No abstract

The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk-boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk-boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principle calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunneling spectroscopy, we probe the unique signatures of the rotational symmetry of the one-dimensional states located at step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.

Conductivity measurements on double-stranded DNA molecules deposited by a combing process across a submicron slit between rhenium/carbon metallic contacts reveal conduction to be ohmic between room temperature and 1 kelvin. The resistance per molecule is less than 100 kilohm and varies weakly with temperature. Below the superconducting transition temperature (1 kelvin) of the contacts, proximity-induced superconductivity is observed. These results imply that DNA molecules can be conducting down to millikelvin temperature and that phase coherence is maintained over several hundred nanometers.

We report measurements on ropes of single-walled carbon nanotubes (SWNT) in low-resistance contact to nonsuperconducting (normal) metallic pads, at low voltage and at temperatures down to 70 mK. In one sample, we find a 2 orders of magnitude resistance drop below 0.55 K, which is destroyed by a magnetic field of the order of 1 T, or by a dc current greater than 2.5 microA. These features strongly suggest the existence of superconductivity in ropes of SWNT.

Proximity-induced superconductivity in single-walled carbon nanotubes below 1 kelvin, both in a single tube 1 nanometer in diameter and in crystalline ropes containing about 100 nanotubes, was observed. The samples were suspended between two superconducting electrodes, permitting structural study in a transmission electron microscope. When the resistance of the nanotube junction is sufficiently low, it becomes superconducting and can carry high supercurrents. The temperature and magnetic field dependence of the critical current of such junctions exhibits unusual features related to their strong one-dimensional character.

We report measurements of the flux-dependent orbital magnetic susceptibility of an ensemble of 10(5) disconnected silver rings at 217 MHz. Because of the strong spin-orbit scattering rate in silver this experiment is a test of existing theories on ensemble averaged persistent currents. Below 100 mK the rings exhibit a magnetic signal with a flux periodicity of h/2e consistent with averaged persistent currents, whose amplitude is of the order of 0.3 nA. The sign of the oscillations indicates unambiguously diamagnetism in the vicinity of zero magnetic field. This sign is a priori not consistent with theoretical predictions for average persistent currents. We discuss several possible explanations of this result.

We investigate the organized formation of strain, ripples, and suspended features in macroscopic graphene sheets transferred onto corrugated substrates made of an ordered array of silica pillars with variable geometries. Depending on the pitch and sharpness of the corrugated array, graphene can conformally coat the surface, partially collapse, or lie fully suspended between pillars in a fakir-like fashion over tens of micrometers. With increasing pillar density, ripples in collapsed films display a transition from random oriented pleats emerging from pillars to organized domains of parallel ripples linking pillars, eventually leading to suspended tent-like features. Spatially resolved Raman spectroscopy, atomic force microscopy, and electronic microscopy reveal uniaxial strain domains in the transferred graphene, which are induced and controlled by the geometry. We propose a simple theoretical model to explain the structural transition between fully suspended and collapsed graphene. For the arrays of high density pillars, graphene membranes stay suspended over macroscopic distances with minimal interaction with the pillars' apexes. It offers a platform to tailor stress in graphene layers and opens perspectives for electron transport and nanomechanical applications.

We report the design and measurement of Superconducting/normal/superconducting (SNS) proximity DC squids in the long junction limit, i.e. superconducting loops interrupted by two normal metal wires roughly a micrometer long. Thanks to the clean interface between the metals, at low temperature a large supercurrent flows through the device. The dc squid-like geometry leads to an almost complete periodic modulation of the critical current through the device by a magnetic flux, with a flux periodicity of a flux quantum h/2e through the SNS loop. In addition, we examine the entire field dependence, notably the low and high field dependence of the maximum switching current. In contrast with the well-known Fraunhoffer-type oscillations typical of short wide junctions, we find a monotonous gaussian extinction of the critical current at high field. As shown in [15], this monotonous dependence is typical of long and narrow diffusive junctions. We also find in some cases a puzzling reentrance at low field. In contrast, the temperature dependence of the critical current is well described by the proximity effect theory, as found by Dubos et al. [16] on SNS wires in the long junction limit. The switching current distributions and hysteretic IV curves also suggest interesting dynamics of long SNS junctions with an important role played by the diffusion time across the junction.