Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice

TL;DR

This paper analyzes the topological phases of spin-singlet superconductivity in the hyperhoneycomb lattice, revealing a rich phase diagram with topologically nontrivial line-nodal states, trivial fully gapped states, and the effects of doping, symmetry, and spin-orbit coupling.

Contribution

It provides an analytical derivation of the full phase diagram of topological superconducting states in the hyperhoneycomb lattice using symmetry and topology, including the effects of doping and lattice deformations.

Findings

Line-nodal state is topologically nontrivial with Majorana flat bands.

Higher doping leads to a fully gapped, topologically trivial state.

Point nodal state at low doping has nontrivial topology with Fermi surface arcs.

Abstract

We establish the topology of the spin-singlet superconducting states in the bare hyperhoneycomb lattice and derive analytically the full phase diagram using only symmetry and topology in combination with simple energy arguments. The phase diagram is dominated by two states preserving time-reversal symmetry. We find that the line-nodal state dominating at low doping levels is topologically nontrivial and exhibits surface Majorana flat bands, which we show perfectly match the bulk-boundary correspondence using Berry phase approach. At higher doping levels we find a fully gapped state with trivial topology. By analytically calculating the topological invariant of the line nodes, we derive the critical point between the line-nodal and fully gapped states as a function of both pairing parameters and doping. We find that the line-nodal state is favored not only at lower doping levels but also if symmetry-allowed deformations of the lattice is present. Adding simple energy arguments we establish that a fully gapped state with broken time-reversal symmetry likely appears covering the actual phase transition. We find this time-reversal symmetry broken state to be topologically trivial, while we find an additional point nodal state at very low doping levels to have nontrivial topology with associated Fermi surface arcs. We eventually address the robustness of the phase diagram to generalized models also including adiabatic spin-orbit coupling, and show how all but the point nodal state are reasonably stable.