Inversion-protected higher-order topological superconductivity in monolayer WTe2

Monolayer WTe2, an inversion-symmetric transition metal dichalcogenide, has recently been established as a quantum spin Hall insulator and found superconducting upon gating. Here we show that generally a superconducting inversion-symmetric quantum spin Hall material whose normal state is ``effectively gapped", such as gated monolayer WTe2, can be an inversion-protected topological crystalline superconductor featuring ``higher-order topology" if the superconductivity is parity-odd. We explicitly demonstrate how the bulk-boundary correspondence naturally emerges in such type of superconductors within a two-dimensional minimal model. We then study the pairing symmetry of superconducting WTe2 with a microscopic model, and find two types of self-consistently obtained exotic pairings. First is an odd-parity pairing that possesses a nontrivial bulk symmetry indicator and hosts two Majorana Kramers pairs localizing at opposite corners. Even when the conventional pairing is energetically favored, we find that an intermediate in-plane field exceeding the Pauli limit stabilizes an equal-spin pairing aligning with the field. Our findings suggest gated monolayer WTe2 is a playground for exotic odd-parity superconductivity, and possibly the first material realization for inversion-protected Majorana corner modes without utilizing proximity effect.