Chiral quasiparticle tunneling between quantum Hall edges in proximity with a superconductor

We study a two-terminal graphene Josephson junction with contacts shaped to form a narrow constriction, less than $100\mathrm{nm}$ in length. The contacts are made from type-II superconducting contacts and able to withstand magnetic fields high enough to reach the quantum Hall regime in graphene. In this regime, the device conductance is determined by edge states, plus the contribution from the constricted region. In particular, the constriction area can support supercurrents up to fields of $\sim 2.5\mathrm{T}$. Additionally, enhanced conductance is observed through a wide range of magnetic fields and gate voltages. This additional conductance and the appearance of supercurrent is attributed to the tunneling between counterpropagating quantum Hall edge states along opposite superconducting contacts.

Figure 1

(a) Schematic of the graphene Josephson junction with asymmetric contacts, measured with a four-probe current-biased setup. The finger of the $\mathsf{T}$-shaped contact is separated from the opposing contact by about $90\mathrm{nm}$. (b) Three-dimensional (3D) representation of the $\mathsf{T}$-shaped junction illustrating the graphene-hBN stack with the graphite back gate. (c) Differential resistance $R=dV/dI$ vs dc bias current $I_{\text{dc}}$ and gate voltage $V_G$ taken at a perpendicular magnetic field of $B=2\mathrm{T}$. Pockets of suppressed resistance (superconductivity) are observed at several gate voltages through the region including on the quantum Hall plateaus, at the transition between two filling factors, and in the semiclassical region. The arrows at the top edge denote transitions between the different filling factors $\nu$, while the white, dashed line denotes $V_G$ at which the cyclotron radius becomes equal to half the constriction width $l$ (the onset of the semiclassical region). (d), (e) Resistance vs $I_{\text{dc}}$ for selected gate values. (d) shows enhanced zero-bias resistance, a signature of the superconducting gap. (e) demonstrates the observance of supercurrent.

Figure 2

The dependence of differential resistance $R$ on magnetic field: $B=2.5\mathrm{T}+\delta B$ as a function of gate voltages $V_G$ and bias current. (a) Resistance dips at $I_{\text{dc}}=0\mathrm{nA}$ indicate pockets of supercurrent. (b) Superconducting signatures are fully suppressed at $I_{\text{dc}}=5\mathrm{nA}$. (c) The resistance difference $\mathrm{\Delta }R$ between $I_{\text{dc}}=5$ and $0\mathrm{nA}$. No periodic oscillations of supercurrent in field are observed. This suggests that the supercurrent is not mediated by the QH states along the graphene edges, as a superconducting quantum interference device (SQUID)-like pattern would be expected to emerge.

Figure 3

Field-dependent conductance. (a) The fan diagram of measured conductance from 0 to 7 T. The blue dashed line represents the boundary at which the cyclotron radius is half the constriction length $r=45\text{nm}$. The magenta dashed lines follow the centers of the $\nu =2,6$ plateaus. (b) The measured conductance as a function of back gate voltages $V_G$ taken at several magnetic fields from 2 to $7\mathrm{T}$. (c) Schematic of the QH edge states at the constriction. Each edge state is statistically distributed around a central location (blue lines). At the constriction, a significant overlap in the distributions of the opposing edge states is expected, mediating tunneling. (d) Enhancement in the measured conductance $\mathrm{\Delta }G$ for the marked line cuts in (a) at $\nu =2,6$ along the center of the QH plateaus. The dots are the measured data, while the solid lines are fitted conductances simulating the contribution due to tunneling via overlapping QH states running along the graphene-superconductor interface.