Dirac Electron System Research Articles

Nonlinear optical response in multiband Dirac-electron system

Nonlinear optical response in multiband Dirac-electron system

Diamond lattice in single-component molecular crystals comprising tetrabenzoporphyrin neutral radicals.

A single-component molecular radical crystal of CoIII(tbp˙-)(CN)2, where tbp = tetrabenzoporphyrinato ligand, exhibiting a diamond lattice was fabricated as a potential candidate for a three-dimensional Dirac electron system. Band structure calculations revealed that the Fermi energy level was located at the Dirac point. A small electrical resistivity of 160 Ω cm was observed at 2 K under the application of 2.4 GPa. Furthermore, substituting CoIII by FeIII or MnIII led to the introduction of local magnetic moments into the diamond-lattice system. MIII(tbp˙-)L2 crystals will open up uncharted fields in the study of the Dirac electron systems.

Dirac Cone Formation in Single-Component Molecular Conductors Based on Metal Dithiolene Complexes

Single-component molecular conductors exhibit a strong connection to the Dirac electron system. The formation of Dirac cones in single-component molecular conductors relies on (1) the crossing of HOMO and LUMO bands and (2) the presence of nodes in the HOMO–LUMO couplings. In this study, we investigated the possibility of Dirac cone formation in two single-component molecular conductors derived from nickel complexes with extended tetrathiafulvalenedithiolate ligands, [Ni(tmdt)2] and [Ni(btdt)2], using tight-biding models and first-principles density-functional theory (DFT) calculations. The tight-binding model predicts the emergence of Dirac cones in both systems, which is associated with the stretcher bond type molecular arrangement. The DFT calculations also indicate the formation of Dirac cones in both systems. In the case of [Ni(btdt)2], the DFT calculations, employing a vdW-DF2 functional, reveal the formation of Dirac cones near the Fermi level in the nonmagnetic state after structural optimization. Furthermore, the DFT calculations, by utilizing the range-separated hybrid functional, confirm the antiferromagnetic stability in [Ni(btdt)2], as observed experimentally.

Charged magnons on the surface of a topological insulator

We study a system of two-dimensional Dirac electrons (as is realized on the surface of a 3D topological insulator) coupled to an array of localized spins. The spins are coupled ferromagnetically to each other, forming an ordered ground state with low-energy spin-wave excitations (magnons). The Dirac electrons couple to the spins through a spin-dependent effective Zeeman field. The out-of-plane effective Zeeman field therefore serves as a Dirac mass that gaps the electronic spectrum. Once a spin is flipped, it creates a surrounding domain in which the sign of the Dirac mass is opposite to that of the rest of the sample. Therefore, an electronic bound state appears on the domain wall, as predicted by Jackiw and Rebbi. However, in a quantum magnet, a localized spin flip does not produce an eigenstate. Instead, the eigenstates correspond to delocalized spin waves (magnons). As in the case of the single flipped spin, the delocalized magnon also binds an in-gap electronic state. We name this excitation a `Jackiw-Rebbi-Magnon' (JRM) and study its signature in the dynamic spin susceptibility. When the sample is tunnel-coupled to an electronic reservoir, a magnon produced in a system without any electrons hybridizes with a JRM (which binds a single electron), producing magnon-JRM polaritons. For such a system, we identify a quantum phase transition when the magnon-JRM polariton energy falls below that of the fully polarized ferromagnetic ground state.

Strain-induced massless Dirac fermion state of the molecular conductor α-(BEDT-TTF)2I3

Uniaxial pressure can dramatically change the properties of low-dimensional systems and induce electronic phase transitions. The first-discovered molecular massless Dirac electron system α-(BEDT-TTF)2I3 has intensively been studied because of its unique features, such as the Fermi energy being very close to the Dirac point, strong electron correlation, and the quantum phase transition from the charge-ordered insulating state. However, the Dirac state is realized only under high pressure of 15 kbar, which limits the measurement of physical properties (e.g., experimental determination of band dispersion and density of states). Here, we demonstrate that the Dirac state of α-(BEDT-TTF)2I3 can be realized by applying uniaxial bending strain without confining it in a pressure cell. Uniaxial strain below 1% completely suppresses the metal–insulator transition observed at ambient pressure. Under strain, a characteristic temperature dependence of magnetoresistance associated with the formation of the n = 0 Landau level is observed, indicating the realization of the massless Dirac state.

