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For inversion-symmetric topological insulators and superconductors characterized by ${\mathbb Z}_{2}$ topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling…
A time-reversal invariant Kitaev-type model is introduced in which spins (Dirac matrices) on the square lattice interact via anisotropic nearest-neighbor and next-nearest-neighbor exchange interactions. The model is exactly solved by…
Two-dimensional second-order topological superconductors host zero-dimensional Majorana bound states at their boundaries. In this work, focusing on rotation-invariant crystalline topological superconductors, we establish a bulk-boundary…
Topological phases in one-dimensional superconducting systems are commonly characterized by symmetry-protected invariants. These invariants determine the number of Majorana zero-energy boundary modes but do not specify their corresponding…
We propose a simple model consisting of a magnetic domain wall proximity-coupled to an $s$-wave superconductor for realization of Majorana zero-energy modes. A spin-dependent gauge transformation translates the rotating magnetic profile…
We examine the topological properties of a spin-singlet superconductor with Rashba and Dresselhaus (110) spin-orbit couplings. We demonstrate that there are several topological invariants in the Bogoliubov-de Gennes (BdG) Hamiltonian by…
We discuss a (2+1) dimensional topological superconductor with $N_f$ left- and right-moving Majorana edge modes and a $\mathbb{Z}_2\times \mathbb{Z}_2$ symmetry. In the absence of interactions, these phases are distinguished by an integral…
We study a chain of ferromagnetic nano-particles or ferromagnetic molecule/atoms on a substrate of fully gapped superconductors. We find that under quite realistic conditions, the fermion-number-parity symmetry $Z_2^f$ can spontaneously…
It has recently been realized that zero modes with projective non-Abelian statistics, generalizing the notion of Majorana bound states, may exist at the interface between a superconductor and a ferromagnet along the edge of a fractional…
Topological materials rely on engineering global properties of their bulk energy bands called topological invariants. These invariants, usually defined over the entire Brillouin zone, are related to the existence of protected edge states.…
We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial dimensions $d\ge 1$. When the Fermi level lies in a spectral gap or a mobility gap, the topological properties, e.g., the integral quantization of…
Topological insulator (TI) nanowires in proximity with conventional superconductors have been proposed as a tunable platform to realize topological superconductivity and Majorana zero modes (MZM). The tuning is done using an axial magnetic…
We study the competition of disorder and superconductivity for a one-dimensional p-wave superconductor in incommensurate potentials. With the increase in the strength of the incommensurate potential, the system undergoes a transition from a…
We present a comprehensive study of two of the most experimentally relevant extensions of Kitaev's spinless model of a 1D p-wave superconductor: those involving (i) longer range hopping and superconductivity and (ii) inhomogeneous…
We consider theoretically the physics of bulk topological superconductivity accompanied by boundary non-Abelian Majorana zero modes in semiconductor-superconductor (SM-SC) hybrid systems consisting of finite wires in the presence of…
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of…
We present a new scheme for Majorana modes in systems with nonsymmporhic-symmetry-protected band degeneracy. We reveal that when the gapless fermionic excitations are encoded with conventional superconductivity and magnetism, which can be…
The interplay of disorder and short finite wire length is the crucial physics hindering progress in the semiconductor-superconductor nanowire platform for realizing non-Abelian Majorana zero modes (MZM). Disorder effectively segments the…
In light of recent progress in the study of amorphous topological phases, we investigate the effects of structural disorder on the topological properties of a two-dimensional quantum spin Hall insulator modeled by the Bernevig-Hughes-Zhang…
We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians H(k,r) that vary slowly with adiabatic…