Fermi Liquid Fixed Point Deformations due to Codimension Two Defects

TL;DR

This work identifies a geometric mechanism by which codimension-two defects induce a marginally relevant renormalization-group flow in a three-dimensional Fermi liquid. The running arises from kinematic particle-hole asymmetry created by defect geometry, without requiring dynamical impurity degrees of freedom, and is captured within an EFT formulation that treats dislocations (dislons) as world-sheet degrees of freedom. A key result is the one-loop beta function for angular-minned defect couplings, $\beta_n = -\frac{k_F}{2\pi v_F} g_n^2$, which yields a logarithmic flow in the polar regions of the Fermi surface and is cut off by finite defect length or by leakage in the longitudinal direction. Depending on the UV sign of the coupling and the relative size of the dislon Debye frequency, the system can approach a Kondo-like screened fixed point or potentially enter a non-Fermi-liquid regime if the dislon becomes relevant above $\omega_D^d$. Overall, extended defects can induce nontrivial low-energy physics in conventional metals through purely geometric RG effects, with the defect length setting the infrared scale of the flow.

Abstract

We show that codimension-two defects in Fermi liquids deform the renormalization group flow via a marginally relevant coupling. The mechanism for generating the flow is distinct from the case of the Kondo problem (codimension-three defects) in that the effective particle-hole asymmetry that leads to the log running is due to the spatial anisotropy generated by the defect. The mechanism for the log generation has a simple geometric explanation which shows that hole fluctuations are suppressed as the incoming momentum is taken to be along the direction of the defect. The RG flow time is shown to scale with the length of the defect. We also show that the dislon, the Goldstone mode localized to the defect, couples in a non-derivative fashion to the bulk fermions and becomes relevant above the dislons' Debye frequency which depends upon the defect tension.

Figures (3)

• Figure 1: One loop correction to the Kondo coupling
• Figure 2: Allowed intermediate states in one loop scattering correction due to $z-$momentum conservation on the Fermi sphere. The solid sphere represents the FS, and the dashed outer/inner lines bounds the particle/hole phase space in the EFT. We see that when the incoming momentum is along the defect (z-direction) the kinematics induce a particle-hole asymmetry since only particle states are available above the pole.
• Figure 3: One-loop correction to the dislocation scattering vertex.