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Shuichi Murakami

Publications and source records attributed to Shuichi Murakami.

At least 91 records · Page 5Linked to original sources
arXiv2019

A diagnosis scheme for topological degeneracies at high-symmetry momenta

Theories of symmetry-based indicators and topological quantum chemistry, while powerful in diagnosing gapped topological materials, cannot be directly applied to diagnosing band degeneracies at high-symmetry momenta due to the violation of the compatibility conditions. Here we design a recursive protocol that utilizes indicators of maximal subgroups to infer the topological nature of band degeneracies at high-symmetry lines. For demonstration, the method is used to predict the existence of iso-energy Weyl points and a node-line cage, respectively, in the phonon bands of In2Te and ZrSiO.

cond-mat.mtrl-sci↗
arXiv2019

Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators

We show that a slab of a three-dimensional inversion-symmetric higher-order topological insulator (HOTI) in class A is a 2D Chern insulator, and that in class AII is a 2D $Z_2$ topological insulator. We prove it by considering a process of cutting the three-dimensional inversion-symmetric HOTI along a plane, and study the spectral flow in the cutting process. We show that the $Z_4$ indicators, which characterize three-dimensional inversion-symmetric HOTIs in classes A and AII, are directly related to the $Z_2$ indicators for the corresponding two-dimensional slabs with inversion symmetry, i.e. the Chern number parity and the $Z_2$ topological invariant, for classes A and AII respectively. The existence of the gapless hinge states is understood from the conventional bulk-edge correspondence between the slab system and its edge states. Moreover, we also show that the spectral-flow analysis leads to another proof of the bulk-edge correspondence in one- and two-dimensional inversion-symmetric insulators.

cond-mat.mes-hall↗
arXiv2019

Glide-symmetric magnetic topological crystalline insulators with inversion symmetry

It is known that three-dimensional magnetic systems with glide symmetry can be characterized by a $Z_2$ topological invariant together with the Chern number associated with the normal vector of the glide plane, and they are expressed in terms of integrals of the Berry curvature. In the present paper, we study the fate of this topological invariant when inversion symmetry is added while time-reversal symmetry is not enforced. There are two ways to add inversion symmetry, leading to space groups No.~13 and No.~14. In space group No.~13, we find that the glide-$Z_2$ invariant is expressed solely from the irreducible representations at high-symmetry points in $k$-space. It constitutes the $\mathbb{Z}_2\times \mathbb{Z}_2$ symmetry-based indicator for this space group, together with another $\mathbb{Z}_2$ representing the Chern number modulo 2. In space group No.~14, we find that the symmetry-based indicator $\mathbb{Z}_2$ is given by a combination of the glide-$Z_2$ invariant and the Chern number. Thus, in space group No.~14, from the irreducible representations at high-symmetry points we can only know possible combinations of the glide-$Z_2$ invariant and the Chern number, but in order to know each value of these topological numbers, we should calculate integrals of the Berry curvature. Finally, we show that in both cases, the symmetry-based indicator $\mathbb{Z}_4$ for inversion symmetric systems leading to the higher-order topological insulators is directly related with the glide-$Z_2$ invariant and the Chern number. As an independent approach to these results, we also construct all invariants from the layer construction for these space groups, and we show complete agreement with the above results for the topological invariants constructed from $k$-space topology.

cond-mat.mes-hall↗
arXiv2019

Topological semimetal phases manifested in transition metal dichalcogenides intercalated with 3d metals

In the search for stable topological semimetals with clean band profiles, we have screened all the 3$d$ metal-intercalated transition-metal dichalcogenides (3dI-TMDCs) by performing hybrid-functional-based ab initio calculations. Two classes of topological materials featuring twelve Weyl nodes in the $k_z=0$ plane (without spin-orbit interactions) are identified: (a) time-reversal-breaking Weyl semimetals VT$_3$X$_6$ (ferromagnetic) and (b) spinless Weyl semimetals MnT$_3$X$_6$ (nonmagnetic), where T=Nb, Ta; X=S, Se. VNb$_3$S$_6$, prototypical of class (a), is half-metallic with only two bands crossing at the Fermi level to form Weyl nodes. MnNb$_3$S$_6$ in the nonmagnetic phase is essentially a spinless version of VNb$_3$S$_6$ featuring an equally clean and simple band profile. Although the space group symmetry (P6$_3$22) implies that the degeneracy between the two bands is lifted for $k$ away from the Weyl nodes, the gap remains extremely small ($\ll$ 0.1 meV) along a loop connecting the Weyl nodes. This quasi-nodal-line degeneracy is explained in terms of the quasi-mirror symmetry of the lattice, induced by the in-plane twofold rotation axes, and the specific orbital nature of the bands. 3dI-TMDCs are chemically and thermally stable stoichiometric compounds containing no toxic elements and are a viable platform for the study of topological condensed-matter physics.

