Critical fermi surfaces and non-fermi liquid metals

TL;DR

This work develops a scaling framework for quantum critical metals in which an entire Fermi surface disappears yet remains sharply defined, yielding a critical Fermi surface with no Landau quasiparticles. The authors formulate a general scaling form for the single-particle spectral function with possible angular dependence of the exponents, and extend the scaling to thermodynamics and two-particle correlators, including a distinctive 2Kf surface. They explore the consequences of angle-dependent exponents, predicting finite-temperature regimes with gapless Fermi arcs and applying the framework to cuprates, heavy-fermion systems, and Mott transitions via a slave-particle mean-field theory. The study provides a coherent route to understand strange-metal behavior, non-Fermi-liquid excitations, and Fermi-surface reconstructions, with clear experimental signatures in ARPES, transport, and quantum oscillations.

Abstract

At certain quantum critical points in metals an entire Fermi surface may disappear. A crucial question is the nature of the electronic excitations at the critical point. Here we provide arguments showing that at such quantum critical points the Fermi surface remains sharply defined even though the Landau quasiparticle is absent. The presence of such a critical Fermi surface has a number of consequences for the universal phenomena near the quantum critical point which are discussed. In particular the structure of scaling of the universal critical singularities can be significantly modified from more familiar criticality. Scaling hypotheses appropriate to a critical fermi surface are proposed. Implications for experiments on heavy fermion critical points are discussed. Various phenomena in the normal state of the cuprates are also examined from this perspective. We suggest that a phase transition that involves a dramatic reconstruction of the Fermi surface might underlie a number of strange observations in the metallic states above the superconducting dome.

Figures (7)

• Figure 1: Possible schematic zero temperature phase diagram showing the onset of magnetism in a heavy fermion metal. The magnetic phase is a 'local moment magnetic metal' where the local moments are not part of the Fermi surface unlike in the heavy Fermi liquid. The Fermi surface needs to reconstruct across such a quantum phase transition.
• Figure 2: Possible schematic zero temperature phase diagram for a half-filled single band repulsive Hubbard model on a non-bipartite lattice. $U$ is the Hubbard interaction strength and $t$ is the hopping amplitude. The Fermi surface of the metal needs to disappear at the Mott transition.
• Figure 3: Possible schematic zero temperature phase diagram for the cuprate materials showing the evolution of the 'underlying normal' ground state as a function of doping. The large Fermi surface of the overdoped metal is presumed to disappear at a critical doping $x_c$ to an underdoped metal with a qualitatively different 'small' Fermi surface.
• Figure 4: Evolution of the ground state momentum distribution $n(k)$ across a second order phase transition where the Fermi surface disappears, such as the Mott transition of Fig. \ref{['mottpdia']}. (a) $n(k)$ in the Fermi liquid with a discontinuity $Z$ at the Fermi surface. (b) $n(k)$ in the Mott insulator which is smooth as a function of $k$. (c) $n(k)$ at the critical point - the discontinuity of (a) has just vanished and is replaced by a kink singularity.
• Figure 5: Finite temperature crossovers near a second order Mott transition with angle dependent exponents on the critical Fermi surface.