Berry phase is closely related to various phenomena, including transport phenomena and topological electronic states. Furthermore, by focusing on the distribution and topological structure of Berry curvature in reciprocal space, we can understand the fundamental properties of related phenomena and topological materials. Recent studies, mainly focusing on semiconductor materials, have indeed discovered magnetic oscillations in Weyl semimetals, nonlinear Hall effect due to Berry phase monopoles, and chiral quantum anomalies through related theoretical studies. In magnetic topological semimetals, on the other hand, it is possible to artificially control the spatial distribution of Berry curvature by applying a magnetic field. Through a systematic investigation on magnetic semimetal candidates, from constructing effective models to calculating transport coefficients, we showed that novel properties discovered by experimental groups [Uchida group and Kawasaki group] are related to the motion of Weyl nodes in the momentum space. These materials may lead to the study of topological phenomena induced by magnetic dynamics (see "Electromagnetism in \(k\) space and spin motive Force" below).

1. K. S. Takahashi, H. Ishizuka, et al. Sci. Adv. 4, eaar7880 (2018).

2. A. Nakamura, S. Nishihaya, et al. Phys. Rev. B 109, L121108 (2024).

3. A. Nakamura, S. Nishihaya, et al. submitted (2024).

Long-range magnetic textures, such as magnetic skyrmion, give rise to rich transport properties in magnetic metals, such as the anomalous Hall effect related to spin chirality, a.k.a. topological Hall effect. In addition to the topological Hall effect, recent studies on non-centrosymmetric magnets find that the spin-orbit interaction of itinerant electrons gives rise to novel contributions related to spin chirality, i.e., the chiral Hall effect. In this work, we discuss that the spin-orbit interaction has a distinct, yet significant, effect on the anomalous Hall effect related to spin chirality in centrosymmetric magnets. Using a scattering theory method, we find that the anomalous Hall effect related to scalar spin chirality in a two-dimensional Luttinger model is suppressed by more than one order of magnitude compared to the quadratic dispersion, and the contributions similar to the chiral Hall effect in Rashba model vanishes. At the same time, a novel term related to vector spin chirality occurs, which gives different Hall conductivity for the Bloch and Neel skyrmions, thereby enabling the detection of the skyrmion helicity. The striking differences demonstrate the rich effect of crystal symmetry on the chirality-related anomalous Hall effect in materials with strong spin-orbit interaction.

1. R. Terasawa, bachelor thesis [卒業論文] (Tokyo Institute of Technology, Mar. 2023).

2. R. Terasawa, H. Ishizuka, Phys. Rev. B 109, L060407 (2024).

Steady current in metals induces a thermal gradient, a phenomenon known as the Peltier effect. The Peltier effect is one of the fundamental phenomena in the thermoelectric properties of materials and is also used in applications such as refrigerators. In this work, we show that an analogous phenomenon occurs by phonons in a non-centrosymmetric material, e.g., ferroelectrics, subject to linearly-polarized light. Under the light illumination, an energy current of phonons occurs through a nonlinear optical effect similar to the bulk photovoltaic effect. We formulate the nonlinear Peltier coefficient of the photogalvanic energy current carried by phonons using nonlinear response theory. From the general formula, we show that the photogalvanic energy current occurs only in a non-centrosymmetric system with two or more optical phonon bands. We demonstrate the generation of the photogalvanic energy current using a one-dimensional ion chain with three ions in a unit cell, which predicts the generation of an experimentally observable energy current using available THz-infrared light sources.

1. H. Ishizuka, M. Sato, Phys. Rev. B 110, L020303 (2024).

Magnetic textures like skyrmions and domain walls coupled to itinerant electrons give rise to rich transport phenomena such as anomalous Hall effect and nonreciprocal current. Such phenomena are interesting from applications, which the transport phenomena are potential probe for electrically detecting magnetic textures in nano-scale devices. Here, we show that an anomalous Hall effect proportional to the net magnetic monopole charge occurs from skew scattering when the magnetic texture couples to itinerant electrons in a non-centrosymmetric system with spin-orbit interaction. This mechanism gives rise to a finite anomalous Hall effect in a ferromagnetic domain wall whose spins rotate in the xy plane, despite no out-of-plane magnetic moment. We also discuss the relation between the magnetic texture contributing to the anomalous Hall effect and the crystal symmetry. The results demonstrate rich features arising from the interplay of spin-orbit interaction and magnetic textures and their potential for detecting various magnetic textures in nanoscale devices.

