Tunnelling spectroscopy of Andreev states in graphene

Abstract

A normal conductor placed in good contact with a superconductor can inherit its remarkable electronic properties 1,2 . This proximity e ect microscopically originates from the formation in the conductor of entangled electron-hole states, called Andreev states [3][4][5][6][7][8] . Spectroscopic studies of Andreev states have been performed in just a handful of systems 9-13 . The unique geometry, electronic structure and high mobility of graphene 14,15 make it a novel platform for studying Andreev physics in two dimensions. Here we use a full van der Waals heterostructure to perform tunnelling spectroscopy measurements of the proximity e ect in superconductor-graphenesuperconductor junctions. The measured energy spectra, which depend on the phase di erence between the superconductors, reveal the presence of a continuum of Andreev bound states. Moreover, our device heterostructure geometry and materials enable us to measure the Andreev spectrum as a function of the graphene Fermi energy, showing a transition between di erent mesoscopic regimes. Furthermore, by experimentally introducing a novel concept, the supercurrent spectral density, we determine the supercurrent-phase relation in a tunnelling experiment, thus establishing the connection between Andreev physics at finite energy and the Josephson e ect. This work opens up new avenues for probing exotic topological phases of matter in hybrid superconducting Dirac materials [16][17][18] .When a normal quantum conductor (N) is sandwiched between two superconductors (S), a current can flow in the absence of any voltage, due to the Josephson effect 1 . This macroscopic supercurrent is driven by the difference between the order parameter phases of the two superconductors, ϕ. Microscopically, it corresponds to the coherent flow of Cooper pairs through the conductor, which is made possible by successive Andreev reflections at the N/S interfaces, where electrons (holes) are reflected as oppositespin holes (electrons) (Fig. 1a). Due to this process, resonant electron-hole states form in the central conductor, known as Andreev bound states (ABS) 3-6 . They lie as energy levels inside the superconducting gap [−∆, ∆], only negative-energy states being populated in the ground state (Fig. 1b). Crucially, the Andreev energy E n (ϕ) depends on ϕ, and each populated ABS carries in response a supercurrent (1/φ 0 )(∂E n /∂ϕ), where φ 0 = /2e is the reduced flux quantum, with the reduced Planck constant and e the elementary charge. The overall phase-dependent Andreev spectrum is shown in Fig. 1c and depends on geometric and microscopic parameters 7,8 , such as the conductor dimensions that determine the number of ABS, the scattering processes in the conductor and the contact's transparency. Strong ABS phase dependence, and therefore a prominent proximity effect, is achieved in ballistic systems with transparent N/S interfaces 7,8 .Graphene (G) can exhibit low contact resistance and weak scattering when connected to superconducting electrodes 19,20 . These properties, combined with t...

Local density of states in clean two-dimensional superconductor–normal metal–superconductor heterostructures

“…The results presented here for the LDOS actually resemble those reported in Ref. [41] for a S-graphene-S junction, especially for high gate voltages when the graphene Fermi energy is away from the Dirac point. The main differences are: (i) the experimental results typically show a soft gap at low energies, contrary to the hard gap that we obtain, and (ii) the modulation of the LDOS in our simulations decays with the magnetic flux more rapidly than in the experiments.…”

“…IV we present a discussion of the magnetic-field modulation of the LDOS in close connection to the work of Ref. [41] and present an analytical relation between LDOS and the supercurrent in fully transparent junctions. Finally, Sec.…”

“…To illustrate the magnetic flux modulation of the LDOS, we follow Ref. [41] and assume that A loop /A N = 7.5 and consider a normal metal of length L = 0.2ξ and width W = 0.7ξ. We show in Fig.…”

“…In experimental setups, like that of Ref. [41], the superconducting phase difference is controlled by incorporating the weak link into a superconducting loop and applying a weak magnetic field. For this reason, we analyze in this section the role of the application of a weak external magnetic field perpendicular to the SNS junction and study also the role of having a finite width.…”

Probing the electronic structure of graphene near and far from the Fermi level via planar tunneling spectroscopy

“…3c show a well-defined staircase pattern. Similar patterns have been reported previously in twodimensional electron systems, 7 and in STS studies of graphene 8,9 , though not at = 18 . These staircase patterns arise from highly compressible LLs for which the Fermi level is pinned at a constant energy as they are filled with charge.…”