Noncentrosymmetric conductors are an interesting material platform, with rich spintronic functionalities 1,2 and exotic superconducting properties 3,4 typically produced in polar systems with Rashba-type spin-orbit interactions 5 . Polar conductors should also exhibit inherent nonreciprocal transport [6][7][8] , in which the rightward and leftward currents di er from each other. But such a rectification is di cult to achieve in bulk materials because, unlike the translationally asymmetric p-n junctions, bulk materials are translationally symmetric, making this phenomenon highly nontrivial. Here we report a bulk rectification e ect in a three-dimensional Rashba-type polar semiconductor BiTeBr. Experimentally observed nonreciprocal electric signals are quantitatively explained by theoretical calculations based on the Boltzmann equation considering the giant Rashba spin-orbit coupling. The present result o ers a microscopic understanding of the bulk rectification e ect intrinsic to polar conductors as well as a simple electrical means to estimate the spin-orbit parameter in a variety of noncentrosymmetric systems.The effect of the lattice symmetry on the electronic states is a fundamental issue in condensed matter physics. In particular, broken inversion symmetry in the crystal structure generally causes spin band splitting which modifies the electronic ground state, affecting transport properties represented by the superconductivity in noncentrosymmetric systems 3,4 or spin-related transport in nonmagnetic materials 1,2 . Among them, Rashba-5 and Dresselhaus 9 -type spin-orbit interactions are two well-known textbook models which have succeeded in explaining a variety of exotic phenomena in systems without inversion symmetry.Although the Rashba effect has been conventionally studied at surfaces or interfaces [10][11][12][13][14] , the recent discovery of three-dimensional (3D) materials which host a large Rashba-type band splitting [15][16][17][18] pave the way towards exploring novel transport originating from the 3D chiral spin-texture of the electronic band. BiTeX (X = I, Br) is one such bulk polar semiconductor, in which Bi, Te and X layers are stacked alternately so that the mirror symmetry along the c axis is broken (Fig. 1a). The resultant Rashba-type spin splitting of the electronic bands has been confirmed by angle-resolved photoemission spectroscopy (ARPES) 15,16 and the transport signatures of the split Fermi surface have been reported by quantum oscillations in resistance 19 or thermoelectric coefficients 20 . However, characteristic magneto-transport reflecting the spin polarization in the electronic band or polarity of the crystal has been elusive, except for photocurrent experiments on BiTeBr 21 . One of the manifestations of lattice symmetry breaking in electric transport is the rectification effect. In the presence of an in-plane magnetic field, the Rashba-type spin band splitting is modulated to become asymmetric along a direction perpendicular to both the polar axis and the magnetic field (Fig. ...

We theoretically study the quantized anomalous Hall effect (QAHE) in skyrmion crystal (SkX) without external magnetic field. The emergent magnetic field in SkX could be gigantic as much as ∼ 4000T when its lattice constant is ∼ 1nm. The band structure is not flat but has a finite gap in the low electron-density regime. We also study the conditions to realize the QAHE for the skyrmion size, carrier density, disorder strength and temperature. Comparing the SkX and the system under the corresponding uniform magnetic field, the former is more fragile against the temperature compared with the latter since the gap is reduced by a factor of ∼ 1/5, while they are almost equally robust against the disorder. Therefore, it is expected that the QAHE of SkX system is realized even with strong disorder at room temperature when the electron density of the order of one per a skyrmion.Magnetic skyrmion is a topological spin texture in ferromagnets 1 . After the early theoretical proposals in magnets 2-4 , the study of magnetic skyrmion is growing rapidly since it was discovered experimentally [5][6][7] . The periodic array of skyrmions, i.e., a skyrmion crystal (SkX), is realized at interfaces 7 or in bulk chiral magnets such as B20 compounds 5,6 . An emergent magnetic field, generated in the background skyrmion spin texture. Namely, a skyrmion has one magnetic flux Φ 0 = h/e acting on the conduction electrons coupled to it. When the skyrmions form a periodic lattice, i.e., a SkX, the emergent magnetic field reaches ∼ 4000T assuming the uniform averaged flux for the skyrmion size and the lattice constant of SkX of the order of ∼ 1nm. The effective magnetic field is proportional to λ −2 , where λ is the skyrmion radius. Since the size of the skyrmion is 3nm for MnGe 11 , 18nm for MnSi 9 , and 70nm for FeGe 13 , the corresponding emergent magnetic field is ∼ 1100T, 28T, and 1T, respectively.This emergent magnetic field leads to the Hall effect 8 . Most of the studies focus on the Hall effect in metallic systems with large electron density 9-12 . This so-called topological Hall conductivity σ xy is usually small compared with the longitudinal conductivity σ xx , i.e., the Hall angle σ xy /σ xx is typically of the order of 10 −2 at most 11 . Up to now, we regard skyrmions as the source of the real space emergent magnetic field. When the size of the skyrmion becomes comparable to the mean free path, it is expected that the crossover from the real to momentum space Berry curvature occurs. One can regard the case of pyrochlore ferromagnet as the limit of large emergent magnetic field, where the spin chirality is defined for each unit cell of tetrahedron 14 . In this case, there is no Landau Level (LL) formation, but the band structure is formed by taking into account the solid angle of the spin, and the intrinsic anomalous Hall effect appears whose conductance is given by the integral of the Berry curvature in momentum space 15 . A more drastic example is the quantized anomalous Hall effect (QAHE) in magnetic topological insulator (TI)...