1. J. Mochida, bachelor thesis [卒業論文] (Tokyo Institute of Technology, Mar. 2022).

2. J. Mochida, H. Ishizuka. New J. Phys 26, 063031 (2024).

We show that the magnetic precession of ferromagnetic moments in a noncentrosymmetric magnetic Weyl semimetal induces an electric current through a mechanism analogous to the adiabatic charge pumping. The current is a consequence of a Berry phase in the momentum space resulting from the circular motion of Weyl nodes induced by the precession. This mechanism resembles the Faraday effect, namely, induced magnetic field by circular electric current; the circular motion of Weyl nodes induces magnetic charge current in the momentum space, which results in a Berry phase that describes the adiabatic pump. Experimentally, the phenomenon is similar to spin motive force, which is an electric current induced by magnetic precision in the presence of the spatial gradient of magnetization. However, unlike the conventional spin motive force, this current occurs without a magnetization gradient. The result demonstrates a nontrivial interplay between the topological electronic state and magnetic dynamics.

1. A. Harada, bachelor thesis [卒業論文] (Tokyo Institute of Technology, Sep. 2021).

2. A. Harada, H. Ishizuka. Phys. Rev. B 107, 195202 (2023).

We argue that the unusually strong electron-electron interactions in the narrow bands in moire superlattices originate from well-localized Wannier orbitals with small radius \(\xi\) . Enhanced overlaps of electronic wavefunctions, enabled by such orbitals, result in a strong el-el superlattice umklapp scattering. We identify the umklapp scattering processes as a source of the strong temperature-dependent resistivity observed in these systems [1]. In a simple model, the umklapp scattering predicts a T-dependent resistivity that grows as \(T^2\) and is getting bigger as the Wannier orbital radius decreases [2]. We quantify the enhancement in el-el scattering by the Kadowaki-Woods (KW) ratio, a quantity that is sensitive to umklapp scattering but, helpfully, insensitive to the effects due to the high density of electronic states. Our analysis predicts anomalously large KW ratio values that clearly indicate the importance of the umklapp el-el processes and their impact on the T-dependent resistivity.

1. A. Jaoui, H. Ishizuka et al. Nat. Phys. 18, 633 (2022).

2. H. Ishizuka, L. Levitov. New J. Phys. 24, 052001 (2022).

Cr trihalides are 2d magnets showing rich magnetic orders in atomically thin devices, such as ferromagnetic and antiferromagnetic orders, depending on the setup. In recent years, thin films of this material has captured interest from spintronics view point as they show rich transport behaviors related to the magnetism. In this work, we found that the Cr trihalides are an ideal candidate for studying magnon photogalvanic effect, the photocurrent of magnons carrying spin angular momentum. In particular, we develop a general theory for the photogalvanic spin current through a magnetic resonance process. Using the nonlinear response formalism, we find the nonlinear conductivity consists of two contributions that involve one and two magnon bands; the latter is a contribution unknown to date. We argue that the two-band process produces a large photogalvanic spin current in the antiferromagnetic phase of bilayer Cr trihalides. This work demonstrates a route to the studies on the photogalvanic effect of spin angular momentum in realistic materials.

1. H. Ishizuka, M. Sato. Phys. Rev. Lett. 129, 107201 (2022).

Shift current is a kind of photovoltaic effect seen in bulk materials. While this phenomenon was known for several decades, the phenomenon has recaptured interest from the viewpoint of perovskite solar cells and Berry phase. In recent series of works, we studied the photovoltaic effect using nonequilibrium Green's function method. We found that the shift current show distinct properties from the conventional electron transport, such as non-trivial position dependence [1] and formation of photocurrent in Anderson insulators [2]. These results are consistent with recent experiments (Tokura-Kanazawa group, Kawasaki group).

1. H. Ishizuka, N. Nagaosa. New J. Phys. 19, 033015 (2017).

2. H. Ishizuka, N. Nagaosa. Proc. Natl. Acad. Sci. 118, e2012642118 (2021).

Nonlinear optical responses are often used as a probe for studying electronic properties. For the topological materials, studies so far focused on the photogalvanic electric current, which requires the breaking of inversion symmetry. In this work we present the theory for orbital current response in inversion-symmetric topological insulators. We find a symmetry-allowed orbital current response that occurs in centrosymmetric materials under illumination by the linearly polarized light. The sign of the dc nonlinear conductivity reflects the \(\mathbb Z_2\) index and the conductivity changes the sign at the phase transition. We derive a general result, and discuss its application to Bernevig-Hughes-Zhang model and \(1T^\prime\) phase of transition metal dichalcogenides. Experimental setups for the observation of the orbital current are also discussed.