cond-mat.str-el↗
arXiv2019

Pressure-induced topological phase transition in noncentrosymmetric elemental Tellurium

Recent progress in understanding the electronic band topology and emergent topological properties encourage us to reconsider the band structure of well-known materials including elemental substances. Controlling such a band topology by external field is of particular interest from both fundamental and technological view point. Here we report the pressure-induced topological phase transition from a semiconductor to a Weyl semimetal in elemental tellurium probed by transport measurements. Pressure variation of the periods of Shubnikov-de Haas oscillations, as well as oscillations phases, shows an anomaly around the pressure theoretically predicted for topological phase transition. This behavior can be well understood by the pressure-induced band deformation and resultant band crossing effect. Moreover, effective cyclotron mass is reduced toward the critical pressure, potentially reflecting the emergence of massless linear dispersion. The present result paves the way for studying the electronic band topology in well-known compounds and topological phase transition by the external field.

cond-mat.mtrl-sci↗
arXiv2019

Non-Bloch Band Theory of Non-Hermitian Systems

In spatially periodic Hermitian systems, such as electronic systems in crystals, the band structure is described by the band theory in terms of the Bloch wave functions, which reproduce energy levels for large systems with open boundaries. In this paper, we establish a generalized Bloch band theory in one-dimensional spatially periodic tight-binding models. We show how to define the Brillouin zone in non-Hermitian systems. From this Brillouin zone, one can calculate continuum bands, which reproduce the band structure in an open chain. As an example, we apply our theory to the non-Hermitian Su-Schrieffer-Heeger model. We also show the bulk-edge correspondence between the winding number and existence of the topological edge states.

cond-mat.mes-hall↗
arXiv2019

Topological band structure of surface acoustic waves on a periodically corrugated surface

Surface acoustic waves (SAWs) are elastic waves localized on a surface of an elastic body. We theoretically study topological edge modes of SAWs for a corrugated surface. We introduce a corrugation forming a triangular lattice on the surface of an elastic body. We treat the corrugation as a perturbation, and construct eigenmodes on a corrugated surface by superposing those for the flat surface at wavevectors which are mutually different by reciprocal lattice vectors. We thereby show emergence of Dirac cones at the $K$ and $K'$ points analytically. Moreover, by breaking the time-reversal symmetry, we show that the Dirac cones open a gap, and that the Chern number for the lowest band has a nonzero value. It means existence of topological chiral edge modes of SAWs in the gap.

cond-mat.mes-hall↗
arXiv2019

Topological linelike bound states in the continuum

Bound states in the continuum (BIC) have been studied mainly in optics. Recently, electronic BIC have been proposed. They appear as points in the momentum space and are protected topologically by the Chern number. In this study, we propose a type of BIC protected by the winding number, which is one of the topological invariants. These BIC appear as lines in the momentum space, and are realized in a multilayer model consisting of honeycomb-lattice layers. We show band structure and spatial localization of the BIC in this model. The wave numbers at which the BIC appear can be explained in terms of topology in the momentum space.

cond-mat.mes-hall↗
arXiv2018

Nodal-line semimetal superlattices

Spatial modulations, such as multilayers, to realize topological materials have recently been studied in theoretical and experimental works. In this paper, we investigate properties of the multilayers of the nodal-line semimetal (NLS) and the normal insulator. We consider two types of multilayers, with the stacking direction being perpendicular or parallel to the plane where the nodal line lies. In particular, we show that when the stacking direction is parallel to the plane, the nodal lines remain but they change their shapes because of the folding of the Brillouin zone. We also study the multilayers with magnetization. One can expect that the quantum anomalous Hall (QAH) phase emerges in some cases, depending on the direction of the magnetization. If the magnetization is along the $C_2$-invariant axis, the multilayer becomes the Weyl semimetal phase if the $C_2$-invariant axis intersects the nodal lines, and otherwise it becomes the QAH phases.