Negative transverse magnetoresistance due to the negative off-diagonal mass in linear dispersion materials

This study calculated the magnetoresistance (MR) in the Dirac electron system, Dresselhaus–Kip–Kittel (DKK) model, and nodal-line semimetals based on the semiclassical Boltzmann theory, with particular focus on the detailed energy dispersion structure. The negative off-diagonal effective-mass was found to induce negative transverse MR owing to the energy dispersion effect. The impact of the off-diagonal mass was more prominent in case of a linear energy dispersion. Further, Dirac electron systems could realize negative MR even if the Fermi surface was perfectly spherical. The obtained negative MR in the DKK model may explain the long-standing mystery in p-type Si.

Quantum Hall Effect in Bulk (Multilayered) Organic Crystal

The multilayer quantum Hall effect is discovered in an organic massless Dirac electron system, α-(BETS)2I3 under pressure at low temperatures and a magnetic field of approximately 1 T.

Spin pumping into anisotropic Dirac electrons

We study spin pumping into an anisotropic Dirac electron system induced by microwave irradiation to an adjacent ferromagnetic insulator theoretically. We formulate the Gilbert damping enhancement due to the spin current flowing into the Dirac electron system using second-order perturbation with respect to the interfacial exchange coupling. As an illustration, we consider the anisotropic Dirac system realized in bismuth to show that the Gilbert damping varies according to the magnetization direction in the ferromagnetic insulator. Our results indicate that this setup can provide helpful information on the anisotropy of the Dirac electron system.

Predicted Novel Type of Photoinduced Topological Phase Transition Accompanied by Collision and Collapse of Dirac-cone Pair in Organic Salt α-(BEDT-TTF)2I3

Photoinduced topological phase transitions in the Dirac-electron systems have attracted intensive research interest since its theoretical prediction in graphene, where the application of circularly polarized light opens a gap at the Dirac points and renders the system a topologically nontrivial Chern insulator phase through breaking the time-reversal symmetry. However, most of the previously studied phenomena in two-dimensional Dirac systems are basically based on the same physicical mechanism, i.e., the gap opening in the Dirac electron bands with circularly polarized light, and it is lacking in variety of the physics. In this paper, we theoretically predict a novel type of photoinduced topological phase transition accompanied by collision and collapse of gapped Dirac points in the organic salt $\alpha$-(BEDT-TTF)$_2$I$_3$. By constructing the Floquet theory for this compound, we demonstrate that the irradiation of elliptically polarized light causes collision of the Dirac points through the photoinduced band deformation and their collapse, which eventually results in the topological phase transition from a topological semimetal with gapped Dirac cones to a normal insulator when the elliptical axis is oriented at a specfic angle with respect to the crystallographic axes. We argue that this novel photoinduced phase transition can be experimentally detected by the measurement of Hall conductivity. The present work enriches the fundamental physics of photoinduced topological phase transitions and thus contribute to development of this rapidly growing research field.

Dynamical Phase Transitions in the Photodriven Charge-Ordered Dirac-Electron System.

We study photoinduced phase transitions and charge dynamics in the interacting Dirac-electron system with a charge-ordered ground state theoretically by taking an organic salt α-(BEDT-TTF)_{2}I_{3}. By analyzing the extended Hubbard model for this compound using a combined method of numerical simulations based on the time-dependent Schrödinger equation and the Floquet theory, we observe successive dynamical phase transitions from the charge-ordered insulator to a gapless Dirac semimetal and, eventually, to a Chern insulator phase under irradiation with circularly polarized light. These phase transitions occur as a consequence of two major effects of circularly polarized light, i.e., closing of the charge gap through melting the charge order and opening of the topological gap by breaking the time-reversal symmetry at the Dirac points. We demonstrate that these photoinduced phenomena are governed by charge dynamics of driven correlated Dirac electrons.

