Inter-Landau-level Andreev Reflection at the Dirac Point in a Graphene Quantum Hall State Coupled to a ${\mathrm{NbSe}}_2$ Superconductor

Superconductivity and the quantum Hall effect are distinct states of matter occurring in apparently incompatible physical conditions. Recent theoretical developments suggest that the coupling of the quantum Hall effect with a superconductor can provide fertile ground for realizing exotic topological excitations such as non-Abelian Majorana fermions or Fibonacci particles. As a step toward that goal, we report observation of Andreev reflection at the junction of a quantum Hall edge state in a single layer graphene and a quasi-two-dimensional niobium diselenide (${\mathrm{NbSe}}_2$) superconductor. Our principal finding is the observation of an anomalous finite-temperature conductance peak located precisely at the Dirac point, providing a definitive evidence for inter-Landau-level Andreev reflection in a quantum Hall system. Our observations are well supported by detailed numerical simulations, which offer additional insight into the role of the edge states in Andreev physics. This study paves the way for investigating analogous Andreev reflection in a fractional quantum Hall system coupled to a superconductor to realize exotic quasiparticles.

Figure 1

(a) (top) AR in graphene at $B=0$. The red (blue) dashed line shows retro (specular) AR. (bottom) Classical picture of AR at the interface of QH edge state and superconductor based on skipping orbit. The electron and hole orbits have the same chirality for intraband process. (b) Schematic of the experimental measurement setup of hBN protected graphene devices. For $R_{xy}$ measurement current is injected between $A$ and $D$, voltage is measured between $B$ and $C$. For the two probe conductance measurement of the SLG-${\mathrm{NbSe}}_2$ junction voltage is applied at $A$, and the current is measured at $D$. (c) $R_{xy}$ of device 2 at $B=10\mathrm{T}$ showing symmetry broken QH plateaus. (d) Two-terminal gate response of device 1 between $\mathrm{Au}\text{−}\mathrm{SLG}\text{−}{\mathrm{NbSe}}_2$ at $B=9.8\mathrm{T}$ and $V_{\mathrm{SD}}=0\mathrm{mV}$. (e) Activation plot for device 3 at the Dirac point for different magnetic fields; the corresponding insulating gaps are shown on the figure. We note that the resistance changes by up to 3 orders of magnitude over the range of the fits. (f) $dI/dV$ as a function of $V_{\mathrm{SD}}$ measured in device 1 at $B=9.8\mathrm{T}$ on the $\nu =2$ LL at the positions $A$ and $B$ marked in (d); BCS peaks are present at 240 mK (red) but not at 10 K (black). (g) 2D color map of normalized $dI/dV$ versus $V_{\mathrm{SD}}$ as a function of temperature at $B=9.8\mathrm{T}$ for device 3. Superconductivity vanishes at around 2 K. The black dashed line is the theoretical temperature dependence of the BCS gap. The cut lines are shown at 240 mK and 2.5 K. (h) The gate responses of device 1 for 6 T at $V_{\mathrm{SD}}=0$ (black) and for $|e{V}_{\mathrm{SD}}|>\mathrm{\Delta }$ (red). The former has enhanced conductance.

Figure 2

(a) The anomalous conductance peak at the DP shown in several devices on a log scale. (b) The conductance peak in device 2 at different magnetic fields shows the decrement of the amplitude with increasing $B$. (c) The conductance peak amplitude increases with increasing temperature. The red dashed lines in the last two panels display fitting of the peak line shape with Eq. (1). (d) No conductance peak at the DP is seen for $T>T_C$.

Figure 3

(a) 2D color map of log($G$) in device 3 plotted as a function of ${\mathrm{V}}_{\mathrm{BG}}$ and $B$ showing the presence of the anomalous peak precisely at the DP, which vanishes above 5.6 T. (b) Area of the peak plotted as a function of $1/T$ showing activated behavior with an effective gap of $\mathrm{\Delta }{E}_{\mathrm{eff}}\sim 248\mu \mathrm{eV}$. In the inset, the amplitude of the conductance peak in device 3 is used to show the activated behavior, which gives $\mathrm{\Delta }{E}_{\mathrm{eff}}\sim 150\mu \mathrm{eV}$.

Figure 4

(a) An experimental phase diagram in energy and magnetic field. Solid black squares are the superconducting gaps measured using bias spectroscopy as a function of $B$. The solid red squares and solid purple hexagons show the insulating gaps of device 2 and device 3 as a function of $B$, where the thick lines are a guide to the eye. The anomalous conductance peak at the DP is observed in the region enclosed by the dashed black ovals. (b) Schematic of the inter-Landau-level AR process at the DP.

Figure 5

Panel (a) shows numerical results based on the canted antiferromagnetic (CAF) model, and panel (b) for the isospin ferromagnet (IFM) model. The chemical potential is quoted in units of the hopping parameter $t$. The band diagram and the peak at the Dirac point are shown as insets.