Research

See also:

• K. Nakazawa, H. F. Legg, J. Klinovaja, and D. Loss, "Interband contributions to nonlinear transport in semiconductor nanostructures," Phys. Rev. B 111, 125305 (2025). 

• K. Nakazawa, H. F. Legg, R. M. A. Dantas, J. Klinovaja, and D. Loss, "Probing Fermi-surface spin-textures via the nonlinear Shubnikov-de Haas effect." arXiv:2601.13510.

Detection and control of spin–orbit interaction (SOI) are crucial not only for fundamental physics but also for the development of future electronic and quantum devices. In particular, semiconductor nanostructures have recently attracted significant attention as promising platforms for quantum information technologies, where precise manipulation of SOI constitutes an essential building block.

In this work, we theoretically investigate the detectability of SOI through nonlinear transport phenomena, namely current responses that are second order in the applied electric field. While previous studies based on the Boltzmann theory [1] suggested that momentum-cubic SOI can contribute to nonlinear transport, we demonstrate that band effects originating from the quantum metric partially suppress the detectability of SOI.

To overcome this limitation, we focus on quantum oscillations in the nonlinear conductivity, referred to as the nonlinear Shubnikov–de Haas effect. We find that the phase of these quantum oscillations is extremely sensitive to SOI, making it a powerful probe of the SOI-induced spin structure on the Fermi surface.

Our results provide new insights into the detection of spin–orbit interaction in semiconductor nanostructures and offer valuable guidance toward their application in quantum information devices.

[1] R. M. A. Dantas et al., Phys. Rev. B 107, L241202 (2023). 

See also:

• T. Yamaguchi, K. Nakazawa, and A. Yamakage, "Microscopic Theory of Nonlinear Hall Effect Induced by Electric Field and Temperature Gradient," Phys. Rev. B 109, 205117 (2024).

• K. Nakazawa, T. Yamaguchi, and A. Yamakage, "Nonlinear charge transport properties in chiral tellurium," Phys. Rev. Materials 8, L091601 (2024). 

• K. Nakazawa, T. Yamaguchi, and A. Yamakage, "Nonlinear charge and thermal transport properties induced by orbital magnetic moment in chiral crystal cobalt monosilicide," Phys. Rev. B 111, 045161 (2025).

• T. Nomoto, A. Kikkawa, K. Nakazawa, T. Yamaguchi, and F. Kagawa, "Observation of the nonlinear chiral thermoelectric Hall effect in tellurium," Nat. Phys. 21, 1920-1925 (2025). 

    Chirality degrees of freedom suggests interesting relation to the nature. We so far discussed the chirality dependent phenomenon “Nonlinear Chiral Thermo-Electric (NCTE) Hall effect,” in which current flows in the direction of the cross product of the electric field and the temperature gradient. We microscopically formulated this effect revealing that the asymmetric property of both Berry curvature and the orbital magnetic moment is responsible, while the demonstration in the actual material is yet to be clarified. 

We studied this NCTE Hall effect in chiral Te and B20-type CoSi based on ab initio calculation. For chiral Te, we clarify that the NCTE Hall current can flow parallel to the chiral axis, whereas such behaviour is absent for the second-order response to the DC electric field. Quantitative estimation predicts the large NCTE Hall current, which is sufficiently detectable in experiments, and the orbital magnetic moment will play an important role in the vicinity of the top of the valence band. We observed the similar aspects for CoSi, but here we found that the Berry curvature contribution is cancelled from its symmetry and only the orbital magnetic moment coming from the multi-fold chiral fermions contributes dominantly. Recent experimental verification in chiral Te confirmed that the sign of the NCTE current changes with crystal chirality, that it is bilinear with respect to electric field and temperature gradient, and that it shows quasi-quantitative agreement with our theory.

See also:

• K. Nakazawa, Y. Kato, and Y. Motome, “Magnetic, transport and topological properties of Co-based shandite thin films”, Commun. Phys. 7, 48 (2024).

• K. Nakazawa, Y. Kato, and Y. Motome, "Topological transitions by magnetization rotation in kagome monolayers of ferromagnetic Weyl semimetal Co-based shandite", Phys. Rev. B 110, 085112 (2024).

    Co3Sn2S2, which has a stacked Co-kagome lattice structure [Fig. 1(a)], has attracted attention as a candidate for ferromagnetic Weyl semimetals. Recently the quantum anomalous Hall effect has been theoretically proposed in the monolayer, awaiting its experimental realization. To clarify how the Weyl points in the three-dimensions appear in two-dimensional atomically thin films, we have systematically investigated the magnetism, band topology, and transport properties of Co3Sn2S2 atomic layer thin films [Fig. 1(b)] with one, two, and three Co-kagome layers, considering the case of Sn- and S- surface terminatiion (Sn-end and S-end), respectively, based on ab initio calculations. As a result, we found that the ferromagnetic state realize in the Sn-end systems, and that the distribution of Weyl points and the behavior of transport coefficients behave systematically as the number of layers increases, with a natural connection to the bulk system [Fig. 1(c)]. On the other hand, in the S-end system, interlayer antiferromagnetism appears in the bilayer system, and the anomalous Hall and Nernst effects disappear, showing significantly different behaviors depending on the number of layers. Furthermore, we have studied in detail how the band topology changes depending on the magnetization angle in kagome monolayers. We found the various quantum Hall states with different Chern numbers and clarified that the topological transition point differs depending on the direction of magnetization angle in Sn-end system. In particular, we found a "planar quantum anomalous Hall effect" in which the Hall conductivity is quantized when the magnetization is oriented in the in-plane direction perpendicular to the kagome bond. 

See also:

• K. Nakazawa, Y. Kato, and Y. Motome, “Asymmetric modulation of the Majorana excitation spectra and nonreciprocal thermal transport in the Kitaev spin liquid under a staggered magnetic field”, Phys. Rev. B 105, 165152 (2022).

