Related papers: Boundary RG Flows for Fermions and the Mod 2 Anoma…
We study boundary states for Dirac fermions in d=1+1 dimensions that preserve Abelian chiral symmetries, meaning that the left- and right-moving fermions carry different charges. We derive simple expressions, in terms of the fermion charge…
Usually, a left-moving fermion in d=1+1 dimensions reflects off a boundary to become a right-moving fermion. This means that, while overall fermion parity $(-1)^F$ is conserved, chiral fermion parity for left- and right-movers individually…
It is known that the $2+1$d single Majorana fermion theory has an anomaly of the reflection, which is canceled out when 16 copies of the theory are combined. Therefore, it is expected that the reflection symmetric boundary condition is…
It has recently been demonstrated that protected supersymmetry emerges on the boundaries of one-dimensional intrinsically fermionic symmetry protected trivial (SPT) phases. Here we investigate the boundary supersymmetry of one-dimensional…
Majorana bound states are interesting candidates for applications in topological quantum computation. Low energy models allowing to grasp their properties are hence conceptually important. The usual scenario in these models is that two…
Extending the results of a previous paper, we consider boundary conditions for spinor fields and other fields of non-zero spin in the AdS/CFT correspondence. We calculate the RG-flow induced by double trace perturbations dual to bulk spinor…
Boundary conditions for a massless Dirac fermion in 2+1 dimensions where the space is a half-plane are discussed in detail. It is argued that linear boundary conditions that leave the Hamiltonian Hermitian generically break $C$ $P$ and $T$…
We calculate the ground state current densities for 2+1 dimensional free fermion theories with local, translationally invariant boundary states. Deformations of the bulk wave functions close to the edge and boundary states both may cause…
Recently Gaiotto [1] considered conformal defects which produce an expansion of infrared local fields in terms of the ultraviolet ones for a given renormalization group flow. In this paper we propose that for a boundary RG flow in two…
A junction between two boundaries of a topological superconductor (TSC), mediated by localized edge modes of Majorana fermions, is investigated. The tunneling of fermions across the junction depends on the magnetic flux. It breaks the…
Majorana modes and fractional fermions are two types of edge zero modes appearing separately in topological superconductors and dimerized chains. Here we reveal how to harvest both types of edge modes simultaneously in an exotic chain. Such…
We derive a semi-classical formula for computing the spectrum of bound states made of Majorana fermions in a generic non-integrable 2d quantum field theory with a set of degenerate vacua. We illustrate the application of the formula in a…
We study the p-wave superconducting wire with a periodically modulated chemical potential and show that the Majorana edge states are robust against the periodic modulation. We find that the critical amplitude of modulated potential, at…
Certain one-dimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point. A finite system of length $L$ possesses two ground states with an energy…
We investigate interference of Majorana fermions (MFs) in NS junctions. A general formula of charge conductance G for NS junctions with two MFs is derived based on the low energy effective model. It is found that G for two MFs takes various…
The zig-zag symmetry transition is a phase transition in 1D quantum wires, in which a Wigner lattice of electrons transitions to two staggered lattices. Previous studies model this transition as a Luttinger liquid coupled to a Majorana…
Majorana fermion dynamics may arise at the edge of Kitaev wires or superconductors. Alternatively, it can be engineered by using trapped ions or ultracold atoms in an optical lattice as quantum simulators. This motivates the theoretical…
In this paper we study the interaction between magnetic monopoles and massless fermions. In the low energy limit, the monopole's magnetic field polarizes the fermions into purely in-going and out-going modes. Unitarity requires that the UV…
We propose to realize Majorana fermions (MFs) on an edge of a two-dimensional topological insulator in the proximity with s-wave superconductors and in the presence of transverse exchange field h. It is shown that there appear a pair of MFs…
A conformally invariant theory of Majorana fermions in 2<d<4 with O(N) symmetry is studied using Operator Product Expansions and consistency relations based on the cancellation of shadow singularities. The critical coupling G_{*} of the…