Evidence for topological contribution to spin shift current in antiferromagnetic Ti$$_{4}$$C$$_{3}$$

The shift current is a non-linear photocurrent generally associated with the underlying quantum geometry. However, a topological origin for the shift photocurrent in non-centrosymmetric systems has recently been proposed. The corresponding topological classification goes beyond the ten-fold paradigm and is associated with the presence of a reverting Thouless pump (RTP). In this work we perform a first-principles computational analysis of antiferromagnetic monolayer within the family of MXenes, Ti[Formula: see text]C[Formula: see text]. This material is centrosymmetric, however, magnetic ordering violates inversion symmetry. We demonstrate evidence of an RTP in each spin-sector which has been perturbed, destroying quantization of the invariant. Nevertheless, a giant spin-resolved shift current persists. We further investigate the mid-gap edge states and classification of the system as a fragile topological insulator to which trivial bands have been coupled.