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Noncentrosymmetric superconductors can support flat bands of zero-energysurface states in part of their surface Brillouin zone. This requires that theyobey time-reversal symmetry and have a sufficiently strongtriplet-to-singlet-pairing ratio to exhibit nodal lines in the bulk. Thesebands are protected by a winding number that relies on chiral symmetry, whichis realized as the product of time-reversal and particle-hole symmetry. Wereveal a way to stabilize a flat band in the entire surface Brillouin zone,while the bulk dispersion is fully gapped. This idea could lead to a robustplatform for quantum computation and represents an alternative route tostrongly correlated flat bands in two dimensions, besides twisted bilayergraphene. The necessary ingredient is an additional spin-rotation symmetry thatforces the direction of the spin-orbit-coupling vector not to depend on themomentum component normal to the surface. We define a winding number whichleads to flat zero-energy surface bands due to bulk-boundary correspondence. Wediscuss under which conditions this winding number is nonzero in the entiresurface Brillouin zone and verify the occurrence of zero-energy surface statesby exact numerical diagonalization of the Bogoliubov-de Gennes Hamiltonian fora slab. In addition, we consider how a weak breaking of the additional symmetryaffects the surface band, employing first-order perturbation theory and aquasiclassical approximation. We find that the surface states and the bulk gappersist for weak breaking of the additional symmetry but that the band does notremain perfectly flat. The broadening of the band strongly depends on thedeviation of the spin-orbit-coupling vector from its unperturbed direction aswell as on the spin-orbit-coupling strength and the triplet-pairing amplitude.

Complete zero-energy flat bands of surface states in fully gapped chiral noncentrosymmetric superconductors