Interacting flat-band Majorana modes at surfaces of noncentrosymmetric superconductors

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Topological properties of solids currently form one of the most active areas in condensed matter physics. These are global properties of their electronic structure that are connected with the existence of robust electronic states localized at their surfaces. A specific type of topological solid is realized by superconductors that possess strong spin-orbit coupling and time-reversal symmetry but lack spatial inversion symmetry. If the superconducting order parameter has nodes (zeroes) in momentum space, such systems should support dispersionless zero-energy Majorana surface states. The Majorana property means that they are their own antiparticles. The absence of dispersion implies that there is a macroscopic number of them, which makes these systems particularly intriguing. The present project addresses the stability of the dispersionless zero-energy Majorana states. On the one hand, it extends our preliminary work by exploring under what conditions the states are shifted to nonzero energies by the spontaneous breaking of time-reversal or spatial symmetries. On the other, the project studies the effects of (unavoidable) interactions between the Majorana states. The interacting Majorana states form a fascinating novel many-body system since its energy contains only the contribution from the interactions - the kinetic energy is zero due to the absence of dispersion. We plan to derive the relevant interacitons, study the ground state and low-lying excitations of the corresponding models, and make predictions for suitable experimental probes.