Wigner crystallization at large fine structure constant

We consider the fate of the Wigner crystal state in a two-dimensional system of massive Dirac electrons as the effective fine structure constant $\ensuremath{\alpha}$ is increased. In a Dirac system, larger $\ensuremath{\alpha}$ naively corresponds to stronger electron-electron interactions, but it also implies a stronger interband dielectric response that effectively renormalizes the electron charge. We calculate the critical density and critical temperature associated with quantum and thermal melting of the Wigner crystal state using two independent approaches. We show that at $\ensuremath{\alpha}\ensuremath{\gg}1$, the Wigner crystal state is best understood in terms of logarithmically interacting electrons, and that both the critical density and the melting temperature approach a universal, $\ensuremath{\alpha}$-independent value. We discuss our results in the context of recent experiments in twisted bilayer graphene near the magic angle.

Emergent plasmonic excitations in Mexican-hat and bell-shaped bands of hybridized Dirac electrons in graphene/topological insulator heterostructures

Stacking a graphene monolayer onto a three-dimensional topological insulator results in a van der Waals heterostructure that can serve as a versatile platform for rich emergent exotic physics. In particular, the Dirac electrons of the graphene and that of the two-dimensional surface states of the topological insulator hybridize effectively, leading to the emergence of two distinct electronic bands around the Fermi level, with respective Mexican-hat and bell shapes. In this paper, we explore the emergent collective plasmonic excitations in the representative heterostructure of graphene/${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$, combining first-principles calculations and low-energy effective Hamiltonian descriptions. We discover two different plasmon modes of the system, and our band-resolved analysis allows us to attribute the two modes to the intraband transitions within the Mexican-hat and bell-shaped bands, respectively. We also analyze the relative strengths and damping rates of the plasmon modes upon variations of the bias potential across the heterojunction, enabling potential experimental detections of those collective excitations. These findings provide alternate avenues for regulating the electronic states and plasmonic excitations in the hybridized Dirac electron systems for potential device applications.

Observation of dimension-crossover of a tunable 1D Dirac fermion in topological semimetal NbSixTe2

Condensed matter systems in low dimensions exhibit emergent physics that does not exist in three dimensions. When electrons are confined to one dimension (1D), some significant electronic states appear, such as charge density wave, spin-charge separations, and Su-Schrieffer-Heeger (SSH) topological state. However, a clear understanding of how the 1D electronic properties connects with topology is currently lacking. Here we systematically investigated the characteristic 1D Dirac fermion electronic structure originated from the metallic NbTe2 chains on the surface of the composition-tunable layered compound NbSixTe2 (x = 0.40 and 0.43) using angle-resolved photoemission spectroscopy. We found the Dirac fermion forms a Dirac nodal line structure protected by the combined widetilde {M_y} and time-reversal symmetry T and proves the NbSixTe2 system as a topological semimetal, in consistent with the ab-initio calculations. As x decreases, the interaction between adjacent NbTe2 chains increases and Dirac fermion goes through a dimension-crossover from 1D to 2D, as evidenced by the variation of its Fermi surface and Fermi velocity across the Brillouin zone in consistence with a Dirac SSH model. Our findings demonstrate a tunable 1D Dirac electron system, which offers a versatile platform for the exploration of intriguing 1D physics and device applications.

