EQuAL Seminar: Liam Cohen

"Chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact: from universal conductance scaling to Andreev scattering of e/3 quasiparticles"

One dimensional conductors are described by the theory of Luttinger liquids, a non-Fermi liquid state characterized by a power law suppression of the tunneling density of states near the Fermi level which goes as (E - EF)1/g -1. This manifests experimentally in the tunneling conductance which should exhibit power-law behavior with exponent “1/g-1” in both voltage bias and temperature. While in general “g” is a non-universal parameter determined by the details of the inter-mode interactions in the wire, the edge states of the fractional quantum Hall (FQH) effect provide a unique 1D system in which “g" becomes quantized as a result of the edge bordering a topologically non-trivial bulk. Using a graphene quantum point contact made entirely of van der Waals materials, we directly interface the ν = 1/3 and ν = 1 edges at a single point and study the resulting tunneling characteristics. We demonstrate, in the weak tunneling limit, universal scaling behavior of the conductance consistent with the prediction that g = ν = 1/3. In the opposite limit, surprisingly, at large bias voltages and temperatures, or as the QPC becomes more open, we observe that the conductance saturates to 1/2 e2/h. Additionally, whenever the conductance exceeds 1/3 e2/h, a negative voltage downstream of the QPC develops. This result can be attributed to the Andreev-like reflection of incoming e/3 quasiparticles at the point contact. We exploit this process to realize a nearly dissipation-free D.C. voltage step-up transformer, which has a maximum integrated gain of 1.45 and power efficiency of 97%. This result implies that the heterojunction can be made nearly adiabatic, demonstrating a significant improvement in the state-of-the-art for quantum Hall mesoscopic devices.