Quantum-Critical Fluctuations in 2D Metals: Strange Metals and Superconductivity in Antiferromagnets and in Cuprates

TL;DR

This paper presents a unified model based on quantum-critical fluctuations described by the dissipative XY model, explaining the strange metal behavior and superconductivity in diverse 2D materials like cuprates and heavy-fermion compounds.

Contribution

It introduces a common statistical mechanical framework for quantum-criticality in various 2D materials, emphasizing topological excitations over traditional spin-wave theories.

Findings

Fluctuations follow a separable momentum and frequency dependence, scaling as tanh(ω/2T).

Experimental neutron scattering data align with the predicted fluctuation form.

The model accounts for marginal Fermi-liquid behavior and d-wave superconductivity in these compounds.

Abstract

The anomalous transport and thermodynamic properties in the quantum-critical region, in the cuprates, and in the quasi-two dimensional Fe-based superconductors and heavy-fermion compounds, have the same temperature dependences. This can occur only if, despite their vast microscopic differences, a common statistical mechanical model describes their phase transitions. The antiferromagnetic (AFM)-ic models for the latter two, just as the loop-current model for the cuprates, map to the dissipative XY model. The solution of this model in 2+1 D reveals that the critical fluctuations are determined by topological excitations, vortices and a variety of instantons, and not by renormalized spin-wave theories of the Landau-Ginzburg-Wilson type, adapted by Moriya, Hertz and others for quantum-criticality. The absorptive part of the fluctuations is a separable function of momentum ${\bf q}$, measured from the ordering vector, and of the frequency $\omega$ and the temperature $T$ which scale as $\tanh(\omega/2T)$ at criticality. Direct measurements of the fluctuations by neutron scattering in the quasi-two-dimensional heavy fermion and Fe-based compounds, near their antiferromagnetic quantum critical point, are consistent with this form. Such fluctuations, together with the vertex coupling them to fermions, lead to a marginal fermi-liquid, with the imaginary part of the self-energy $\propto max(\omega, T)$ for all momenta, a resistivity $\propto T$, a $T \ln T$ contribution to the specific heat, and other singular fermi-liquid properties common to these diverse compounds, as well as to d-wave superconductivity. This is explicitly verified, in the cuprates, by analysis of the pairing and the normal self-energy directly extracted from the recent high resolution angle resolved photoemission measurements.