We discuss electric transport through a point contact which bridges Majorana fermion modes appearing at edges of two helical superconductors. The contents focus on the effects of interference and interaction unique to the Majorana fermions and the role of spin-orbit interaction (SOI). Besides the Josephson current, the quasiparticle conductance depends sensitively on the phase difference and re...

What distinguishes trivial superfluids from topological superfluids in interacting many-body systems where the number of particles is conserved? Building on a class of integrable pairing Hamiltonians, we present a number-conserving, interacting variation of the Kitaev model, the Richardson-Gaudin-Kitaev chain, that remains exactly solvable for periodic and antiperiodic boundary conditions. Our ...

Ettore Majorana has been missing for 74 years, but his most important legacy in physics is lately very much in the news. The still-hypothetical Majorana fermion is in a sense a completely ‘real’ particle — its mathematical representation doesn’t have an imaginary part — it is, therefore, its own antiparticle. Whereas particle physics was the context of the original proposal — and experiments ai...

The existence of three generations of neutrinos and their mass mixing are the deep mysteries of our universe. The history of neutrino physics can be traced back to Majorana’s elegant work on a real solution of the Dirac equation – known as the Majorana fermion. A cutting-edge step towards understanding the nature of neutrino has been taken by the experimental discovery of neutrino mass mixing d...

The Fermion Spherical harmonics [Y m l (θ, φ) for half-odd-integer l and m presented in a previous paper] are shown to have the same eigenfunction properties as the well-known Boson Spherical Harmonics [Y m l (θ, φ) for integer l and m]. The Fermion functions are shown to differ from the Boson functions in so far as the ladder operators M+ (M−) that ascend (descend) the sequence of harmonics ov...

We present a formalism that extends the Majorana-construction to arbitrary spin (j, 0)⊕(0, j) representation spaces. For the example case of spin-1, a wave equation satisfied by the Majorana-like (1, 0) ⊕ (0, 1) spinors is constructed and its physical content explored. The (j, 0) ⊕ (0, j) Majorana-construct is found to possess an unusual classical and quantum field theoretic structure. Relevanc...

The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for Lüscher’s gauge-invariant lattice formulation of chiral gauge theories. We can explicitly construct the fermion integration measure globally over the gauge-field configuration space in the arbitrary topological sector; there is no global obstruction corresponding to the Witten ano...

The report discusses the spinless-fermion (holon) representation of the t-J model and describes a new analytical representation in which fermion operators are directly related to the physical electron operators and have spin. A simple, leading-order, treatment of the magnetic dynamics allows to take into account the spin-liquid aspect of the ground state. The obtained effective model, in compar...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.