Electronic spin-triplet nematic with a twist

TL;DR

This paper investigates a three-dimensional model where itinerant electrons exhibit a spin-triplet nematic order driven by quadrupole interactions, revealing fluctuation-induced first-order transitions and the emergence of intertwined modulated states, including potential coexistence with p-wave superconductivity.

Contribution

It introduces a fermionic quantum order-by-disorder analysis of spin-triplet nematic order, uncovering a pre-emptive modulated state and coexistence with p-wave superconductivity, extending understanding of nematic quantum phase transitions.

Findings

Quantum fluctuations turn the nematic transition first-order at low temperatures.

A modulated nematic state intertwined with helical spin modulation is stabilized.

Possible coexistence of this nematic state with p-wave superconductivity.

Abstract

We analyze a model of itinerant electrons interacting through a quadrupole density-density repulsion in three dimensions. At the mean field level, the interaction drives a continuous Pomeranchuk instability towards $d$-wave, spin-triplet nematic order, which simultaneously breaks the SU(2) spin-rotation and spatial rotational symmetries. This order results in spin antisymmetric, elliptical deformations of the Fermi surfaces of up and down spins. We show that the effects of quantum fluctuations are similar to those in metallic ferromagnets, rendering the nematic transition first-order at low temperatures. Using the fermionic quantum order-by-disorder approach to self-consistently calculate fluctuations around possible modulated states, we show that the first-order transition is pre-empted by the formation of a nematic state that is intertwined with a helical modulation in spin space. Such a state is closely related to $d$-wave bond density wave order in square-lattice systems. Moreover, we show that it may coexist with a modulated, $p$-wave superconducting state.