Nuclear magnetic relaxation and Knight shift due to orbital interaction in Dirac electron systems

• Published in: The Journal of physics and chemistry of solids 2019-05, Vol.128, p.138-143
• Main Authors: Maebashi, Hideaki, Hirosawa, Tomoki, Ogata, Masao, Fukuyama, Hidetoshi
• Format: Article
• Language: English
• Subjects: Bismuth; Diamagnetism; Dirac electron systems; Nuclear magnetic resonance; Permittivity
• ISSN: 0022-3697; 1879-2553
• DOI: 10.1016/j.jpcs.2017.12.034

We study the nuclear magnetic relaxation rate and Knight shift in the presence of the orbital and quadrupole interactions for three-dimensional Dirac electron systems (e.g., bismuth–antimony alloys). By using recent results of the dynamic magnetic susceptibility and permittivity, we obtain rigorous results of the relaxation rates (1/T1)orb and (1/T1)Q, which are due to the orbital and quadrupole interactions, respectively, and show that (1/T1)Q gives a negligible contribution compared with (1/T1)orb. It is found that (1/T1)orb exhibits anomalous dependences on temperature T and chemical potential μ. When μ is inside the band gap, (1/T1)orb∼T3log(2T/ω0) for temperatures above the band gap, where ω0 is the nuclear Larmor frequency. When μ lies in the conduction or valence bands, (1/T1)orb∝TkF2log(2vFkF/ω0) for low temperatures, where kF and vF are the Fermi momentum and Fermi velocity, respectively. The Knight shift Korb due to the orbital interaction also shows anomalous dependences on T and μ. It is shown that Korb is negative and its magnitude significantly increases with decreasing temperature when μ is located in the band gap. Because the anomalous dependences in Korb is caused by the interband particle-hole excitations across the small band gap while (1/T1)orb is governed by the intraband excitations, the Korringa relation does not hold in the Dirac electron systems.