Topological superconductivity in hexagonal lattice systems

Topological superconductors are amongst the most desired phase of quantum matter, as they can host so-called midgap states in their energy spectra, commonly known as Majorana zero modes. In particular, chiral – i.e., time-reversal breaking – superconductors can be characterised by the Chern number, just like quantum Hall insulators.

Hexagonal lattices systems are promising platforms in the search for topological superconduc- tors. These lattices rose to prominence following the experimental fabrication of the graphene and other two-dimensional van der Waals materials, including the recently discovered “twisted materials”.

The functional renormalisation group is well suited to discern between competing many-body instabilities in an unbiased way. We employ the truncated-unity formulation of the functional renormalisation group to calculate rich phase diagrams with magnetic, charge-density wave, and superconducting phases. Moreover, we calculate the Chern numbers associated with the superconducting instabilities. [1] Finally, we show the drastic effect of spin-orbit coupling to our results, expected to be relevant for heterostructures and non-centrosymmetric materials.