Metallogenic quantum criticality: Fermi surface nucleation at transitions between gapped phases

Abstract

Continuous quantum phase transitions in interacting many-body systems exhibit universal phenomena that are largely independent of microscopic details. An organizing principle distilled from canonical examples such as the magnetic transition in Ising models is that the low-energy physics of transitions between gapped phases is governed by scale-invariant quantum field theories with gapless degrees of freedom at isolated points in momentum space. In this paper, we show that this principle can fail in a radical way: an entire gapless Fermi surface can emerge at a quantum critical point separating two fully gapped insulators. These exotic phase transitions are dubbed \textit{metallogenic quantum critical points} (MGQCP). We construct a controlled family of effective field theories for MGQCPs between distinct fractional Chern insulators and propose a periodically modulated quantum Hall bilayer as a minimal microscopic setting. The critical theory exhibits an unusual mixture of physical signatures: while transport and compressibility follow scaling laws compatible with a conformal field theory, the electron spectral function develops a power-law non-analyticity at the Fermi momentum, characteristic of non-Fermi-liquid metals. We discuss how the concept of MGQCP may shed new light on critical phenomena in moire materials with tunable Chern bands. More generally, our results point to a broader class of quantum critical phenomena in which extended manifolds of gapless excitations emerge in momentum space despite being absent in both neighboring phases.