Noncentrosymmetric Metals Research Articles

Berry curvature induced magnetotransport in 3D noncentrosymmetric metals

We study the magnetoelectric and magnetothermal transport properties of noncentrosymmetric metals using semiclassical Boltzmann transport formalism by incorporating the effects of Berry curvature (BC) and orbital magnetic moment (OMM). These effects impart quadratic-B dependence to the magnetoelectric and magnetothermal conductivities, leading to intriguing phenomena such as planar Hall effect, negative magnetoresistance (MR), planar Nernst effect and negative Seebeck effect. The transport coefficients associated with these effects show the usual oscillatory behavior with respect to the angle between the applied electric field and magnetic field. The bands of noncentrosymmetric metals are split by Rashba spin–orbit coupling except at a band touching point (BTP). For Fermi energy below (above) the BTP, giant (diminished) negative MR is observed. This difference in the nature of MR is related to the magnitudes of the velocities, BC and OMM on the respective Fermi surfaces, where the OMM plays the dominant role. The absolute MR and planar Hall conductivity show a decreasing (increasing) trend with Rashba coupling parameter for Fermi energy below (above) the BTP.

Kramers nodal line metals

Recently, it was pointed out that all chiral crystals with spin-orbit coupling (SOC) can be Kramers Weyl semimetals (KWSs) which possess Weyl points pinned at time-reversal invariant momenta. In this work, we show that all achiral non-centrosymmetric materials with SOC can be a new class of topological materials, which we term Kramers nodal line metals (KNLMs). In KNLMs, there are doubly degenerate lines, which we call Kramers nodal lines (KNLs), connecting time-reversal invariant momenta. The KNLs create two types of Fermi surfaces, namely, the spindle torus type and the octdong type. Interestingly, all the electrons on octdong Fermi surfaces are described by two-dimensional massless Dirac Hamiltonians. These materials support quantized optical conductance in thin films. We further show that KNLMs can be regarded as parent states of KWSs. Therefore, we conclude that all non-centrosymmetric metals with SOC are topological, as they can be either KWSs or KNLMs.

Tunable spin-valley coupling in layered polar Dirac metals

In non-centrosymmetric metals, spin-orbit coupling induces momentum-dependent spin polarization at the Fermi surfaces. This is exemplified by the valley-contrasting spin polarization in monolayer transition metal dichalcogenides with in-plane inversion asymmetry. However, the valley configuration of massive Dirac fermions in transition metal dichalcogenides is fixed by the graphene-like structure, which limits the variety of spin-valley coupling. Here, we show that the layered polar metal BaMnX2 (X = Bi, Sb) hosts tunable spin-valley-coupled Dirac fermions, which originate from the distorted X square net with in-plane lattice polarization. We found that BaMnBi2 has approximately one-tenth the lattice distortion of BaMnSb2, from which a different configuration of spin-polarized Dirac valleys is theoretically predicted. This was experimentally observed as a clear difference in the Shubnikov-de Haas oscillation at high fields between the two materials. The chemically tunable spin-valley coupling in BaMnX2 makes it a promising material for various spin-valleytronic devices.

Role of Berry curvature in the generation of spin currents in Rashba systems

We study the background (equilibrium), linear and nonlinear spin currents in 2D Rashba spin-orbit coupled systems with Zeeman splitting and in 3D noncentrosymmetric metals using modified spin current operator by inclusion of the anomalous velocity. The linear spin Hall current arises due to the anomalous velocity of charge carriers induced by the Berry curvature. The nonlinear spin current occurs due to the band velocity and/or the anomalous velocity. For 2D Rashba systems, the background spin current saturates at high Fermi energy (independent of the Zeeman coupling), linear spin current exhibits a plateau at the Zeeman gap and nonlinear spin currents are peaked at the gap edges. The magnitude of the nonlinear spin current peaks enhances with the strength of Zeeman interaction. The linear spin current is polarized out of plane, while the nonlinear ones are polarized in-plane. We witness pure anomalous nonlinear spin current with spin polarization along the direction of propagation. In 3D noncentrosymmetric metals, background and linear spin currents are monotonically increasing functions of Fermi energy, while nonlinear spin currents vary non-monotonically as a function of Fermi energy and are independent of the Berry curvature. These findings may provide useful information to manipulate spin currents in Rashba spin-orbit coupled systems.