Seebeck Effect of Dirac Electrons

We investigate the Seebeck effect in a three-dimensional Dirac electron system based on the linear response theory and Luttinger’s gravitational potential. The Seebeck coefficient S is defined by S = L12/L11T, where T is the temperature, and L11 and L12 are the longitudinal response coefficients of the charge current to the electric field and to the temperature gradient, respectively; L11 is the electric conductivity and L12 is the thermoelectric conductivity. We consider randomly-distributed impurity potentials as the source of the momentum relaxation of electrons and microscopically calculate the relaxation rate and the vertex corrections of L11 and L12 due to the impurities. It is confirmed that L11 and L12 are related through Mott’s formula in low temperatures when the chemical potential lies above the gap (|μ| > Δ), irrespective of the linear dispersion of the Dirac electrons and unconventional energy dependence of the lifetime of electrons. Alternatively, when the chemical potential lies in the bandgap (|μ| < Δ), Seebeck coefficient functions similar to that of conventional semiconductors; its dependences on the chemical potential, μ, and the temperature, T, are partially captured by S ∝ (Δ − μ)/kBT for μ > 0. The Seebeck coefficient takes a relatively large value |S| \( \simeq \) 1.7 mV/K at T \( \simeq \) 4.3 K for Δ = 8 meV by assuming doped bismuth.

Narrow Zero Mode in Organic Massless Dirac Electron System α-(BEDT-TTF)2I3

We investigated the interlayer magnetoresistance in an organic massless Dirac electron system α-(BEDT-TTF)2I3 under pressure. We experimentally demonstrate that the width of the zero mode owing to carrier scattering is much narrower than that of the other Landau levels.

Theoretical Model for a Novel Electronic State in a Dirac Electron System Close to Merging: An Imaginary Element between Sulphur and Selenium

Topological materials with Dirac electron systems have been extensively studied. Organic crystalline materials form a unique group of such compounds with well-defined crystal structures. While most organic compounds require high pressures to exhibit Dirac-cone-type band structures, the title compound, α-STF2I3, has garnered increasing interest due to its Dirac-cone-type band structure under ambient pressure. Various experiments have been conducted under ambient pressure; their results can be compared with those of theoretical calculations to obtain insights into Dirac electron systems. However, structural disorder peculiar to the STF molecules in the solid-state has prevented any type of theoretical calculation of the states. In this study, we report a new method for calculating intermolecular interactions in disordered systems based on the extended Hückel approximation. This method enables band calculations, suggesting that this material is a rare example of a system close to merging. The obtained band structure indicates that the characteristic disorder in the STF solids distributed electrons equally on the sulphur and selenium atoms as if they belong to an imaginary element between sulphur and selenium and are arranged without disorder.

Large Diamagnetism and Electromagnetic Duality in Two-Dimensional Dirac Electron System.

A Dirac electron system in solids mimics relativistic quantum physics that is compatible with Maxwell's equations, with which we anticipate unified electromagnetic responses. We find a large orbital diamagnetism only along the interplane direction and a nearly temperature-independent electrical conductivity of the order of e^{2}/h per plane for the new 2D Dirac organic conductor, α-(BETS)_{2}I_{3}, where BETS is bis(ethylenedithio)tetraselenafulvalene. Unlike conventional electrons in solids whose nonrelativistic effects bifurcate electric and magnetic responses, the observed orbital diamagnetism scales with the electrical conductivity in a wide temperature range. This demonstrates that an electromagnetic duality that is valid only within the relativistic framework is revived in solids.

Spin Transport in a Two-Dimensional Tilted Dirac Electron System

We propose that spin current in an organic conductor, α-(BETS)2I3, is an appropriate physical quantity to detect the topological nature of the material whose electrons obey a quasi-two-dimensional Dirac equation.

Three-dimensional Dirac Electron System in a Diamond Lattice

Three-dimensional Dirac Electron System in a Diamond Lattice

Chemistry and Physics of Molecular Conductors

Molecular conductors demonstrate science of π electron systems where low-dimensionality and strong electron correlation play indispensable roles. Molecular conductors have been developed by collaboration between chemistry and physics. Chemistry prepares new materials that open new physics. On the other hand, deep insight of physics is fed back to new concepts of material design. This review describes cation radical salts of TTF (Tetrathiafulvalene) derivatives, DCNQI (N,N′-Dicyanobenzoquinonediimine)-Cu π-d systems, frustrated dimer-Mott systems, and single-component molecular Dirac electron systems from viewpoints of multi-dimensional and multi-orbital characters.