    The Kitaev model with bond-dependent interactions has attracted attention since the ground state is exactly the spin liquid and the elementary excitations are described by the itinerant Majorana fermion and localized Z2 flux, which appear as a consequence of the fractionalization of the spin degrees of freedom. Recently, half-integer quantum thermal Hall effect due to the Chern insulating state of the Majorana fermion under magnetic field has been discussed as a prime fingerprint of the fractionalization, and asymmetric Majorana excitation spectra in momentum space due to non-uniform magnetic and electrostatic fields have also been discussed as a alternative method of the detection of Majorana fermions. However, no systematic study including heat transport has been performed to detect such fractionalization. 

    We have investigated Majorana excitation spectra and the resulting thermal transport in a Kitaev spin liquid on a honeycomb lattice under the staggered and uniform magnetic fields. First, we confirmed that the Majorana excitations are asymmetrically distorted by the sublattice symmetry breaking caused by staggered magnetic fields, and that various excitation spectra are realized depending on the magnitude and direction of the uniform and staggered magnetic fields. Furthermore, we found that the nonreciprocal thermal transport arises due to the asymmetric Majorana band structure and that the thermal current has a characteristic magnetic field dependence. These results may help in the detection of the Majorana excitations.

See also:

• K. Nakazawa, K. Hoshi, J. J. Nakane, J. Ohe, and H. Kohno, "Topological Spin Hall Effect in Antiferromagnets Driven by Vector Neel Chirality", Phys. Rev. B 109, L241105 (2024).

• J. J. Nakane, K. Nakazawa, and H. Kohno, "Topological Hall effect in weakly canted antiferromagnets", Phys. Rev. B 101, 174432 (2020).

    Antiferromagnets (AFM) are expected to be applied to spintronics devices because of their advantages over ferromagnets, such as small leakage magnetic field and fast spin dynamics. One of the methods to generate spin currents in AFM materials is the topological spin Hall effect (TSHE): the spin Hall effect induced by the spin chirality of the Néel vector. TSHE has been discussed mainly in antiferromagnetic Skyrmion system, which is the skyrmion structures formed by Néel vectors. However, the physical picture of TSHE in AFM metals is not understanded in detail.

    We have formulated TSHE by analytical calculations based on the field theory and shown that the essence of TSHE is not in scalar chirality but in vector chirality, and the TSHE does not induced by AFM skyrmion but induced by AFM meron (half skyrmion) systems [middle figures]. Also, we found the interesting structure of the Néel vectors which arises when the uniform components ℓ form the skyrmion [left figures]. Furthermore, we found that TSHE increases in regions where the coupling between the magnetic structure and conduction electrons is weak, and revealed that the physical reason for this is transverse spin dephasing[6][right figures], which exists universally in antiferromagnetic metals. Furthermore, our collaborators executed numerical calculations based on the Landauer-Büttiker method confirmed the results we obtained analytically. This TSHE relates to the topological Hall effect in the canting AFM. 

See also:

• K. Nakazawa and H. Kohno, “Weak coupling theory of topological Hall effect”, Phys. Rev. B 99, 174425 (2019).

• L. Vistoli, W. Wang, A. Sander, Q. Zhu, B. Casals, R. Cichelero, A. Barthélémy, S. Fusil, G. Herranz, S. Valencia, R. Abrudan, E. Weschke, K. Nakazawa, H. Kohno, J. Santamaria, W. Wu, V. Garcia, and M. Bibes, “Giant topological Hall effect in correlated oxide thin films”, Nat. Phys. 15, 67-72 (2019).

• K. Nakazawa, M. Bibes, and H. Kohno, “Topological Hall effect from strong to weak coupling”, J. Phys. Soc. Jpn. 87, 033705 (2018). The 29th Outstanding Paper Award of the Physical Society of Japan 

    Conduction electron systems interacting with magnetized structures with spin chirality exhibit the Hall effect (topological Hall effect; THE), which has been intensively investigated especially in skyrmion systems. The THE is usually explained by the picture that the conduction electron system acquires the Berry phase through the interaction with magnetization, but the Berry phase interpretation is no longer valid when the interaction is weak or the spatial variation of magnetic structure is fast. Recently, small skyrmions with radii of few nm have been found, hence it is important to investigate THE in a wide parameter range. 

    We have performed analytical calculations based on field theory to investigate how the physical picture of the topological Hall effect varies from strong to weak coupling and from long to short wavelengths. First, we clarified the region in which the Berry phase picture is established, and found that there are two intermediate regions between the strong and weak coupling regions. The boundary between these two regions is determined by the precession length and the diffusion length of the conduction electrons, and when the diffusion length is longer than precession length, the effective magnetic field becomes nonlocal. The relationship between our weak coupling theory and the giant topological Hall effect discovered in Mn oxides is discussed. 

See also:

• K. Nakazawa and H. Kohno, “Effect of vertex correction to chirality-induced anomalous Hall effect”, J. Phys. Soc. Jpn. 83, 073707 (2014).

    The anomalous Hall effect due to spin chirality, a non-coplanar spin configuration, studied previously for the case of weak exchange coupling [1] is reexamined here by taking account of vertex corrections due to normal impurities. This amounts to considering the diffusive nature of electron motion, as well as spin conservation at the scattering from normal impurities, and introduces the spin diffusion length. The preexisting circular persistent current [2], responsible for the anomalous Hall response, is identified by calculating the “typical” magnitude of the equilibrium current.

[1] G. Tatara and H. Kawamura, J. Phys. Soc. Jpn. 71, 2613 (2002). 

[2] G. Tatara and H. kohno, Phys. Rev. B 67, 113316 (2003).