Topology and Symmetry of Quantum Materials via Nonlinear Optical Responses

We review recent progress in the study of photogalvanic effects and optical second-harmonic generation in topological and noncentrosymmetric metals.

Electron–Electron Scattering and Resistivity in Non-Centrosymmetric Metals

The quadratic low-temperature dependence of resistance in ordinary metals is determined by the momentum relaxation due to electron-electron scattering in the presence Umklapp processes and scattering on impurities. In metals without inversion center spin-orbit interaction of electrons with crystal lattice lifts spin degeneracy of electron states and splits each band on two bands. The temperature dependence of electron-electron collisions scattering rate is found using the matrix kinetic equation including the electron-impurity and electron-electron intra and inter band scattering. It is shown that in clean enough case when the energy of band splitting exceeds the electron-impurity scattering rate but at the same time it is much smaller than the Fermi energy the square low-temperature dependence of resistivity is still valid.

Dynamical polarization and plasmons in noncentrosymmetric metals

We study the dynamical polarization function and plasmon modes for spin-orbit coupled noncentrosymmetric metals (NCMs). These systems have different Fermi surface topology for Fermi energies above and below the spin degenerate point which is also known as the band touching point (BTP). We calculate the exact dynamical polarization function numerically and also provide its analytical expression in the long wavelength limit. We obtain the plasmon dispersion within the framework of random phase approximation. In NCMs, there is a finite energy gap in between intra and interband particle hole continuum (PHC) for vanishing excitation wavevector. In the long wavelength limit, the width of interband PHC behaves differently for Fermi energies below and above the BTP as a clear signature of the Fermi surface topology change. We find a single undamped optical plasmon mode lying in between the intra and interband PHC for Fermi energies above and below the BTP. The plasmon mode below the BTP has smaller velocity than that of above the BTP. It is interesting to find that as we tune the Fermi energy around the BTP, the plasmon mode becomes damped within a range of e-e interaction strength. For Fermi energies above and below the BTP, we also obtain an approximate analytical result of plasma frequency and plasmon dispersion which match well with their numerical counterparts in the long wavelength limit. The plasmon dispersion is $\propto q^2$ with $q$ being the wave vector for plasmon excitation in the long wavelength limit. We find that varying the carrier density with fixed e-e interaction strength or vice versa does not change the number of undamped plasmon mode, although damped plasmon modes can be more in number for some values of these parameters. We demonstrate our results by calculating the loss function and optical conductivity which can be measured in experiments.

Anomalous hydrodynamic transport in interacting noncentrosymmetric metals

In highly conductive metals with sufficiently strong momentum-conserving scattering, the electron momentum is regarded as a long-lived quantity, whose dynamics is described by an emergent hydrodynamic theory. In this paper, we develop an electron hydrodynamic theory for noncentrosymmetric metals, where a novel class of electron fluids is realized by lowering crystal symmetries and the resulting geometrical effects. The obtained hydrodynamic equation suggests a nontrivial analogy between electron fluids in noncentrosymmetric metals and chiral fluids in vacuum, and predicts novel hydrodynamic transport phenomena, that is, asymmetric Poiseuille flow and anomalous edge current. Our theory also gives a hydrodynamic description of the counterpart of various anomalous transport phenomena such as the quantum nonlinear Hall effect. Furthermore, we give a symmetry consideration on the hydrodynamic equation and propose several experimental setups to realize such anomalous hydrodynamic transport in the existing hydrodynamic materials, including bilayer graphene and Weyl semimetals.

