Local Observations of Orbital Diamagnetism and Excitation in Three-Dimensional Dirac Fermion Systems Bi$_{1-x}$Sb$_x$

TL;DR

This study uses $^{209}$Bi NMR spectroscopy to investigate the orbital diamagnetism and excitations of Dirac fermions in Bi$_{1-x}$Sb$_x$ alloys, revealing robust diamagnetic responses and orbital excitations related to strong spin-orbit coupling.

Contribution

It provides the first direct NMR-based measurement of orbital susceptibility and excitation in three-dimensional Dirac fermion systems Bi$_{1-x}$Sb$_x$, highlighting the effects of strong spin-orbit coupling.

Findings

Large diamagnetism observed via NMR in Bi$_{1-x}$Sb$_x$ alloys.

Orbital excitation follows cubic temperature dependence.

Enhanced intraband diamagnetism due to strong spin-orbit coupling.

Abstract

Dirac fermions display a singular response against magnetic and electric fields. A distinct manifestation is large diamagnetism originating in the interband effect of Bloch bands, as observed in bismuth alloys. Through $^{209}$Bi NMR spectroscopy, we extract diamagnetic orbital susceptibility inherent to Dirac fermions in the semiconducting bismuth alloys Bi$_{1-x}$Sb$_x$ ($x = 0.08 - 0.16$). The $^{209}$Bi hyperfine coupling constant provides an estimate of the effective orbital radius. In addition to the interband diamagnetism, Knight shift includes an anomalous temperature-independent term originating in the enhanced intraband diamagnetism under strong spin-orbit coupling. The nuclear spin-lattice relaxation rate $1/T_1$ is dominated by orbital excitation and follows cubic temperature dependence in the extensive temperature range. The result demonstrates the robust diamagnetism and low-lying orbital excitation against the small gap opening, whereas $x$-dependent spin excitation appears at low temperatures.