Local Observations of Orbital Diamagnetism and Excitation in Three-Dimensional Dirac Fermion Systems Bi1−xSbx

Abstract

Dirac fermions display a singular response against magnetic and electric fields. A distinct manifestation is the large diamagnetism originating in the interband effect of Bloch bands, as observed in bismuth alloys. Through 209Bi NMR spectroscopy, we extract diamagnetic orbital susceptibility inherent to Dirac fermions in the semiconducting bismuth alloys Bi1−xSbx (x = 0.08–0.16). The 209Bi hyperfine coupling constant provides an estimate of the effective orbital radius. In addition to the interband diamagnetism, the NMR 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/T1 is dominated by orbital excitation and follows cubic temperature dependence in an 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.