arXiv subjects

Masahiko Higuchi

Publications and source records attributed to Masahiko Higuchi.

17 recordsLinked to original sources

arXiv2024

Conventional and unconventional anomalous velocities in multiband systems

The anomalous velocity has been derived so far based on the single-band approximation. In this paper, the anomalous velocity is derived accounting for multiple energy bands. It is shown that when multiple energy bands are considered, the anomalous velocity is actually derived from the velocity term which goes to zero under the single-band approximation. It is also shown that the anomalous velocity based on the single-band approximation is derived improperly from the velocity term which becomes zero in considering multiple energy bands. Furthermore, it is found that unconventional types of anomalous velocity may appear in addition to the conventional anomalous velocity. These unconventional anomalous velocities are perpendicular to the electric field and come from the singularity of the magnetic Bloch function in the magnetic Brillouin zone. It is confirmed that conventional and unconventional anomalous velocities can also be derived not only from the steady-state perturbation theory but also from the time-dependent perturbation theory in which a time-dependent vector potential yielding the uniform electric field is treated as a perturbation.

cond-mat.other↗

arXiv2023

Relativistic Tight-Binding Model for Hexagonal Lattice: Application to Graphene

A non-perturbative relativistic tight-binding (TB) approximation method applicable to crystalline material immersed in a magnetic field was developed in 2015. To apply this method to any material in the magnetic field, the electronic structure of the material in absence of a magnetic field must be calculated. In this study, we present the relativistic TB approximation method for graphene in a zero magnetic field. The Hamiltonian and overlap matrix is constructed considering the nearest neighbouring atomic interactions between the $s$ and $p$ valence orbitals, where the relativistic hopping and overlap integrals are calculated using the relativistic version of the Slater-Koster table. The method of constructing the Hamiltonian and overlap matrix and the resulting energy-band structure of graphene in the first Brillouin zone is presented in this paper. It is found that there is an appearance of a small band-gap at the $\textbf{K}$ points (also known as the spin-orbit gap) due to the relativistic effect, whose magnitude is $25$ $μ$eV.

cond-mat.mtrl-sci↗

arXiv2023

Quantized Hall conductance in graphene by nonperturbative magnetic-field-containing relativistic tight-binding approximation method

In this study, we conducted a numerical investigation on the Hall conductance ($σ_{Hall}$) of graphene based on the magnetic energy band structure calculated using a nonperturbative magnetic-field-containing relativistic tight-binding approximation (MFRTB) method. The nonperturbative MFRTB can revisit two types of plateaus for the dependence of $σ_{Hall}$ on Fermi energy. One set is characterized as wide plateaus (WPs). These WPs have filling factors (FFs) of 2, 6, 10, 14, etc. and are known as the half-integer quantum Hall effect. The width of WPs decreases with increasing FF, which exceeds the decrease expected from the linear dispersion relation of graphene. The other set is characterized by narrow plateaus (NPs), which have FFs of 0, 4, 8, 12, etc. The NPs correspond to the energy gaps caused by the spin-Zeeman effect and spin-orbit interaction. Furthermore, it was discovered that the degeneracy of the magnetic energy bands calculated using the nonperturbative MFRTB method leads to a quantized $σ_{Hall}$.

cond-mat.mes-hall↗

arXiv2022

Theoretical description of the first-order phase transition of aluminum from a superconducting to normal state by the current-density functional theory for superconductors

We show that the current-density functional theory for superconductors (sc-CDFT) can describe the magnetic-field-induced first-order phase transition of aluminum from a superconducting state to a normal state. This is accomplished by introducing a model for the magnetic field dependence of the attractive interaction between superconducting electrons. This model states that the surface potential well produced by the penetrating magnetic field leads to the magnetic field dependence of the attractive interaction. Specifically, the electron density near the surface increases with the magnetic field due to the surface potential well, which causes the reduction in the attractive interaction due to the screening effect. We also develop the calculation scheme to solve the gap equation of the sc-CDFT with taking into account the magnetic field dependence of the attractive interaction. It is shown that calculation results of the magnetic field dependence of the superconducting gap are in good agreement with experimental results of the first-order phase transition.

cond-mat.supr-con↗

arXiv2022

Second-order phase transition of silicon from a band insulator to metal induced by strong magnetic fields

