Abstract 26 January 2016

New phases from interacting Majorana fermions

Marcel Franz,  University of British Columbia, Canada

Vortices in the Fu-Kane model (describing a superconducting surface of a 3D topological insulator) are known to host Majorana zero modes. By adjusting a single system parameter -- the global chemical potential -- the zero modes can be tuned to the regime of strong interactions. In this talk I will describe the simplest interacting system that can be built from these ingredients: a 1D Majorana chain with nearest neighbor hopping and the most local 4-fermion interaction. The system exhibits a complex phase diagram with interesting phases and phase transitions between them. These include a gapless Ising phase for attractive interactions separated from a doubly degenerate gapped phase at strong coupling by a quantum critical point in the tricritical Ising universality class. For weak repulsive interactions we find an interesting gapless phase with coexisting Luttinger liquid and Ising degrees of freedom. The latter is separated from a 4-fold degenerate gapped phase at strong coupling by a novel generalization of the commensurate-incommensurate transition.



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