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 $\omega \simeq {\Delta }_0$.

arXiv comment21 pages; journal version

References in corpus (49)

• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Nematic Fermi Fluids in Condensed Matter Physics
• Quantum Theory of a Nematic Fermi Fluid
• Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order
• 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
• On the low energy properies of fermions with singular interactions
• Enhancement of superconductivity near a nematic quantum critical point
• Are non-Fermi-liquids stable to Cooper pairing?
• Low Energy Dynamics of the Spinon-Gauge System
• Soft Fermi Surfaces and Breakdown of Fermi Liquid Behavior
• Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point
• Gauge-invariant response functions of fermions coupled to a gauge field
• 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
• Universal heat conduction in the iron-arsenide superconductor KFe2As2 : Evidence of a d-wave state
• Exotic d-wave superconductivity in strongly hole doped K(x)Ba(1-x)Fe2As2
• Perturbative non-Fermi liquids from dimensional regularization
• Non-analytic corrections to the Fermi-liquid behavior
• Fermi surface fluctuations and single electron excitations near Pomeranchuk instability in two dimensions
• Ising nematic quantum critical point in a metal: a Monte Carlo study
• Gauge Fields and Pairing in Double-Layer Composite Fermion Metals
• Non-perturbative behavior of the quantum phase transition to a nematic Fermi fluid
• The Strange Metal State of the Electron-Doped Cuprates
• Large $N$ theory of critical Fermi surfaces
• Monte Carlo Studies of Quantum Critical Metals
• Anomalous dynamical scaling from nematic and U(1)-gauge field fluctuations in two dimensional metals
• Singular perturbation theory for interacting fermions in two dimensions
• Exact critical exponents for the antiferromagnetic quantum critical metal in two dimensions
• Chiral non-Fermi Liquids
• Quantum-critical pairing with varying exponents
• A controlled expansion for certain non-Fermi liquid metals
• Two dimensional non-Fermi liquid metals: a solvable large N limit
• Nonanalytic corrections to the specific heat of a three-dimensional Fermi liquid
• Quantum critical metals in $4-\epsilon$ dimensions
• Superconducting instability in non-Fermi liquids
• 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
• Superconductivity near a nematic quantum critical point -- the interplay between hot and lukewarm regions
• Thermodynamics of a Fermi liquid beyond the low-energy limit
• The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal
• Low energy collective modes, Ginzburg-Landau theory, and pseudogap behavior in superconductors with long-range pairing interactions
• The effect of Fermi surface curvature on low-energy properties of fermions with singular interactions
• The unreasonable effectiveness of Eliashberg theory for pairing of non-Fermi liquids
• Cooper channel and the singularities in the thermodynamics of a Fermi liquid
• Specific Heat of a Quantum Critical Metal
• Two-point function of a $d=2$ quantum critical metal in the limit $k_F\to \infty$, $N_f\to 0$ with $N_f{k}_F$ fixed
• Beyond mean-field corrections to the quasiparticle spectrum of superfluid Fermi gases

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