Ferromagnetic Quantum Critical Point in Noncentrosymmetric Systems.

Ferromagnetic quantum criticality in clean metals has proven elusive due to fermionic soft modes that drive the transition first order. We show that noncentrosymmetric metals with a strong spin-orbit interaction provide a promising class of materials for realizing a ferromagnetic quantum critical point in clean systems. The spin-orbit interaction renders massive the soft modes that interfere with quantum criticality in most materials, while the absence of spatial inversion symmetry precludes the existence of new classes of soft modes that could have the same effect.

Thermoelectric and optical probes for a Fermi surface topology change in noncentrosymmetric metals

Noncentrosymmetric metals such as ${\mathrm{Li}}_{2}{({\mathrm{Pd}}_{1\ensuremath{-}x}{\mathrm{Pt}}_{x})}_{3}\mathrm{B}$ have different Fermi surface topology below and above the band touching point where spin-degeneracy is not lifted by the spin-orbit coupling. We investigate thermoelectric and optical response as probes for this Fermi surface topology change. We show that the chemical potential displays a dimensional crossover from three-dimensional to one-dimensional characteristics as the descending Fermi energy crosses the band touching point. This dimensional crossover is due to the existence of different Fermi surface topology above and below the band touching point. We obtain an exact expression of relaxation time due to short-range scatterer by solving Boltzmann transport equations self-consistently. The thermoelctric power and figure of merit are significantly enhanced as the Fermi energy goes below the band touching point owing to the underlying one-dimensional-like nature of noncentrosymmteric bulk metals. The value of thermoelectric figure of merit goes beyond two as the Fermi energy approaches to the van Hove singularity for lower spin-orbit coupling. Similarly, the studies of the zero-frequency and finite-frequency optical conductivities in the zero-momentum limit reflect the nature of topological change of the Fermi surface. The Hall coefficient and optical absorption width exhibit distinct signatures in response to the changes in Fermi surface topology.

Gyrotropic Hall effect in Berry-curved materials

We study the ac Hall response induced by passage of dc transport current in two- and three-dimensional metals with gyrotropic point groups -- the gyrotropic Hall effect -- and consider the phenomenon of current-induced optical activity in noncentrosymmetric metals as a physical application of our theory. While the effect is expected to be present in single crystals of any noncentrosymmetric metal, we expect it to be strongest in enantiomorphic Weyl semimetals. Using the semiclassical kinetic equation approach we present several mechanisms underlying the gyrotropic Hall effect. Amongst them, the intrinsic mechanism is determined by the Berry curvature dipole, while extrinsic impurity-induced processes are related to skew scattering and side jump phenomena. In general, the intrinsic and extrinsic contributions can be of similar magnitude. We discuss the gyrotropic Hall effect for all frequencies of practical interest, from the DC transport limit, to optical frequencies. We show that for frequencies that are small compared to relevant band splittings, the trace of the gyrotropic Hall tensor in three-dimensional materials is proportional to a topological, quantized Berry charge, and therefore is robust in gyrotropic Weyl systems. This implies that polycrystals of strongly gyrotropic Weyl semimetals will demonstrate strong current-induced optical activity, whereas the response vanishes for polycrystalline ordinary metals. Therefore, the current-induced optical activity can be considered a valuable tool in identifying the topological nature of a material.

Split Fermi Surfaces of the Spin–Orbit-Coupled Metal Cd2Re2O7 Probed by de Haas–van Alphen Effect

The superconducting pyrochlore oxide Cd2Re2O7 shows a structural transition with inversion symmetry breaking (ISB) at Ts1 = 200 K. A recent theory [L. Fu, Phys. Rev. Lett. 115, 026401 (2015)] suggests that the origin is an electronic instability that leads to a multipolar order in the spin-orbit-coupled metal. To observe the Fermi surface of the low-temperature phase of Cd2Re2O7, we perform de Haas-van Alphen effect measurements by means of magnetic torque. In reference to a calculated band structure, the spin-split Fermi surfaces with large cyclotron masses of 5-9m0 are revealed. The splitting is suggested to be due to an antisymmetric spin-orbit coupling induced by ISB, the strength of which is estimated to be approximately 67 K, which is rather smaller than those of typical non-centrosymmetric metals.

