Higher-Order Topology in Bismuth.

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.

Ballistic edge states in Bismuth nanowires revealed by SQUID interferometry.

The protection against backscattering provided by topology is a striking property. In two-dimensional insulators, a consequence of this topological protection is the ballistic nature of the one-dimensional helical edge states. One demonstration of ballisticity is the quantized Hall conductance. Here we provide another demonstration of ballistic transport, in the way the edge states carry a supercurrent. The system we have investigated is a micrometre-long monocrystalline bismuth nanowire with topological surfaces, that we connect to two superconducting electrodes. We have measured the relation between the Josephson current flowing through the nanowire and the superconducting phase difference at its ends, the current-phase relation. The sharp sawtooth-shaped phase-modulated current-phase relation we find demonstrates that transport occurs selectively along two ballistic edges of the nanowire. In addition, we show that a magnetic field induces 0-π transitions and ϕ0-junction behaviour, providing a way to manipulate the phase of the supercurrent-carrying edge states and generate spin supercurrents.

Strain superlattices and macroscale suspension of graphene induced by corrugated substrates.

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.

Functionalization of DNA G-Wires for patterning and nanofabrication.

DNA structures made of guanine tetrads present remarkable properties and are thus first choice candidates for applications in nanofabrication. Starting from the work of Kotlyar et al., we report here that the klenow exo(-) fragment of DNA polymerase I can extend poly(dG)-poly(dC) from various 5'-modified (dG)(10(-))(dC)(10) templates. This allows the production of end-functionalized four-stranded wires (G-Wires) assembled from the folding of poly(dG) strands. G-Wires bearing thiol moieties can be easily combed on Au and Pt surfaces, whereas a 5' single-stranded overhang of a random sequence provides the unique possibility to assemble complex structures for nanoconstruction purposes.