Propagation of superconducting coherence via chiral quantum-Hall edge channels

Abstract

Recently, there has been significant interest in superconducting coherence via chiral quantum-Hall (QH) edge channels at an interface between a two-dimensional normal conductor and a superconductor (N–S) in a strong transverse magnetic field. In the field range where the superconductivity and the QH state coexist, the coherent confinement of electron- and hole-like quasiparticles by the interplay of Andreev reflection and the QH effect leads to the formation of Andreev edge states (AES) along the N–S interface. Here, we report the electrical conductance characteristics via the AES formed in graphene–superconductor hybrid systems in a three-terminal configuration. This measurement configuration, involving the QH edge states outside a graphene–S interface, allows the detection of the longitudinal and QH conductance separately, excluding the bulk contribution. Convincing evidence for the superconducting coherence and its propagation via the chiral QH edge channels is provided by the conductance enhancement on both the upstream and the downstream sides of the superconducting electrode as well as in bias spectroscopy results below the superconducting critical temperature. Propagation of superconducting coherence via QH edge states was more evident as more edge channels participate in the Andreev process for high filling factors with reduced valley-mixing scattering.

Current correlations of Cooper-pair tunneling into a quantum Hall system

“…where I dc (V + n /2) has been calculated in Eqs. 10, (14), (21), and (23). At → 0 and V 1 → 0, the sum of Floquet factors goes to one, i.e., ∞ n=−∞ J 2 n (2V 1 / ) → 1, and thus we recover the result of Eq.…”

“…Taking into account electron-electron interactions, assuming tunneling into only one channel, and repeating the steps leading to Eqs. (21) and (30) for finite temperatures yields the following result:…”

“…Recent progress in experimental techniques at the nanoscale has allowed experimentalists to create hybrid mesoscopic systems where QH edge states are coupled to other edge states [7][8][9], to quantum dots [6,[10][11][12][13], to Ohmic contacts [14][15][16][17], or to superconductors [18][19][20][21][22]. This development has provided a successful platform to study some of the fundamental questions of mesoscopic physics, such as phase coherence [23][24][25][26][27][28][29], charge [14,[30][31][32] and heat quantization [16,33], equilibration [34][35][36][37][38][39], and entanglement [9,40].…”

Majorana fermions on the quantum Hall edge

“…What might have been seen as a bold question has now become a concrete and tangible possibility [2]. Experimental groups have recently managed to make sufficiently transparent contacts between superconductors and quantum Hall states [3][4][5][6], not only enabling the measurement of a supercurrent [4,7,8], but also establishing the existence of the so called chiral Andreev edge state [9], a one-way hybrid electron-hole mode that propagates along these interfaces [10]. The electron-hole cyclotron orbits in the semiclassical regime were also recently imaged in a focusing experiment [11].…”

Perfect Crossed Andreev Reflection in Dirac Hybrid Junctions in the Quantum Hall Regime

“…The quantum Hall (QH) effect forces charged carriers to move along chiral edge channels which are robust against disorder [34,35]. Recently, hybrid systems cooperating with the QH effect and superconductivity have been fabricated based on graphene [36][37][38][39][40][41] whose lowenergy physics is governed by Dirac fermions. This paves a new way to explore CAR in Dirac materials.…”