Nonlocal superconducting correlations in graphene in the quantum Hall regime

Abstract

We study Andreev processes and nonlocal transport in a three-terminal graphene-superconductor hybrid system under a quantizing perpendicular magnetic field [G.-H. Lee et al., Nature Phys. 13, 693 (2017)]. We find that the amplitude of the crossed Andreev reflection (CAR) processes crucially depends on the orientation of the lattice. By employing Landauer-Büttiker scattering theory, we find that CAR is generally very small for a zigzag edge, while for an armchair edge it can be larger than the normal transmission, thereby resulting in a negative nonlocal resistance. In the case of an armchair edge and with a wide superconducting region (as compared to the superconducting coherence length), CAR exhibits large oscillations as a function of the magnetic field due to interference effects. This results in sign changes of the nonlocal resistance.

Transverse conductance in a three-dimensional Weyl semimetal and Weyl superconductor hybrid under a strong magnetic field

“…The transverse conductance embodies the general topological properties of the magnetic helicity, which is topologically well defined and invariant when all the available states have been summed over. The similar setups have been widely used in studies of the edge excitations, such as the two-dimensional electron gas in hybrid structures [56][57][58][59][60][61][62], graphene [63][64][65], and topological insulator [66,67]. The previous studies suggested that hybrid structures of superconducting topological materials can support the neutral Majorana states [66,[68][69][70].…”

Crossed Andreev reflection in spin-polarized chiral edge states due to the Meissner effect

“…In this regard, a prominent role is played by hybrid systems where quantum Hall effect (QHE) and SC correlations co-exist [56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71]. In particular, QHE edge states at filling factor ν = 1, proximitized via CAR processes, are especially promising for the field of topological quantum computation, since they are predicted to host Majorana bound states (MBSs) [72][73][74].…”

“…Negative resistance.-The presence of CAR processes can be tested in the three-terminal transport setup presented in Fig. 3(a) [1,55,63]. Here, a current I is injected through the left lead (L) and drained at the grounded SC, while the right lead (R) is a floating gate.…”

Quantized conductance with nonzero shot noise as a signature of Andreev edge state

“…There are several promising theoretical proposals of realizing chiral Majorana fermions at the QH-SC interfaces [4,5,7], however, evidence is still inconclusive [8][9][10][11]. The realization of electron-hole hybrid states called Andreev edge states (AESs) [12,13] at the QH-SC interface is an important step in this quest and graphene hosting clean QH edge states at a moderate magnetic field is an ideal platform. The recent developments of several superconductors with a large critical magnetic field and transparent interfaces with high quality graphene have paved the way for a number of interesting experimental observations [14][15][16][17][18][19][20][21][22][23][24][25][26], such as crossed Andreev conversion [18], supercurrents in the QH regime [16], inter-Landau-level Andreev reflection [19], and interference of chiral AESs [21].…”