Nonreciprocal charge transport phenomena are studied theoretically for two-dimensional noncentrosymmetric superconductors under an external magnetic field B. Rashba superconductors, surface superconductivity on the surface of three-dimensional topological insulators (TIs), and transition metal dichalcogenides (TMD) such as MoS2 are representative systems, and the current-voltage I-V characteristics, i.e., V = V (I), for each of them is analyzed. V (I) can be expanded with respect to the current I as V (I) = j=1,∞ aj(B, T )I j , and the (B, T )-dependence of aj depends on the mechanism of the charge transport. Note that the magnetochiral anisotropy in the normal state is expressed by a1(B, T ) = R0 and a2(B, T ) = R0γB with the constant γ. Our analysis is based on the time-dependent Ginzburg-Landau (TDGL) theory, which contains up to third order terms in the momentum of the order parameter. Above the mean field superconducting transition temperature T0, the fluctuation of the superconducting order parameter gives the additional conductivity, i.e., paraconductivity. Extending the analysis of paraconductivity to the nonlinear response, we obtain the nonreciprocal charge transport expressed by a2(B, T ) = a1(T )γ(T )B, where γ converges to a finite value at T = T0. Below T0, the motion of vortices is relevant to the voltage drop, and the dependence of a1 and a2 on B and T is different depending on the system and mechanisms. For Rashba superconductors and superconducting surface state of three dimensional TIs under the in-plane magnetic field, the Kosterlitz-Thouless (KT) transition occurs at TKT, below which the vortices and anti-vortices are bound and the resistivity becomes zero. Therefore, a1(B, T ) and a2(B, T ) are defined only above TKT. In this case, the vortex contributions to the transport coefficients are a1(B, T ) = const. and a2(B, T ) ∼ B(T0 − T ) −1 for T → T0. It is also found near TKT that a1(B, T ) ∼ exp[−(bτc/τ ) 1/2 ] and a2(B, T ) ∼ Bτ −3/2 exp[−(bτc/τ ) 1/2 ] with the reduced temperatures τ (T ) = (T − TKT)/TKT, τc = τ (T0), and an order of unity constant b. Below TKT, both a1(B, T ) and a2(B, T ) vanish, and a3(B, T ) ∼ const. and a4(B, T ) ∼ B become the leading two terms in the expansion. On the other hand, for TMD with the magnetic field perpendicular to the 2D system, the KT transition is gone and the system remains resistive even well below TKT. In this case, there are two possible mechanisms for the nonreciprocal charge transport. One is the anisotropy of the damping constant for the motion of the vortex induced by the external magnetic field and current. In this case, a1(B, T ) ∼ B and a2(B, T ) ∼ B 2 . The other one is the ratchet potential acting on the vortex motion, which gives a1(B, T ) ∼ B and a2(B, T ) ∼ B. Based on these results, we propose the experiments to identify the mechanism of the nonreciprocal transport with the realistic estimates for the order of magnitude of the coefficients a1(B, T ) and a2(B, T ) for each case.

Spin current plays a central role in spintronics. In particular, finding more efficient ways to generate spin current has been an important issue and studied actively. For example, representative methods of spin current generation include spin polarized current injections from ferromagnetic metals, spin Hall effect, and spin battery. Here we theoretically propose a new mechanism of spin current generation based on nonlinear phenomena. By using Boltzmann transport theory, we show that a simple application of the electric field E induces spin current proportional to E 2 in noncentrosymmetric spin-orbit coupled systems. We demonstrate that the nonlinear spin current of the proposed mechanism is supported in the surface state of three-dimensional topological insulators and two-dimensional semiconductors with the Rashba and/or Dresselhaus interaction. In the latter case, the angular dependence of the nonlinear spin current can be manipulated by the direction of the electric field and by the ratio of the Rashba and Dresselhaus interactions. We find that the magnitude of the spin current largely exceeds those in the previous methods for a reasonable magnitude of the electric field. Furthermore, we show that application of AC electric fields (e.g. terahertz light) leads to the rectifying effect of the spin current where DC spin current is generated. These findings will pave a new route to manipulate the spin current in noncentrosymmetric crystals.

How to detect the skyrmion position is a crucial problem in future skyrmionics since it corresponds to the reading process of information. We propose a method to detect the skyrmion position purely electrically by measuring the Hall conductance in a constricted geometry. The Hall conductance becomes maximum when a skyrmion is at the lead position. It is possible to detect the skyrmion position even at room temperature. We find an optimized width of the sample determined by the skyrmion radius. We also investigate the effects of elastic and inelastic scatterings, and finite temperature. We find that the local density of states become minimum at the skyrmion position. Our results will be a basis of future skyrmion electronics.Comment: 5 pages, 8 figure