Quantum-critical fluctuations in 2D metals: strange metals and superconductivity in antiferromagnets and in cuprates

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 , measured from the ordering vector, and of the frequency ω and the temperature T which scale as 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 for all momenta, a resistivity , a 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. This reveals, in agreement with the theory, that the frequency dependence of the attractive irreducible particle–particle vertex in the d-wave channel is the same as the irreducible particle-hole vertex in the full symmetry of the lattice.