Electrical transport studies on graphene have been focused mainly on the linear dispersion region around the Fermi level and, in particular, on the effects associated with the quasiparticles in graphene behaving as relativistic particles known as Dirac fermions. However, some theoretical work has suggested that several features of electron transport in graphene are better described by conventional semiconductor physics. Here we use scanning photocurrent microscopy to explore the impact of electrical contacts and sheet edges on charge transport through graphene devices. The photocurrent distribution reveals the presence of potential steps that act as transport barriers at the metal contacts. Modulations in the electrical potential within the graphene sheets are also observed. Moreover, we find that the transition from the p- to n-type regime induced by electrostatic gating does not occur homogeneously within the sheets. Instead, at low carrier densities we observe the formation of p-type conducting edges surrounding a central n-type channel.

The physics and operating principles of hybrid superconductor-semiconductor devices rest ultimately on the magnetic properties of their elementary subgap excitations, usually called Andreev levels. Here we report a direct measurement of the Zeeman effect on the Andreev levels of a semiconductor quantum dot with large electron g-factor, strongly coupled to a conventional superconductor with a large critical magnetic field. This material combination allows spin degeneracy to be lifted without destroying superconductivity. We show that a spin-split Andreev level crossing the Fermi energy results in a quantum phase transition to a spin-polarized state, which implies a change in the fermionic parity of the system. This crossing manifests itself as a zero-bias conductance anomaly at finite magnetic field with properties that resemble those expected for Majorana modes in a topological superconductor. Although this resemblance is understood without evoking topological superconductivity, the observed parity transitions could be regarded as precursors of Majorana modes in the long-wire limit.

We studied the low-energy states of spin-1/2 quantum dots defined in InAs/InP nanowires and coupled to aluminium superconducting leads. By varying the superconducting gap, ∆, with a magnetic field, B, we investigated the transition from strong coupling, ∆ ≪ TK, to weak coupling, ∆ ≫ TK, where TK is the Kondo temperature. Below the critical field, we observe a persisting zero-bias Kondo resonance that vanishes only for low B or higher temperatures, leaving the room to more robust sub-gap structures at bias voltages between ∆ and 2∆. For strong and approximately symmetric tunnel couplings, a Josephson supercurrent is observed in addition to the Kondo peak. We ascribe the coexistence of a Kondo resonance and a superconducting gap to a significant density of intra-gap quasiparticle states, and the finite-bias sub-gap structures to tunneling through Shiba states. Our results, supported by numerical calculations, own relevance also in relation to tunnelspectroscopy experiments aiming at the observation of Majorana fermions in hybrid nanostructures.