Excitonic instability of two-dimensional tilted Dirac cones

TL;DR

This paper investigates excitonic instability in two-dimensional tilted Dirac cones, revealing how small chemical potential shifts and magnetic fields influence the phenomenon, with NMR experiments supporting the theoretical predictions.

Contribution

It provides a combined theoretical and experimental framework to understand excitonic instability in 2D tilted Dirac systems, emphasizing the role of magnetic fields and chemical potential shifts.

Findings

Excitonic instability is controlled by chemical potential and magnetic field.

NMR relaxation rate probes excitonic-spin fluctuations effectively.

Intervalley nesting between spin-split Fermi pockets is crucial.

Abstract

The electron-electron Coulomb interaction in Dirac-Weyl semimetals harbours a novel paradigm of correlation effects that hybridizes diverse realms of solid-state physics with their relativistic counterpart. Driving spontaneous mass acquisition, the excitonic condensate of strongly-interacting massless Dirac fermions is one such example whose exact nature remains debated. Here, by focussing on the two-dimensional tilted Dirac cones in the organic salt $\alpha$-(BEDT-TTF)$_2$I$_3$, we show that the excitonic instability is controlled by a small chemicalpotential shift and an in-plane magnetic field. In combined analyses based on renormalization-group approaches and ladder approximation, we demonstrate that the nuclear relaxation rate is an excellent probe of excitonic-spin fluctuations in an extended parameter region. Comparative nuclear magnetic resonance (NMR) experiments show good agreements with this result, jointly revealing the importance of intervalley nesting between field-induced, spin-split Fermi pockets of opposite charge polarities. Our work provides an accurate framework to search for excitonic instability of strongly-interacting massless fermions.