Exactly Solvable Majorana-Anderson Impurity Models

Majorana fermions emerge in topological superconductors as end zero modes in one dimension, and vortex-trapped zero modes or chiral edge modes in two dimensions. A question of much recent interest is the effect of electron-electron interactions on such Majorana fermions. We introduce exactly solvable Majorana-Anderson impurity models that describe an interacting Anderson impurity (i) immersed in tight-binding lattices of Majorana modes in one and two dimensions, (ii) coupled to the Majorana end mode of a Kitaev chain, and (iii) coupled to the edge mode of a chiral p-wave superconductor. The Ising slave-spin representation is used to map our interacting models to models of free auxiliary Majorana fermions. In each case, we calculate exact spectral functions for the impurity fermions and observe a nontrivial temperature dependence as a signature of interactions. Spectral functions for the host fermions are also calculated to study the feedback effect of the impurity on the superconducting host. We compare our exact results to those obtained from strong-coupling perturbation theory.