# Topological phase transition from nodal to nodeless d-wave superconductivity in electron-doped cuprate superconductors

## TL;DR

This paper presents a unified topological theory explaining the transition from nodal to nodeless d-wave superconductivity in electron-doped cuprates, highlighting the role of antiferromagnetic order and topological properties.

## Contribution

It introduces a topological framework for understanding the phase transition between nodal and nodeless superconductivity in electron-doped cuprates using the t-J model.

## Key findings

- Nodal phase exhibits protected edge modes and vorticity.
- Transition involves annihilation of nodes with opposite vorticity.
- Nodeless phase emerges as a topological strong-pairing phase.

## Abstract

Unlike the hole-doped cuprates, both nodal and nodeless superconductivity (SC) are observed in the electron-doped cuprates. To understand these two types of SC states, we propose a unified theory by considering the two-dimensional t-J model in proximity to an antiferromagnetic (AF) long-range ordering state. Within the slave-boson mean-field approximation, the d-wave pairing symmetry is still the most energetically favorable even in the presence of the external AF field. In the nodal phase, it is found that the nodes carry vorticity and are protected by the adjoint symmetry of time-reversal and one unit lattice translation. Robust edge modes are obtained, suggesting the nodal d-wave SC being a topological weak-pairing phase. As decreasing the doping concentration or increasing the AF field, the nodes with opposite vorticity annihilate and the nodeless strong-pairing phase emerges. The topological phase transition is characterized by a critical point with anisotropic Bogoliubov quasiparticles, and a universal understanding is thus established for all electron-doped cuprates.