# Collective modes in two dimensional topological superconductors

## TL;DR

This paper investigates collective excitations in two-dimensional topological superconductors using an extended random phase approximation, revealing gapless modes and their potential interactions with quasi-particles.

## Contribution

It provides analytical results for longitudinal collective modes in topological superconductors, considering both non-SOC and strong SOC cases, and explores their quantum field properties.

## Key findings

- Identified gapless longitudinal modes in 2D topological superconductors.
- Calculated effective mode volumes and expressed fields as creation/annihilation operators.
- Analyzed potential interactions between collective modes and quasi-particles.

## Abstract

Collective modes in two dimensional topological superconductors are studied by an extended random phase approximation theory while considering the influence of vector field of light. In two situations, the s-wave superconductors without spin-orbit-coupling (SOC), and the hybrid semiconductor and s-wave superconductor layers with strong SOC, we get the analytical results for longitudinal modes which are found to be indeed gapless. Further more, the effective modes volumes can be calculated, the electric and magnetic fields can be expressed as the creation and annihilation operators of such modes. So, one can study the interaction of them with other quasi-particles through fields.