Topological states of multiband superconductors with interband pairing

We study the effects of interband pairing in two-band <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>s</a:mi></a:math>-wave and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>d</b:mi></b:math>-wave superconductors with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi mathvariant="bold">D</c:mi><c:mrow><c:mn>4</c:mn><c:mi>h</c:mi></c:mrow></c:msub></c:math> symmetry in both time-reversal invariant as well as time-reversal symmetry-breaking states. The presence of interband pairing qualitatively changes the nodal structure of the superconductor: nodes can (dis)appear, merge, and leave high-symmetry locations when interband pairing is tuned. Furthermore, in the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>d</e:mi></e:math>-wave case, we find that also the boundary modes change qualitatively when interband pairing increases: flat zero-energy Andreev bound states gap out and transition to helical edge states.