1. M. Davydova, M. Serbyn, H. Ishizuka. Phys. Rev. B 105, L121407 (2022).

The efficiency of optical emitters can be dramatically enhanced by reducing the effective mode volume (the Purcell effect). Here we predict an analogous enhancement for electron-phonon (el-ph) scattering, achieved by compressing the electronic Wannier orbitals. Reshaping of Wannier orbitals is a prominent effect in graphene moire superlattices (SLs) where the orbitals are tunable by the twist angle. A reduction of the orbital effective volume leads to an enhancement in the effective el-ph coupling strength, yielding the values considerably bigger than those known for pristine monolayer graphene. The enhanced coupling boosts the el-ph scattering rates, pushing them above the values predicted from the enhanced spectral density of electronic excitations. The enhanced phonon emission and scattering rates are manifest in the observables such as electron-lattice cooling and the linear- \(T\) resistivity, both of which are directly tunable by the moire twist angle.

1. H. Ishizuka, A. Fahimniya, F. Guinea, L. Levitov. Nano Lett. 21, 7465 (2021).

The non-collinear spin configurations give rise to many nontrivial phenomena related to the Berry phase. They are often related to the vector and scalar spin chiralities. The scalar spin chirality leads to the topological Hall effect in metals, while the vector spin chirality to the ferroelectricity of spin origin, i.e., multiferroics in insulators. However, the role of the vector spin chirality in conducting systems has not yet been elucidated. Here we show theoretically that the spin correlation with vector spin chirality in chiral magnets scatters electrons asymmetrically, resulting in nonreciprocal transport phenomena, i.e., electrical magnetochiral effect. This asymmetric scattering appears in the leading-order scattering term, implying a large nonreciprocity in the charge and spin currents. We find that the temperature and magnetic field dependence of the eMCE reproduces that observed in MnSi. Our results reveal the microscopic mechanism of eMCE and its potential in producing a large nonreciprocal response.

1. H. Ishizuka, N. Nagaosa. Nat. Commun. 11, 2986 (2020).

We theoretically propose a method of rectifying spin current with a linearly polarized electromagnetic wave in inversion-asymmetric magnetic insulators. To demonstrate the proposal, we consider quantum spin chains as a simple example; these models are mapped to fermion (spinon) models via Jordan-Wigner transformation. Using a nonlinear response theory, we find that a dc spin current is generated by the linearly polarized waves. The spin current shows rich anisotropic behavior depending on the direction of the electromagnetic wave. This is a manifestation of the rich interplay between spins and the waves; inverse Dzyaloshinskii-Moriya, Zeeman, and magnetostriction couplings lead to different behaviors of the spin current. The resultant spin current is insensitive to the relaxation time of spinons, a property of which potentially benefits a long-distance propagation of the spin current. An estimate of the required electromagnetic wave is given.

1. H. Ishizuka, M. Sato. Phys. Rev. Lett. 122, 197702 (2019).

2. H. Ishizuka, M. Sato. Phys. Rev. B 100, 224411 (2019).

Electron scattering by impurities plays a central role in the transport phenomena. Non-magnetic impurities and randomness are the major cause of resistivity, and sometimes, electron scattering by multiple impurities brings about a nontrivial electronic states such as Anderson localization. In contrast, multiple scattering by localized moments were far less studied. In a series of recent works, we studied the Hall effect caused by multiple magnetic impurities. We find that the multiple magnetic scattering produces a Hall effect proportional to scalar spin chirality prominent in clean metals. We argued that the competition of spin Berry phase mechanism and multiple magnetic scattering causes a sign change of Hall conductivity with increasing temperature[1], an anomalous Hall effect that increases with increasing temperature [2], and large Hall angle reaching 0.1 [3]. These features are consistent with recent experimental observations, which have been known but remained a mystery.

1. H. Ishizuka, N. Nagaosa. Sci. Adv. 4, eaap9962 (2018).

2. Y. Kato, H. Ishizuka. Phys. Rev. Appl. 12, 021001 (2019).

3. H. Ishizuka, N. Nagaosa. Phys. Rev. B 103, 235148 (2021).

4. Y. Fujishiro, N. Kanazawa, H. Ishizuka, et al. Nat. Commun. 12, 317 (2021).

5. M. Uchida, S. Sato, H. Ishizuka, et al. Sci. Adv. 7, eabl5381 (2021).