Collective excitations and stability of a non-Fermi liquid state near a quantum-critical point of a metal

Abstract

We examine the spectral properties of collective excitations with finite angular momentum $l$ for a system of interacting fermions near a Pomeranchuk quantum critical point, both in the Fermi liquid and non-Fermi liquid regimes. Previous studies found that deep in the Fermi liquid regime, the spectral functions for even and odd $l$ behave differently - the latter is suppressed compared to the former because of kinematic constraints on scattering processes. The main focus of our paper is to understand how the spectral functions for even and odd $l$ evolve as the system enters the non-Fermi liquid regime. We obtain the full scaling function for the electron polarization bubble at arbitrary $l$, which interpolates between the Fermi liquid and non-Fermi liquid regimes. We show that collective excitations for all $l$ remain stable and causal throughout the crossover and right at the quantum critical point.

Figures (5)

• Figure 1: Diagrams for the polarization bubble $\Pi_l$. In commonly adopted notations, diagrams (a,b) are the two self‐energy diagrams, diagram (c) is the Maki–Thompson diagram, and diagrams (d,e) are the two Aslamazov–Larkin diagrams. In all diagrams the external momentum $\bm{q}=0$, the external frequency $\omega$ is finite, and the side vertices (black dots) are $\mathcal{V}_{\!l}(\bm{k})=\cos(l\,\theta_{\bm{k}\hat{x}})$, where $\theta_{\bm{k}\hat{x}}$ is the angle between the internal fermion momentum $\bm{k}$ and the $x$‐axis. The wavy line is the propagator of near-critical $l=0$ charge fluctuations, Eq. \ref{['chi']}.
• Figure 2: The scaling function $\mathcal{F}(x)$ from Eq. \ref{['nn_6']}, where $x = \omega_{FL}/\omega$. The limit $x=0$ corresponds to a QCP and $x \gg 1$ to the FL regime. The scaling function is normalized to $\mathcal{F}(0) =1$. In the inset we compare the exact $\mathcal{F}(x)$ and its approximate form presented in the text.
• Figure 3: Ladder of vertex corrections for the side vertex in the particle-hole polarization. Each wavy line is the near-critical bosonic propagator. In the FL regime, it can be approximated as static.
• Figure 4: The lowest order diagrams for the self-energy (a) and vertex renormalization (b).
• Figure 5: The scaling function, normalized to its value at QCP.