Topological Pair-Density-Wave Superconducting States

TL;DR

This paper demonstrates that a topological pair-density-wave superconducting state in 2D ladder models hosts Majorana zero modes, characterized by a charge-4e order parameter and requiring bosonization for analysis.

Contribution

It introduces a topological PDW superconducting state with Majorana zero modes, analyzed via bosonization, highlighting its exotic charge-4e pairing and topological properties.

Findings

Presence of Majorana zero modes at boundaries and junctions.

The PDW state exhibits a charge-4e superconducting order.

Conventional mean-field theory is insufficient; bosonization is used.

Abstract

We show that the pair-density-wave (PDW) superconducting state emergent in extended Heisenberg-Hubbard models in two-leg ladders is topological in the presence of an Ising spin symmetry and supports a Majorana zero mode (MZM) at an open boundary and at a junction with a uniform $d$-wave one-dimensional superconductor. Similarly to a conventional finite-momentum paired state, the order parameter of the PDW state is a charge-$2e$ field with finite momentum. However, the order parameter here is a {\it quartic} electron operator and conventional mean-field theory cannot be applied to study this state. We use bosonization to show that the 1D PDW state has a MZM at a boundary. This superconducting state is an exotic topological phase supporting Majorana fermions with finite-momentum pairing fields and charge-$4e$ superconductivity.