One-dimensional scattering of two-dimensional fermions near quantum criticality

Abstract

Forward and backscattering play an exceptional role in the physics of two-dimensional interacting fermions. In a Fermi liquid, both give rise to a non-analytic ${\omega }^2\log (\omega )$ form of the fermionic scattering rate at second order in the interaction. Here we argue that higher powers of $\log (\omega )$ appearin the backscattering contribution at higher orders. We show that these terms come from "planar" processes, which are effectively one-dimensional. This is explicitly demonstated by extending a Fermi liquid to the limit of $N\gg 1$ fermionic flavors, when only planar processes survive. We sum the leading logarithms for the case of a 2D Fermi liquid near a nematic transition and obtain an expression for the scattering rate at $T=0$ to all orders in the interaction. For a repulsive interaction, the resulting rate is logarithmically suppressed, and the result is valid down to $\omega =0$. For an attractive interaction, the ground state is an $s$-wave superconductor with a gap ${\Delta }_0$. We show that in this case the scattering rate increases as $\omega$ is reduced towards ${\Delta }_0$. At $\omega \ge {\Delta }_0$, the behavior of the scattering rate is rather unconventional as many pairing channels compete near a nematic critical point, and $s$-wave wins only by a narrow margin. We take superconductivity into consideration and obtain the scattering rate also at smaller $\omega \simeq {\Delta }_0$.

21 pages; journal version

References in corpus (15)

• Iron-Based Superconductors: current status of materials and pairing mechanism
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Enhancement of superconductivity near a nematic quantum critical point
• Are non-Fermi-liquids stable to Cooper pairing?
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Phenomenology of the normal state in-plane transport properties of high-$T_c$ cuprates
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Large $N$ theory of critical Fermi surfaces
• A controlled expansion for certain non-Fermi liquid metals
• Quantum critical metals in $4-\epsilon$ dimensions
• Normal state properties of quantum critical metals at finite temperature
• Supersymmetric low-energy theory and renormalization group for a clean Fermi gas with a repulsion in arbitrary dimensions
• The effect of Fermi surface curvature on low-energy properties of fermions with singular interactions
• Cooper channel and the singularities in the thermodynamics of a Fermi liquid
• Specific Heat of a Quantum Critical Metal

Cited by in corpus (3)

• Free energy and specific heat near a quantum critical point of a metal
• Ultraviolet-Infrared Mixing in Marginal Fermi Liquids
• Quasiparticle scattering in a superconductor near a nematic critical point: resonance mode and multiple attractive channels