Berry curvature dipole in Weyl semimetal materials: An ab initio study

Noncentrosymmetric metals are anticipated to exhibit a $dc$ photocurrent in the nonlinear optical response caused by the Berry curvature dipole in momentum space. Weyl semimetals (WSMs) are expected to be excellent candidates for observing these nonlinear effects because they carry a large Berry curvature concentrated in small regions, i.e., near the Weyl points. We have implemented the semiclassical Berry curvature dipole formalism into an $ab~initio$ scheme and investigated the second-order nonlinear response for two representative groups of materials: the TaAs-family type-I WSMs and MoTe$_2$-family type-II WSMs. Both types of WSMs exhibited a Berry curvature dipole, in which type-II Weyl points are usually superior to the type-I because of the strong tilt. Corresponding nonlinear susceptibilities in several materials promise a nonlinear Hall effect in the $dc$ field limit, which is within the experimentally detectable range.

Polar instability under electrostatic doping in tetragonal SnTiO3

How to make the metallicity compatible with a polar structure for forming a ``polar metal'' has been an interesting and important topic since the polar structure was discovered in metallic $\mathrm{LiOs}{\mathrm{O}}_{3}$. Here, we present robust polar instability under electrostatic doping in tetragonal $\mathrm{SnTi}{\mathrm{O}}_{3}$ based on our first-principles calculations. The mechanism for polar distortion surviving free carriers is investigated from the ``weak-coupling'' perspective. The contributions of different interactions between two polar modes in a ``ferroelectric'' phase transition are also studied. We found that the short-range interaction contributes the most for lowering the total energy during the ferroelectricphase transition. Moreover, the dipole-dipole interaction between two polar modes of oxygen atoms provides the largest energy gain among local interactions, which cannot be screened out by doping. We propose that the promising candidates for noncentrosymmetric metals obtained by doping are ferroelectrics with bonding states responsible for polar distortions away from the Fermi level. We believe that this mechanism sheds light on a method to obtain noncentrosymmetric metals from a large amount of ferroelectric perovskite oxides by doping.

Kinetic orbital moments and nonlocal transport in disordered metals with nontrivial band geometry

We study the effects of spatial dispersion in disordered noncentrosymmetric metals. These include the kinetic magnetoelectric effect, natural optical activity of metals, as well as the so-called dynamic chiral magnetic effect as a particular case of the latter. These effects are determined by the linear in the wave vector of an electromagnetic perturbation contribution to the conductivity tensor of a material, and stem from the magnetic moments of quasiparticles near the Fermi surface. We identify new disorder-induced contributions to these magnetic moments that come from the skew scattering and side jump processes, familiar from the theory of anomalous Hall effect. We show that at low frequencies the spatial dispersion of the conductivity tensor comes mainly either from the skew scattering or intrinsic contribution, and there is always a region of frequencies in which the intrinsic mechanism dominates. Our results imply that in clean three-dimensional metals, current-induced magnetization is in general determined by impurity skew scattering, rather than intrinsic contributions. Intrinsic effects are expected to dominate in cubic enantiomorphic crystals with point groups $T$ and $O$, and in polycrystalline samples, regardless of their mobility.

Superconductivity in magnetic multipole states

Stimulated by recent studies of superconductivity and magnetism with local and global broken inversion symmetry, we investigate the superconductivity in magnetic multipole states in locally noncentrosymmetric metals. We consider a one-dimensional zigzag chain with sublattice-dependent antisymmetric spin-orbit coupling and suppose three magnetic multipole orders: monopole order, dipole order, and quadrupole order. It is demonstrated that the Bardeen-Cooper-Schrieffer state, the pair-density wave (PDW) state, and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state are stabilized by these multipole orders, respectively. We show that the PDW state is a topological superconducting state specified by the nontrivial $\mathbb{Z}_2$ number and winding number. The origin of the FFLO state without macroscopic magnetic moment is attributed to the asymmetric band structure induced by the magnetic quadrupole order and spin-orbit coupling.

