# Screening and Topological Order in Thin Superconducting Films

## TL;DR

This paper develops a 2D effective theory for thin superconducting films interacting with 3D electromagnetic fields, analyzing plasma oscillations, charge-vortex interactions, and topological order.

## Contribution

It introduces a novel low-energy effective theory for thin superconducting films coupled to 3D electromagnetic fields and explores their topological properties.

## Key findings

- Derived the effective 2D low-energy theory for thin films
- Analyzed plasma oscillations and charge-vortex interactions
- Assessed the topological order in superconducting films

## Abstract

We derive an effective two-dimensional low-energy theory for thin superconducting films coupled to a three-dimensional fluctuating electromagnetic field. Using this theory we discuss plasma oscil- lations, interactions between charges and vortices and extract the energy of a vortex. Having found that the effective theory properly describes the long distance physics, we then use it to investigate to what extent the superconducting film is a topologically ordered phase of matter.