cond-mat.mes-hall↗
arXiv2018

Phonon Angular Momentum Induced by Temperature Gradient

Phonon modes in crystals can have angular momenta in general. It nevertheless cancels in equilibrium when the time-reversal symmetry is preserved. In this paper we show that when a temperature gradient is applied and heat current flows in the crystal, the phonon distribution becomes off-equilibrium, and a finite angular momentum is generated by the heat current. This mechanism is analogous to the Edelstein effect in electronic systems. This effect requires crystals with sufficiently low crystallographic symmetries, such as polar or chiral crystal structures. Because of the positive charges of the nuclei, this phonon angular momentum induces magnetization. In addition, when the crystal can freely rotate, this generated phonon angular momentum is converted to a rigidbody rotation of the crystal, due to the conservation of the total angular momentum. Furthermore, in metallic crystals, the phonon angular momentum will be partially converted into spin angular momentum of electrons.

cond-mat.mes-hall↗
arXiv2018

Electrides as a New Platform of Topological Materials

Recent discoveries of topological phases realized in electronic states in solids have revealed an important role of topology, which ubiquitously appears in various materials in nature. Many well-known materials have turned out to be topological materials, and this new viewpoint of topology has opened a new horizon in material science. In this paper we find that electrides are suitable for achieving various topological phases, including topological insulating and topological semimetal phases. In the electrides, in which electrons serve as anions, the bands occupied by the anionic electrons lie near the Fermi level, because the anionic electrons are weakly bound by the lattice. This property of the electrides is favorable for achieving band inversions needed for topological phases, and thus the electrides are prone to topological phases. From such a point of view, we find many topological electrides, Y$_2$C (nodal-line semimetal (NLS)), Sc$_2$C (insulator with $π$ Zak phase), Sr$_2$Bi (NLS), HfBr (quantum spin Hall system), and LaBr (quantum anomalous Hall insulator), by using ab initio calculation. The close relationship between the electrides and the topological materials is useful in material science in both fields.

cond-mat.mtrl-sci↗
arXiv2018

Orbital Edelstein effect as a condensed-matter analog of solenoid

We theoretically study current-induced orbital magnetization in a chiral crystal. This phenomenon is an orbital version of the Edelstein effect. We propose an analogy between the current-induced orbital magnetization and an Ampère field in a solenoid in classical electrodynamics. In order to quantify this effect, we define a dimensionless parameter from the response coefficient relating a current density with an orbital magnetization. This dimensionless parameter can be regarded as a number of turns within a unit cell when the crystal is regarded as a solenoid, and it represents how "chiral" the crystal is. By focusing on the dimensionless parameter, one can design band structure which realizes induction of large orbital magnetization. In particular, a Weyl semimetal with all the Weyl nodes close to the Fermi energy can have a large value of this dimensionless parameter, which can exceed that of a classical solenoid.

cond-mat.mes-hall↗
arXiv2018

A cascading nonlinear magneto-optical effect in topological insulators

Topological insulators (TIs) are characterized by possessing metallic (gapless) surface states and a finite band-gap state in the bulk. As the thickness of a TI layer decreases down to a few nanometer, hybridization between the top and bottom surfaces takes place due to quantum tunneling, consequently at a critical thickness a crossover from a 3D-TI to a 2D insulator occurs. Although such a crossover is generally accessible by scanning tunneling microscopy, or by angle-resolved photoemission spectroscopy, such measurements require clean surfaces. Here, we demonstrate that a cascading nonlinear magneto-optical effect induced via strong spin-orbit coupling can examine such crossovers. The helicity dependence of the time-resolved Kerr rotation exhibits a robust change in periodicity at a critical thickness, from which it is possible to predict the formation of a Dirac cone in a film several quintuple layers thick. This method enables prediction of a Dirac cone using a fundamental nonlinear optical effect that can be applied to a wide range of TIs and related 2D materials.

cond-mat.mtrl-sci↗
arXiv2018

Topological semimetals studied by ab initio calculations

In topological semimetals such as Weyl, Dirac, and nodal-line semimetals, the band gap closes at points or along lines in k space which are not necessarily located at high-symmetry positions in the Brillouin zone. Therefore, it is not straightforward to find these topological semimetals by ab initio calculations because the band structure is usually calculated only along high-symmetry lines. In this paper, we review recent studies on topological semimetals by ab initio calculations. We explain theoretical frameworks which can be used for the search for topological semimetal materials, and some numerical methods used in the ab initio calculations.

