Recently, quantum Hall state analogs in classical mechanics attract much attention from topological points of view. Topology is not only for mathematicians but also quite useful in a quantum world. Further it even governs the Newton’s law of motion. One of the advantages of classical systems over solid state materials is its clear controllability. Here we investigate mechanical graphene, which is a spring-mass model with the honeycomb structure as a typical mechanical model with nontrivial topological phenomena. The vibration spectrum of mechanical graphene is characterized by Dirac cones serving as sources of topological nontriviality. We find that the spectrum has dramatic dependence on the spring tension at equilibrium as a natural control parameter, i.e., creation and annihilation of the Dirac particles are realized as the tension increases. Just by rotating the system, the manipulated Dirac particles lead to topological transition, i.e., a jump of the “Chern number” occurs associated with flipping of propagating direction of chiral edge modes. This is a bulk-edge correspondence governed by the Newton’s law. A simple observation that in-gap edge modes exist only at the fixed boundary, but not at the free one, is attributed to the symmetry protection of topological phases.

The band structure of cubic inverse perovskites, Ca 3 PbO and its family, are investigated with the first-principles method. A close observation of the band structure reveals that six equivalent Dirac electrons with a very small mass exist on the line connecting the À-and X-points, and at the symmetrically equivalent points in the Brillouin zone. The discovered Dirac electrons are three-dimensional and remarkably located exactly at the Fermi energy. A tight-binding model describing the low-energy band structure is also constructed and used to discuss the origin of the Dirac electrons in this material. Materials related to Ca 3 PbO are also studied, and some design principles for the Dirac electrons in this series of materials are proposed.KEYWORDS: Dirac electron, inverse perovskite, the first-principles calculation, tight-binding model ''Emergence'' is one of the most important concepts in condensed matter physics. Although this key word often appears in the context of many-body or strong correlation effects, emergent behaviors are also observed in noninteracting systems where the low-energy effective Hamiltonian becomes quite distinct from the original Hamiltonian. The most well-known example is the relativistic Dirac Hamiltonian realized in graphene 1) derived from a nonrelativistic Hamiltonian. Many intriguing properties of graphene can be ascribed to the existence of ''Dirac electrons'' in its low-energy band structure.2) Actually, Dirac electrons in materials have a long history starting from bismuth, which has three-dimensional massive Dirac electrons in its band structure.3) The organic conductor -(BETT-TTF) 2 I 3 is also known to be a material having Dirac electrons near the Fermi energy. 4,5) The most up-todate example is a surface state of a three-dimensional topological insulator, 6) which is extensively studied in these days.In connection with topological insulators, inverse-perovskite materials have attracted much attention recently. For example, it is claimed that Ca 3 NBi enters a topological phase under an appropriate strain engineering scheme. 7) In this paper, we show that cubic inverse perovskites, Ca 3 PbO and its family, have three-dimensional Dirac electrons with a very small mass at the Fermi energy. Although Ca 3 PbO is on the list of potential topological insulators proposed by Klintenberg,8) our close observation of its band structure reveals the existence of bulk (not surface) Dirac electrons on the line connecting the À-and X-points, and at the symmetrically equivalent points in the Brillouin zone. Although some first-principles calculations on this material are available in the literature, 9,10) it is the first time that the existence of Dirac electrons is pointed out. We also construct a tight-binding model that describes the low-energy band structure, and clarify the origin of the Dirac electrons in this material by analyzing the model. We also study the family of Ca 3 PbO, and some design principles for Dirac electrons in this series of materials are proposed on the basis of the ...

