Universal chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact.

One-dimensional conductors are described by Luttinger liquid theory, which predicts a power-law suppression of the single-electron tunneling density of states at low voltages. The scaling exponent is predicted to be quantized when tunneling into a single isolated chiral edge state of the fractional quantum Hall effect. We report conductance measurements across a point contact linking integer and fractional quantum Hall edge states (at fillings 1 and [Formula: see text], respectively). At weak coupling, we observe the predicted universal quadratic scaling with temperature and voltage. At strong coupling, we demonstrate perfect Andreev reflection of fractionalized quasiparticles at the point contact. We use the strong coupling physics to realize a nearly dissipationless direct current voltage step-up transformer, whose gain arises directly from topological fractionalization of electrical charge.

Proximity-Induced Superconductivity in Monolayer MoS2.

Proximity effects in superconducting normal (SN) material heterostructures with metals and semiconductors have long been observed and theoretically described in terms of Cooper pair wave functions and Andreev reflections. Whereas the semiconducting N-layer materials in the proximity experiments to date have been doped and tens of nanometers thick, we present here a proximity tunneling study involving a pristine single-layer transition-metal dichalcogenide film of MoS2 placed on top of a Pb thin film. Scanning tunneling microscopy and spectroscopy experiments together with parallel theoretical analysis based on electronic structure calculations and Green's function modeling allow us to unveil a two-step process in which MoS2 first becomes metallic and then is induced into becoming a conventional s-wave Bardeen-Cooper-Schrieffer-type superconductor. The lattice mismatch between the MoS2 overlayer and the Pb substrate is found to give rise to a topographic moiré pattern. Even though the induced gap appears uniform in location, the coherence peak height of the tunneling spectra is modulated spatially into a moiré pattern that is similar to but shifted with respect to the moiré pattern observed in topography. The aforementioned modulation is shown to originate from the atomic-scale structure of the SN interface and the nature of local atomic orbitals that are involved in generating the local pairing potential. Our study indicates that the local modulation of induced superconductivity in MoS2 could be controlled via geometrical tuning, and it thus shows promise toward the integration of monolayer superconductors into next-generation functional electronic devices by exploiting proximity-effect control of quantum phases.