cond-mat.mtrl-sci↗
arXiv2017

Spinless hourglass nodal-line semimetals

Nodal-line semimetals, one of the topological semimetals, have degeneracy along nodal lines where the band gap is closed. In many cases, the nodal lines appear accidentally, and in such cases it is impossible to determine whether the nodal lines appear or not, only from the crystal symmetry and the electron filling. In this paper, for spinless systems, we show that in specific space groups at $4N+2$ fillings ($8N+4$ fillings including the spin degree of freedom), presence of the nodal lines is required regardless of the details of the systems. Here, the spinless systems refer to crystals where the spin-orbit coupling is negligible and the spin degree of freedom can be omitted because of the SU(2) spin degeneracy. In this case the shape of the band structure around these nodal lines is like an hourglass, and we call this a spinless hourglass nodal-line semimetal. We construct a model Hamiltonian as an example and we show that it is always in the spinless hourglass nodal-line semimetal phase even when the model parameters are changed without changing the symmetries of the system. We also establish a list of all the centrosymmetric space groups, under which spinless systems always have hourglass nodal lines, and illustrate where the nodal lines are located. We propose that Al$_3$FeSi$_2$, whose space-group symmetry is Pbcn (No. 60), is one of the nodal-line semimetals arising from this mechanism.

cond-mat.mtrl-sci↗
arXiv2017

Universal phase transition and band structures for spinless nodal-line and Weyl semimetals

We study a general phase transition between spinless topological nodal-line semimetal and Weyl semimetal phases. We classify topological nodal lines into two types based on their positions and shapes, and their phase transitions depends on their types. We show that the topological nodal-line semimetal becomes the Weyl semimetal by breaking time-reversal symmetry when the nodal lines enclose time-reversal invariant momenta (type-A nodal lines). We also discuss an effect of crystallographic symmetries determining the band structure of the topological nodal-line semimetals. Thanks to protection by the symmetries, the topological nodal-line semimetals can transit into the spinless Weyl semimetals or maintain the nodal lines in many crystals after inversion symmetry is broken.

cond-mat.mes-hall↗
arXiv2017

Topological Phases in a Weyl Semimetal Multilayer

We investigate multilayer systems of a normal insulator and a Weyl semimetal. We calculate the bulk band structure and determine phase diagrams by changing the thickness of the normal insulator and that of the Weyl semimetal layer using two models; one is from the effective model for a Weyl semimetal, and the other is the lattice model. We compare the results between the two models, and found that they agree well. As a result, we find that the multilayer system shows a qualitatively different behavior depending on the stacking direction relative to the displacement vector connecting between two Weyl nodes. When the stacking direction is perpendicular to the displacement vector, the Weyl semimetal and the normal insulator phases appear only. On the other hand, when it is parallel to the displacement vector, the phase diagram is rich, containing not only the Weyl semimetal phases but also the quantum anomalous Hall phases with different Chern numbers. Furthermore, the phase transition can be understood in terms of the trajectory of the Weyl nodes.

cond-mat.mes-hall↗
arXiv2017

Topological Dirac Nodal Lines and Surface Charges in fcc Alkaline Earth Metals

In nodal-line semimetals, the gaps close along loops in ${\bf k}$ space, which are not at high-symmetry points. Typical mechanisms for the emergence of nodal lines involve mirror symmetry and the $π$ Berry phase. Here, we show via ab initio calculations that fcc calcium (Ca), strontium (Sr) and ytterbium (Yb) have topological nodal lines with the $π$ Berry phase near the Fermi level, when spin-orbit interaction is neglected. In particular, Ca becomes a nodal-line semimetal at high pressure. Owing to nodal lines, the Zak phase becomes either $π$ or 0 depending on the wavavector ${\bf k}$, and the $π$ Zak phase leads to surface polarization charge. Carriers eventually screen it, leaving behind large surface dipoles. In materials with nodal lines, both the large surface polarization charge and the emergent drumhead surface states enhance Rashba splitting when heavy adatoms are present, as we have shown to occur in Bi/Sr(111) and in Bi/Ag(111).

cond-mat.mtrl-sci↗