Erratum: Ubiquitous Non-Majorana Zero-Bias Conductance Peaks in Nanowire Devices [Phys. Rev. Lett. 123, 107703 (2019)].

This corrects the article DOI: 10.1103/PhysRevLett.123.107703.

Majorana Corner Modes with Solitons in an Attractive Hubbard-Hofstadter Model of Cold Atom Optical Lattices.

Higher-order topological superconductors hosting Majorana-Kramers pairs (MKPs) as corner modes have recently been proposed in a two-dimensional quantum spin Hall insulator proximity-coupled to unconventional cuprate or iron-based superconductors. Here, we show that such MKPs can be realized using a conventional s-wave superfluid with a soliton in cold atom systems governed by the Hubbard-Hofstadter model. The MKPs emerge in the presence of interaction at the "corners" defined by the intersections of line solitons and the one-dimensional edges of the system. Our scheme is based on the recently realized cold atom Hubbard-Hofstadter lattice and will pave the way for observing possible higher-order topological superfluidity with conventional s-wave superfluids or superconductors.

Ubiquitous Non-Majorana Zero-Bias Conductance Peaks in Nanowire Devices.

We perform tunneling measurements on indium antimonide nanowire-superconductor hybrid devices fabricated for the studies of Majorana bound states. At finite magnetic field, resonances that strongly resemble Majorana bound states, including zero-bias pinning, become common to the point of ubiquity. Since Majorana bound states are predicted in only a limited parameter range in nanowire devices, we seek an alternative explanation for the observed zero-bias peaks. With the help of a self-consistent Poission-Schrödinger multiband model developed in parallel, we identify several families of trivial subgap states that overlap and interact, giving rise to a crowded spectrum near zero energy and zero-bias conductance peaks in experiments. These findings advance the search for Majorana bound states through improved understanding of broader phenomena found in superconductor-semiconductor systems.

Coulomb interaction effects on the Majorana states in quantum wires.

The stability of the Majorana modes in the presence of a repulsive interaction is studied in the standard semiconductor wire-metallic superconductor configuration. The effects of short-range Coulomb interaction, which is incorporated using a purely repulsive δ-function to model the strong screening effect due to the presence of the superconductor, are determined within a Hartree-Fock approximation of the effective Bogoliubov-De Gennes Hamiltonian that describes the low-energy physics of the wire. Through a numerical diagonalization procedure we obtain interaction corrections to the single particle eigenstates and calculate the extended topological phase diagram in terms of the chemical potential and the Zeeman energy. We find that, for a fixed Zeeman energy, the interaction shifts the phase boundaries to a higher chemical potential, whereas for a fixed chemical potential this shift can occur either at lower or higher Zeeman energies. These effects can be interpreted as a renormalization of the g-factor due to the interaction. The minimum Zeeman energy needed to realize Majorana fermions decreases with the increasing strength of the Coulomb repulsion. Furthermore, we find that in wires with multi-band occupancy this effect can be enhanced by increasing the chemical potential, i.e. by occupying higher energy bands.

Majorana fermions in semiconductor nanowires: fundamentals, modeling, and experiment.

After a recent series of rapid and exciting developments, the long search for the Majorana fermion-the elusive quantum entity at the border between particles and antiparticles-has produced the first positive experimental results, but is not over yet. Originally proposed by E Majorana in the context of particle physics, Majorana fermions have a condensed matter analogue in the zero-energy bound states emerging in topological superconductors. A promising route to engineering topological superconductors capable of hosting Majorana zero modes consists of proximity coupling semiconductor thin films or nanowires with strong spin-orbit interaction to conventional s-wave superconductors in the presence of an external Zeeman field. The Majorana zero mode is predicted to emerge above a certain critical Zeeman field as a zero-energy state localized near the order parameter defects, namely, vortices for thin films and wire ends for the nanowire. These Majorana bound states are expected to manifest non-Abelian quantum statistics, which makes them ideal building blocks for fault-tolerant topological quantum computation. This review provides an update on the current status of the search for Majorana fermions in semiconductor nanowires by focusing on the recent developments, in particular the period following the first reports of experimental signatures consistent with the realization of Majorana bound states in semiconductor nanowire-superconductor hybrid structures. We start with a discussion of the fundamental aspects of the subject, followed by considerations on the realistic modeling, which is a critical bridge between theoretical predictions based on idealized conditions and the real world, as probed experimentally. The last part is dedicated to a few intriguing issues that were brought to the fore by the recent encouraging experimental advances.

Nodal-antinodal dichotomy and the two gaps of a superconducting doped Mott insulator.

We study the superconducting state of the hole-doped two-dimensional Hubbard model using cellular dynamical mean-field theory, with the Lanczos method as impurity solver. In the underdoped regime, we find a natural decomposition of the one-particle (photoemission) energy gap into two components. The gap in the nodal regions, stemming from the anomalous self-energy, decreases with decreasing doping. The antinodal gap has an additional contribution from the normal component of the self-energy, inherited from the normal-state pseudogap, and it increases as the Mott insulating phase is approached.