Electron Correlation Effects in Non-Centrosymmetric Metals in the Weak Coupling Regime

The two-dimensional Rashba-Hubbard model is investigated in order to clarify the electron correlation effects in non-centrosymmetric metals. The renormalization effect on Rashba spin-orbit coupling (RSOC) is calculated on the basis of second-order and third-order perturbation theories. We show that RSOC is enhanced by the electron correlation. On the other hand, the spin-splitting of the Fermi momentum (SFM) is robust against the electron correlation effect because the enhancement of RSOC is cancelled by the $k$-mass renormalization. The cancellation is almost perfect in often adopted models in which the momentum dependence of RSOC is linear in the quasiparticle velocity. A small correction to the SFM appears otherwise. We show that the same results are obtained for other antisymmetric spin-orbit couplings in non-centrosymmetric systems, such as the synthetic spin-orbit coupling in cold atoms.

Anomalous Spin Response in the Non-Centrosymmetric Metal CePt3Si

Non-centrosymmetric metals with tetragonal structure are characterized by an antisymmetric Rashba-type spin–orbit interaction, which has been predicted to give rise to anomalous spin susceptibility. Our polarized inelastic neutron scattering measurements in the normal phase of the heavy-fermion superconductor CePt3 Si confirm this prediction. We find that for a finite wave vector along the crystallographic a-direction the spin susceptibility χaa is different from χbb by a factor of two. The effect is even larger than in theoretical calculations based on the Hubbard model, and we speculate that this is due to the strong spin–orbit coupling of rare-earth heavy fermions.

Designing a robustly metallic noncenstrosymmetric ruthenate oxide with large thermopower anisotropy

The existence of ~30 noncentrosymmetric metals (NCSM) suggests a contraindication between crystal structures without inversion symmetry and metallic behaviour. Those containing oxygen are especially scarce. Here we propose and demonstrate a design framework to remedy this property disparity and accelerate NCSM oxide discovery. The primary ingredient relies on the removal of inversion symmetry through displacements of atoms whose electronic degrees of freedom are decoupled from the states at the Fermi level. Density functional theory calculations validate this crystal-chemistry strategy, and we predict a new polar ruthenate exhibiting robust metallicity. We demonstrate that the electronic structure is unaffected by the inclusion of spin-orbit interactions, and that cation-ordered SrCaRu2O6 exhibits a large thermopower anisotropy (|ΔS⊥|~6.3 μV K(-1) at 300 K) derived from its polar structure. Our findings provide chemical and structural selection guidelines to aid in the search of NCSM with enhanced thermopower anisotropy.

Magneto-Electric Effect in Three-Dimensional Coupled Zigzag Chains

Stimulated by recent studies of quantum phases with broken local inversion symmetry, we study the magnetoelectric effect in locally noncentrosymmetric metals. We consider three-dimensional (3D) coupled zigzag chains and demonstrate that the antiferromagnetic moment is induced by the electric current through a staggered antisymmetric spin-orbit coupling. This current-induced magnetism is much larger than that in globally noncentrosymmetric metals. We provide an intuitive understanding of the current-induced antiferromagnetic moment by showing the inverse magnetoelectric effect, that is, the ferroic p-wave charge nematic order accompanied by the asymmetric band structure in the antiferromagnetic state. We also examine conduction electrons coupled to localized spins via Kondo exchange coupling and demonstrate a significant enhancement of the magnetoelectric effect. A possible experimental observation of the magnetoelectric effect in metals is discussed, with focus on LnM_2Al_10 compounds, such as NdRu_Al_10 and TbRu_2Al_10.