Quantum Critical Eliashberg Theory

TL;DR

This paper reviews the quantum critical Eliashberg theory, highlighting its role in understanding non-Fermi liquid behavior, unconventional superconductivity, and the interplay of electronic and bosonic fluctuations near quantum phase transitions.

Contribution

It extends conventional Eliashberg theory to non-Fermi liquid regimes and connects quantum criticality with holographic superconductivity, offering new insights into strongly correlated systems.

Findings

Breakdown of quasiparticle coherence near quantum critical points

Emergence of universal scaling behaviour in non-Fermi liquids

Possibility of Cooper pairing without well-defined quasiparticles

Abstract

Quantum criticality plays a central role in understanding non-Fermi liquid behavior and unconventional superconductivity in strongly correlated systems. In this review, we explore the quantum critical Eliashberg theory, which extends conventional Eliashberg approaches to non-Fermi liquid regimes governed by critical fluctuations. We discuss the theoretical foundations and recent developments in the field, focusing on the interplay between electronic interactions and bosonic modes near quantum phase transitions as described in the Yukawa-coupled version of the Sachdev-Ye-Kitaev model. Special emphasis is placed on the breakdown of quasiparticle coherence, anomalous scaling behaviour, Cooper pairing without quasiparticles, and emergent universality in different physical settings. Starting from a zero-dimensional "quantum-dot" model, we discuss the generalization to higher spatial dimensions and demonstrate the connection between quantum-critical Eliashberg theory and holographic superconductivity. Our analysis provides a perspective on how quantum criticality shapes the dynamics of strongly correlated metals and superconductors.