Observation of spin-momentum locked surface states in amorphous Bi2Se3.

Crystalline symmetries have played a central role in the identification and understanding of quantum materials. Here we investigate whether an amorphous analogue of a well known three-dimensional strong topological insulator has topological properties in the solid state. We show that amorphous Bi2Se3 thin films host a number of two-dimensional surface conduction channels. Our angle-resolved photoemission spectroscopy data are consistent with a dispersive two-dimensional surface state that crosses the bulk gap. Spin-resolved photoemission spectroscopy shows this state has an anti-symmetric spin texture, confirming the existence of spin-momentum locked surface states. We discuss these experimental results in light of theoretical photoemission spectra obtained with an amorphous topological insulator tight-binding model, contrasting it with alternative explanations. The discovery of spin-momentum locked surface states in amorphous materials opens a new avenue to characterize amorphous matter, and triggers the search for an overlooked subset of quantum materials outside of current classification schemes.

Topological Weaire-Thorpe models of amorphous matter.

Amorphous solids remain outside of the classification and systematic discovery of new topological materials, partially due to the lack of realistic models that are analytically tractable. Here we introduce the topological Weaire-Thorpe class of models, which are defined on amorphous lattices with fixed coordination number, a realistic feature of covalently bonded amorphous solids. Their short-range properties allow us to analytically predict spectral gaps. Their symmetry under permutation of orbitals allows us to analytically compute topological phase diagrams, which determine quantized observables like circular dichroism, by introducing symmetry indicators in amorphous systems. These models and our procedures to define invariants are generalizable to higher coordination number and dimensions, opening a route toward a complete classification of amorphous topological states in real space using quasilocal properties.

Topological Phases without Crystalline Counterparts.

We construct a two-dimensional higher-order topological phase protected by a quasicrystalline eightfold rotation symmetry. Our tight-binding model describes a superconductor on the Ammann-Beenker tiling hosting localized Majorana zero modes at the corners of an octagonal sample. In order to analyze this model, we introduce Hamiltonians generated by a local rule, and use this concept to identify the bulk topological properties. We find a Z_{2} bulk topological invariant protecting the corner modes. Our work establishes that there exist topological phases protected by symmetries impossible in a crystal.

Spin-Orbit Interaction and Induced Superconductivity in a One-Dimensional Hole Gas.

Low dimensional semiconducting structures with strong spin-orbit interaction (SOI) and induced superconductivity attracted great interest in the search for topological superconductors. Both the strong SOI and hard superconducting gap are directly related to the topological protection of the predicted Majorana bound states. Here we explore the one-dimensional hole gas in germanium silicon (Ge-Si) core-shell nanowires (NWs) as a new material candidate for creating a topological superconductor. Fitting multiple Andreev reflection measurements shows that the NW has two transport channels only, underlining its one-dimensionality. Furthermore, we find anisotropy of the Landé g-factor that, combined with band structure calculations, provides us qualitative evidence for the direct Rashba SOI and a strong orbital effect of the magnetic field. Finally, a hard superconducting gap is found in the tunneling regime and the open regime, where we use the Kondo peak as a new tool to gauge the quality of the superconducting gap.

Orbital Contributions to the Electron g Factor in Semiconductor Nanowires.

Recent experiments on Majorana fermions in semiconductor nanowires [S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, and C. M. Marcus, Nature (London) 531, 206 (2016)NATUAS0028-083610.1038/nature17162] revealed a surprisingly large electronic Landé g factor, several times larger than the bulk value-contrary to the expectation that confinement reduces the g factor. Here we assess the role of orbital contributions to the electron g factor in nanowires and quantum dots. We show that an L·S coupling in higher subbands leads to an enhancement of the g factor of an order of magnitude or more for small effective mass semiconductors. We validate our theoretical finding with simulations of InAs and InSb, showing that the effect persists even if cylindrical symmetry is broken. A huge anisotropy of the enhanced g factors under magnetic field rotation allows for a straightforward experimental test of this theory.

Dynamical Piezoelectric and Magnetopiezoelectric Effects in Polar Metals from Berry Phases and Orbital Moments.

The polarization of a material and its response to applied electric and magnetic fields are key solid-state properties with a long history in insulators, although a satisfactory theory required new concepts such as Berry-phase gauge fields. In metals, quantities such as static polarization and the magnetoelectric θ term cease to be well defined. In polar metals, there can be analogous dynamical current responses, which we study in a common theoretical framework. We find that current responses to dynamical strain in polar metals depend on both the first and second Chern forms, related to polarization and magnetoelectricity in insulators as well as the orbital magnetization on the Fermi surface. We provide realistic estimates that predict that the latter contribution will dominate, and we investigate the feasibility of experimental detection of this effect.