We report electronic structure and physical properties of metal-doped picene as well as selective synthesis of the phase that exhibits 18 K superconducting transition. First, Raman scattering is used to characterize the number of electrons 2 transferred from the dopants to picene molecules, where a softening of Raman scattering peaks enables us to determine the number of transferred electrons.From this we have identified that three electrons are transferred to each picene molecule in the superconducting doped picene solids. Second, we report pressure dependence of T c in 7 K and 18 K phases of K 3 picene. The 7 K phase shows a negative pressure-dependence, while the 18 K phase exhibits a positive pressure-dependence which cannot be understood with a simple phonon mechanism of BCS superconductivity. Third, we report a new synthesis method for superconducting K 3 picene by a solution process with monomethylamine, CH 3 NH 2 . This method enables us to prepare selectively the K 3 picene sample exhibiting 18 K superconducting transition. The method for preparing K 3 picene with T c = 18 K found here may facilitate clarification of the mechanism of superconductivity.Corresponding author: Takashi Kambe, kambe@cc.okayama-u.ac.jp & Yoshihiro Kubozono, kubozono@cc.okayama-u.ac.jp 3 I. IntroductionRecently a new class of organic superconductors has been discovered in aromatic systems. They are solids of hydrocarbons that include picene, coronene, phenanthrene and 1,2:8,9-dibenzopentacene, 1-6 doped with metal atoms. Namely, the superconductivity was first discovered in potassium-doped picene, K 3 picene, which showed two different superconducting transition temperatures, one with T c = 7 K and the other as high as 18 K. 1 This has been followed by other studies, and the highest T c among these hydrocarbon superconductors to date attains 33 K observed in K 3.45 dibenzopentacene, 6 whose T c is much higher than the highest T c (14.2 K at 8.2 GPa 7 in β'-(BEDT-TTF) 2 ICl 2 ) in charge-transfer organic superconductors. Thus the hydrocarbon superconductors are very attractive from viewpoints of development of new high-T c superconductors as well as fundamental physics of superconductivity.Theoretical calculations for picene superconductors were also achieved, which suggests that the electron-phonon coupling is strong, 8,9 the conduction band comprises four bands arising from two LUMO orbitals, 10 and that strong hybridization between the dopants and molecules invalidates a rigid-band picture. 10The departure from the rigid-band picture was experimentally evidenced by photoemission spectroscopy. 11 This photoemission study clearly showed a metallic ground state for potassium-doped picene films. Our recent resistivity data also indicate a metallic behavior for the K 3 picene phase. 12 Further, a Pauli paramagnetic susceptibility was observed for a K 3 picene bulk sample. 1 These results support a metallic ground state for K 3 picene.The T c for the solid K 3 picene was found to be either 7 or 18 K, 1,2 while the T c of K 3 phenant...

The band structure of Ca3PbO, which possesses a three-dimensional massive Dirac electron at the Fermi energy, is investigated in detail. Analysis of the orbital weight distributions on the bands obtained in the first-principles calculation reveals that the bands crossing the Fermi energy originate from the three Pb-p orbitals and three Ca-d x 2 −y 2 orbitals. Taking these Pb-p and Ca-d x 2 −y 2 orbitals as basis wave functions, a tight-binding model is constructed. With the appropriate choice of the hopping integrals and the strength of the spin-orbit coupling, the constructed model sucessfully captures important features of the band structure around the Fermi energy obtained in the first-principles calculation. By applying the suitable basis transformation and expanding the matrix elements in the series of the momentum measured from a Dirac point, the low-energy effective Hamiltonian of this model is explicitely derived and proved to be a Dirac Hamiltonain. The origin of the mass term is also discussed. It is shown that the spin-orbit coupling and the orbitals other than Pb-p and Ca-d x 2 −y 2 orbitals play important roles in making the mass term finite. Finally, the surface band structures of Ca3PbO for several types of surfaces are investigated using the constructed tight-binding model. We find that there appear nontrivial surface states that cannot be explained as the bulk bands projected on the surface Brillouin zone. The relation to the topological insulator is also discussed.

Localized electrons appear at the zigzag-shaped edge of graphene due to quantum interference. Here we propose a way for harnessing the edge electronic states to make them mobile, by incorporating a topological view point. The manipulation required is to introduce a pattern of strong-weak bonds between neighboring carbon atoms, and to put side by side two graphene sheets with strong-weak alternation conjugating to each other. The electrons with up and down pseudospins propagate in opposite directions at the interface, similar to the prominent quantum spin Hall effect. The system is characterized by a topological index, the mirror winding number, with its root lying in the Su-Schrieffer-Heeger model for polymer. Taking this point of view, one is rewarded by several ways for decorating graphene edge which result in similar mobile electronic states with topological protection. This work demonstrates that celebrated nanotechnology can be used to derive topological states.