Exploring the Novel Spin Transport Properties of Dirac Electron Systems at Low Magnetic Fields

Dirac electron systems provide important platforms for studying the interband effects of magnetic field and the topological properties. The former, which are a result of interband transitions of electrons in the presence of vector potential, give rise to large orbital diamagnetism and the characteristic contribution to Hall conductivity [1–3]. The latter, such as the Berry curvature, have been discovered in the quantized spin Hall effect [4,5]. The effects of the Berry curvature in the linear order of the magnetic field have also been clarified [6].

Recently, M. Ogata et al. studied anomalous spin transport properties in tilted quasi-two-dimensional Dirac electron systems with a finite mass owing to the spin–orbit interaction [7], considering application to Dirac electron systems in the organic conductors α-(BEDT-TTF)₂I₃ [8,9] and α-(BETS)₂I₃ [10,11]. These materials have layered structures that consist of organic molecules and anions, where the organic molecule layers host pseudo-two-dimensional Dirac electron systems. The conduction and valence bands have a pair of Dirac cones tilted in opposite directions in the Brillouin zone. The most prominent advantage of the organic Dirac electron system is that the Fermi energy coincides with the Dirac point, because there is no band overlap. It is also shown that the amount of carrier doping via impurities is only of 1 ppm order [3,9].

In the presence of a gap due to inversion symmetry breaking, as observed in the charge order phase of α-(BEDT-TTF)₂I₃ [8], the Berry phase of the pair of Dirac cones exactly cancels. In contrast, in the presence of a gap due to the spin–orbit interaction, as shown in α-(BETS)₂I₃ [10,11], this cancellation does not occur. However, the effect of the Dirac cone tilt and external magnetic field on the spin transport coefficients has not yet been confirmed.

M. Ogata et al. analytically calculated the conductivity tensors up to the linear order of the magnetic field using the microscopic linear response theory [7]. They found that the spin Hall conductivity becomes nonzero owing to the Berry curvature. The estimated values of spin Hall conductivity using the typical parameters of α-(BEDT-TTF)₂I₃ and α-(BETS)₂I₃ were comparable to that in Pt. They also found that anomalous spin magnetoconductivities, which are odd functions of the applied magnetic field and chemical potential, are finite, even if they are diagonal conductivities (See Fig. 1).

»View larger version

Fig. 1. Chemical potential μ dependences of the diagonal spin magnetoconductivity σ_sxx⁽¹⁾ and σ_syy⁽¹⁾ for several values of the tilting parameter t of a Dirac cone (t = 0: isotropic, t = 1: fully tilted), where Δ and Γ are the gap and the relaxation rate, respectively (the figure was obtained from Fig. 2 of Ref. 7).

The results of the study by M. Ogata et al. reveal the novel spin transport properties due to the Berry curvature and orbital magnetic moment at low magnetic fields in two-dimensional Dirac electron systems [7]. It is expected that these properties will be observed experimentally using the inverse spin Hall effect in α-(BETS)₂I₃ [10,11], where the massive Dirac electron system owing to the spin–orbit interaction appears at ambient pressure.

References

• [1] H. Fukuyama and R. Kubo, J. Phys. Soc. Jpn. 28, 570 (1970). 10.1143/JPSJ.28.570 Link, Google Scholar
• [2] Y. Fuseya, M. Ogata, and H. Fukuyama, J. Phys. Soc. Jpn. 84, 012001 (2015). 10.7566/JPSJ.84.012001 Link, Google Scholar
• [3] A. Kobayashi, Y. Suzumura, and H. Fukuyama, J. Phys. Soc. Jpn. 77, 064718 (2008). 10.1143/JPSJ.77.064718 Link, Google Scholar
• [4] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005). 10.1103/PhysRevLett.95.226801 Crossref, Google Scholar
• [5] D. Xiao, M.-C. Chang, and Q. Niu, Rev. Mod. Phys. 82, 1959 (2010). 10.1103/RevModPhys.82.1959 Crossref, Google Scholar
• [6] V. Könye and M. Ogata, Phys. Rev. Res. 3, 033076 (2021). 10.1103/PhysRevResearch.3.033076 Crossref, Google Scholar
• [7] M. Ogata, S. Ozaki, and H. Matsuura, J. Phys. Soc. Jpn. 91, 023708 (2022). 10.7566/JPSJ.91.023708 Link, Google Scholar
• [8] K. Kajita, Y. Nishio, N. Tajima, Y. Suzumura, and A. Kobayashi, J. Phys. Soc. Jpn. 83, 072002 (2014). 10.7566/JPSJ.83.072002 Link, Google Scholar
• [9] N. Tajima, R. Kato, S. Sugawara, Y. Nishio, and K. Kajita, Phys. Rev. B 85, 033401 (2012). 10.1103/PhysRevB.85.033401 Crossref, Google Scholar
• [10] S. Kitou, T. Tsumuraya, H. Sawahata, F. Ishii, K.-i. Hiraki, T. Nakamura, N. Katayama, and H. Sawa, Phys. Rev. B 103, 035135 (2021). 10.1103/PhysRevB.103.035135 Crossref, Google Scholar
• [11] T. Tsumuraya and Y. Suzumura, Eur. Phys. J. B 94, 17 (2021). 10.1140/epjb/s10051-020-00038-y Crossref, Google Scholar

Author Biographies