Quantum Phase Transition in a Resonant Level Coupled to Interacting Leads

An interacting one-dimensional electron system, the Luttinger liquid, is distinct from the "conventional" Fermi liquids formed by interacting electrons in two and three dimensions. Some of its most spectacular properties are revealed in the process of electron tunneling: as a function of the applied bias or temperature the tunneling current demonstrates a non-trivial power-law suppression. Here, we create a system which emulates tunneling in a Luttinger liquid, by controlling the interaction of the tunneling electron with its environment. We further replace a single tunneling barrier with a double-barrier resonant level structure and investigate resonant tunneling between Luttinger liquids. For the first time, we observe perfect transparency of the resonant level embedded in the interacting environment, while the width of the resonance tends to zero. We argue that this unique behavior results from many-body physics of interacting electrons and signals the presence of a quantum phase transition (QPT). In our samples many parameters, including the interaction strength, can be precisely controlled; thus, we have created an attractive model system for studying quantum critical phenomena in general. Our work therefore has broadly reaching implications for understanding QPTs in more complex systems, such as cold atoms and strongly correlated bulk materials.Comment: 11 pages total (main text + supplementary

Critical Current Scaling in Long Diffusive Graphene-Based Josephson Junctions

We present transport measurements on long, diffusive, graphene-based Josephson junctions. Several junctions are made on a single-domain crystal of CVD graphene and feature the same contact width of ∼9 μm but vary in length from 400 to 1000 nm. As the carrier density is tuned with the gate voltage, the critical current in these junctions ranges from a few nanoamperes up to more than 5 μA, while the Thouless energy, <i>E</i>_Th, covers almost 2 orders of magnitude. Over much of this range, the product of the critical current and the normal resistance <i>I</i>_C<i>R</i>_N is found to scale linearly with <i>E</i>_Th, as expected from theory. However, the value of the ratio <i>I</i>_C<i>R</i>_N/<i>E</i>_Th is found to be 0.1–0.2, which much smaller than the predicted ∼10 for long diffusive SNS junctions