PrBi: Topology meets quadrupolar degrees of freedom

TL;DR

This study investigates PrBi, a topological semimetal with quadrupolar degrees of freedom, revealing a nonmagnetic ground state with quadrupolar moments, a low-temperature phase transition, and implications for topology and correlated electron physics.

Contribution

It provides the first systematic analysis of quadrupolar effects in PrBi, linking topology, low carrier density, and multipolar degrees of freedom in a correlated semimetal.

Findings

PrBi has a non-Kramers doublet ground state with quadrupolar moments.

A quadrupolar phase transition occurs below 0.08 K.

PrBi exhibits non-trivial Berry phase and low carrier density in quantum oscillations.

Abstract

Novel materials incorporating electronic degrees of freedom other than charge, including spin, orbital or valley \textit{et al} have manifested themselves to be of the great interests and applicable potentials. Recently, the multipolar degrees of freedom have attracted remarkable attention in the electronic correlated effects. In this work, we systematically studied the transport, magnetic and thermodynamic properties of the topological semimetal candidate PrBi in the framework of crystalline electric field theory. Our results demonstrate the $\Gamma_3$ non-Kramers doublet as the ground state of Pr$^{3+}$ (4$f^2$) ions. This ground state is nonmagnetic but carries a non-zero quadrupolar moment $\langle\hat{O}_2^0\rangle$. A quadrupolar phase transition is inferred below 0.08 K. No obvious quadrupolar Kondo effect can be identified. Ultrahigh-field quantum oscillation measurements confirm PrBi as a semimetal with non-trivial Berry phase and low total carrier density 0.06 /f.u. We discuss the interplay between low carrier density and $4f^2$ quadrupolar moment, and ascribe the weak quadrupolar ordering and Kondo effect to consequences of the low carrier density. PrBi, thus, opens a new window to the physics of topology and strongly correlated effect with quadrupolar degrees of freedom in the low-carrier-density limit, evoking the need for a reexamination of the Nozi\`{e}res exhaustion problem in the context of multi-channel Kondo effect.