We propose a setup to realize time-reversal-invariant topological superconductors in quantum wires, proximity coupled to conventional superconductors. We consider a model of quantum wire with strong spin-orbit coupling and proximity coupling to two s-wave superconductors. When the relative phase between the two superconductors is ϕ=π a Kramers pair of Majorana zero modes appears at each edge of...

We numerically investigate the surface states of a strong topological insulator in the presence of strong electron-electron interactions. We choose a spherical topological insulator geometry to make the surface amenable to a finite size analysis. The single-particle problem maps to that of Landau orbitals on the sphere with a magnetic monopole at the center that has unit strength and opposite s...

We prove two Lieb-Schultz-Mattis type theorems that apply to any translationally invariant and local fermionic $d$-dimensional lattice Hamiltonian for which fermion-number conservation is broken down the of fermion parity. show when internal symmetry group ${G}_{f}^{\phantom{\rule{0.16em}{0ex}}}$ realized locally (in a repeat unit cell lattice) by nontrivial projective representation, then grou...

We show how to determine the lowest order mixing of all scalar with twofermion two impurity BMN operators in the antisymmetric representation of SO(4). Differentiation on harmonic superspace allows one to derive two-loop anomalous dimensions of gauge invariant operators from this knowledge: the value for the second anomalous correction to the dimension is essentially the square of the two-fermi...

In 1937 the Italian physicist Ettore Majorana proposed the existence of a massless, chargeless, spinless particle that is its own antiparticle. Such a Majorana fermion would have an extraordinarily large phase coherence time, making it an ideal building block for a quantum computer. However, no Majorana fermions are known to exist asfundamental particles. The recent discovery of topological sta...

a new derivation of the quantum boltzmann transport equation for the fermion system from the quantum time evolution equation for the wigner distribution function is presented. the method exhibits the origin of the time - irreversibility of the boltzmann equation. in the present work, the spin dependent and indistinguishibility of particles are also considered.

The review is aimed at highlighting the aspects of topological superconductivity in absence spin-orbit interaction two-dimensional systems with long-range non-collinear spin ordering or magnetic skyrmions. Another purpose to give a brief introduction new concept superconductivity, i.e. higher-order topology including coupled structures. formation Majorana modes due textures discussed. role effe...