Yuriy Bomze

Supercurrent in the quantum Hall regime.

Making a graphene super-edge In superconductors, the electrical current is carried by “Cooper pairs,” formed out of an electron and a hole. This supercurrent will happily cross a thin barrier between two superconductors. But what if a strong magnetic field were applied at the barrier, forcing charge carriers to travel only along the edge of the barrier? Amet et al. explored this regime in a sample consisting of two superconducting electrodes and a graphene barrier under magnetic fields of up to 2 tesla (see the Perspective by Mason). Their transport measurements were consistent with a model in which the supercurrent was carried by the edge states in graphene. Science, this issue p. 966; see also p. 891 Transport measurements show that quantum Hall edge states carry the supercurrent in a graphene Josephson junction. A promising route for creating topological states and excitations is to combine superconductivity and the quantum Hall (QH) effect. Despite this potential, signatures of superconductivity in the QH regime remain scarce, and a superconducting current through a QH weak link has been challenging to observe. We demonstrate the existence of a distinct supercurrent mechanism in encapsulated graphene samples contacted by superconducting electrodes, in magnetic fields as high as 2 tesla. The observation of a supercurrent in the QH regime marks an important step in the quest for exotic topological excitations, such as Majorana fermions and parafermions, which may find applications in fault-tolerant quantum computing.

Quantum phase transition in a resonant level coupled to interacting leads

A Luttinger liquid is an interacting one-dimensional electronic system, quite distinct from the ‘conventional’ Fermi liquids formed by interacting electrons in two and three dimensions. Some of the most striking properties of Luttinger liquids are revealed in the process of electron tunnelling. For example, as a function of the applied bias voltage or temperature, the tunnelling current exhibits a non-trivial power-law suppression. (There is no such suppression in a conventional Fermi liquid.) Here, using a carbon nanotube connected to resistive leads, we create a system that emulates tunnelling in a Luttinger liquid, by controlling the interaction of the tunnelling electron with its environment. We further replace a single tunnelling barrier with a double-barrier, resonant-level structure and investigate resonant tunnelling between Luttinger liquids. At low temperatures, we observe perfect transparency of the resonant level embedded in the interacting environment, and the width of the resonance tends to zero. We argue that this behaviour results from many-body physics of interacting electrons, and signals the presence of a quantum phase transition. Given that many parameters, including the interaction strength, can be precisely controlled in our samples, this is an attractive model system for studying quantum critical phenomena in general, with wide-reaching implications for understanding quantum phase transitions in more complex systems, such as cold atoms and strongly correlated bulk materials.

Observation of Majorana quantum critical behaviour in a resonant level coupled to a dissipative environment

A quantum critical point associated with a carbon nanotube quantum dot that is in contact with dissipative leads exhibits striking non-Fermi-liquid properties and anomalous scaling. The dissipative environment enables the comparison of the system under thermal- and non-equilibrium conditions.

Ballistic Graphene Josephson Junctions from the Short to the Long Junction Regimes

We investigate the critical current I_{C} of ballistic Josephson junctions made of encapsulated graphene-boron-nitride heterostructures. We observe a crossover from the short to the long junction regimes as the length of the device increases. In long ballistic junctions, I_{C} is found to scale as ∝exp(-k_{B}T/δE). The extracted energies δE are independent of the carrier density and proportional to the level spacing of the ballistic cavity. As T→0 the critical current of a long (or short) junction saturates at a level determined by the product of δE (or Δ) and the number of the junctions transversal modes.

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, ETh, covers almost 2 orders of magnitude. Over much of this range, the product of the critical current and the normal resistance ICRN is found to scale linearly with ETh, as expected from theory. However, the value of the ratio ICRN/ETh is found to be 0.1-0.2, which much smaller than the predicted ∼10 for long diffusive SNS junctions.

Retrapping current, self-heating, and hysteretic current-voltage characteristics in ultranarrow superconducting aluminum nanowires

Hysteretic I-V (current-voltage) is studied in narrow Al nanowires. The nanowires have a cross section as small as 50 nm^2. We focus on the retapping current in a down-sweep of the current, at which a nanowire re-enters the superconducting state from a normal state. The retrapping current is found to be significantly smaller than the switching current at which the nanowire switches into the normal state from a superconducting state during a current up-sweep. For wires of different lengths, we analyze the heat removal due to various processes, including electronic and phonon processes. For a short wires 1.5 um in length, electronic thermal conduction is effective; for longer wires 10um in length, phonon conduction becomes important. We demonstrate that the measured retrapping current as a function of temperature can be quantitatively accounted for by the selfheating occurring in the normal portions of the nanowires to better than 20 % accuracy. For the phonon processes, the extracted thermal conduction parameters support the notion of a reduced phase-space below 3-dimensions, consistent with the phonon thermal wavelength having exceeded the lateral dimensions at temperatures below ~ 1.3K. Nevertheless, surprisingly the best fit was achieved with a functional form corresponding to 3-dimensional phonons, albeit requiring parameters far exceeding known values in the literature.