without fixing of any parame- ter and for a wide range of the chemical potential of the F region, is the advantage of the proposed MoS 2 -based superconducting spin valve structure over the grapheneand silicene-based structures [13][14][15][16][17][18]. Therefore, we find that for all incoming electrons with µ 2 < µ F − eV ≤ µ 1 , the AR process is suppressed and the cross-conductance in the right F region depends crucially on the configuration of magnetizations in the two F regions.…”

“…Unfortunately, in ordinary nonrelativistic systems, the small value of the CAR conductance is completely canceled by the conductance of another nonlocal process known as elastic electron cotunneling (CT) which does not involve Copper * leyla.majidi@ipm.ir pairs and is therefore a parasitic process [7]. Recently, it has been demonstrated that the atomically thin twodimensional (2D) crystals such as graphene and silicene are possible areas for CAR processes [13][14][15][16][17][18] where the magnitude of the CAR conductance can be enhanced in normal/superconducting/normal (N/S/N) and ferromagnetic/superconducting/ferromagnetic (F/S/F) hybrid structures. Cayssol [13] has predicted a pure CAR process without any valley-or spin-polarization in graphene-based N/S/N structure at the bias voltage eV = µ (µ is the chemical potential).…”