# Pseudogap crossover in the electron-phonon system

**Authors:** Ilya Esterlis, Steven Kivelson, Douglas Scalapino  
**arXiv:** [1811.10622](https://arxiv.org/abs/1811.10622)  
**Date:** 2018-11-26  
**Summary page:** https://www.summarizepaper.com/en/paper/1811.10622v1/

## Key points

- Utilization of Monte Carlo methods and strong-coupling (bipolaronic) expansion
- Investigation of electron-phonon problem with phonon frequencies much smaller than bare Fermi energy
- Discovery of short-range charge-density wave (CDW) and superconducting (SC) correlations at elevated temperatures
- Notable crossover from normal metallic regime to pseudogap regime as electron-phonon coupling parameter $\lambda_0$ increases
- Emergence of distinct phases at lower temperatures based on $\lambda_0$ value:
- Small $\lambda_0$: superconducting (SC) phase observed, indicating zero resistance behavior
- Large $\lambda_0$: commensurate insulating CDW phase manifested, showing ordered arrangement of charges
- Insight into interplay between electron-phonon interactions and thermodynamic properties in condensed matter systems
- Contribution to understanding fundamental physics principles and exploration of novel electronic phases in materials governed by strong electron-phonon coupling

## Summary

By utilizing Monte Carlo methods and a strong-coupling (bipolaronic) expansion, as well as a weak coupling Migdal-Eliashberg approach, Esterlis et al. investigate the electron-phonon problem with phonon frequencies significantly smaller than the bare Fermi energy. Their research uncovers a fascinating phenomenon at elevated temperatures where short-range charge-density wave (CDW) and superconducting (SC) correlations coexist. As the electron-phonon coupling parameter $\lambda_0$ increases, a notable crossover occurs from a normal metallic regime to a pseudogap regime. This transition is particularly intriguing as it signifies a shift in the material's behavior towards exhibiting characteristics of both metallic and insulating phases. At lower temperatures, distinct phases emerge based on the value of $\lambda_0$. For small values of this parameter, a superconducting (SC) phase is observed, indicating the presence of coherent pairs of electrons exhibiting zero resistance. Conversely, for large $\lambda_0$, a commensurate insulating CDW phase manifests, highlighting an ordered arrangement of charges within the material. The findings presented by Esterlis et al. shed light on the intricate interplay between electron-phonon interactions and thermodynamic properties in condensed matter systems. Their work not only contributes to our understanding of fundamental physics principles but also paves the way for further exploration into novel electronic phases and phenomena in materials governed by strong electron-phonon coupling.