We present the second-order phase transition from a band insulator to metal that is induced by a strong magnetic field. The magnetic-field dependences of the magnetization and energy band gap of a crystalline silicon immersed in a magnetic field are investigated by means of the nonperturbative magnetic-field-containing relativistic tight-binding approximation method [Phys. Rev. B 97, 195135 (2018)]. It is shown that the energy band gap disappears at the critical magnetic field of 2.22x$10^4$ (T). At the critical magnetic field, the magnetic-field dependence of the magnetization exhibits a kink behavior, which means that this phenomenon is the second-order phase transition from a band insulator to metal. It is found that in strong magnetic fields above the critical magnetic field, namely in the metallic phase, the oscillation of the magnetization appears. It is shown that this magnetic oscillation comes from the energy bands in the magnetic Brillouin zone that change from the occupied states to unoccupied states or vice vasa.

cond-mat.mtrl-sci↗

arXiv2021

Cluster Decomposition Principle and Two-Electron Wave Function of the Cooper Pair in the BCS Superconducting State

We present the explicit forms of the maximum eigenvalue and the corresponding eigenfunction for the second-order reduced density matrix (RDM2) of the BCS superconducting state (SS). Using these quantities, we deal with two topics in the present paper. As the first topic, it is shown that the cluster decomposition principle holds in the BCS-SS. This proof gives a theoretical foundation that the abnormal density can be chosen as the order parameter of the SS. As the second topic, it is shown that such an eigenfunction is spin singlet and spatially extends isotopically, and further that the mean distance of two electrons which consists of the above eigenfunction is in a good agreement with Pippard's coherence length. This means that maximum geminal of the RDM2 of the BCS-SS can be regarded as the Cooper pair itself which are condensed to the same energy level in a number of O(N).

cond-mat.supr-con↗

arXiv2021

Reduction of g-factor due to Rashba effect in graphene

Graphene is a highly promising material in the field of spin electronics. Recent experiments on electron spin resonance have observed a reduction in the g-factor of graphene. In our previous paper [J. Phys. Soc. Jpn. 88, 094707 (2019)], we demonstrated that one of sources for this reduction is the diamagnetic property of graphene. However, the diamagnetic property by itself does not fully account for the magnitude of the reduction observed in the experiments. In this paper, we focus on the Rashba effect, which is caused by the work function existing near the surface of graphene. The Rashba effect tilts the spin magnetic moment to the in-plane direction of the graphene sheet, potentially reducing the g-factor. We evaluate this reduction using a simple model system incorporating the Rashba and spin Zeeman effects. We then demonstrate that the resultant g-factor is in close agreement with that observed in the prior experiments, indicating that the Rashba effect is able to account for the remaining reduction in the g-factor of graphene.

cond-mat.mtrl-sci↗

arXiv2016

Current-Density Functional Theory for the superconductor

We present the current-density functional theory for the superconductor immersed in the magnetic field. The order parameter of the superconducting state, transverse component of the paramagnetic current-density, and electron density are chosen as basic variables that uniquely determine the equilibrium properties of the system. In order to construct this theory, the development of the approximate form of the exchange-correlation (xc) energy functional is indispensable as well as the derivation of the effective single-particle equation which makes it possible to reproduce the equilibrium densities mentioned above. The rigorous expression of the xc-energy functional is derived using the technique of the coupling-constant integration. Furthermore, the approximate form of the xc energy functional is proposed such that the energy gap resulting from the effective single-particle equation is consistent with the attractive interaction energy of the system.

cond-mat.supr-con↗

arXiv2016

Calculations of Magnetic properties of metals through the magnetic-field-containing relativistic tight-binding approximation method

Magnetic properties of metals are investigated through electronic structure calculations based on the recently-proposed magnetic-field-containing relativistic tight-binding approximation (MFRTB) method [Phys. Rev. B \textbf{91}, 075122 (2015)]. It is found that electronic energy bands for the metal immersed in the uniform magnetic field have a cluster structure in which multiple energy bands lie within a small energy width. Each cluster corresponds to the energy level that is derived on the basis of the semiclassical approximation. While the cluster is responsible for the de Haas-van Alphen (dHvA) oscillations, constituent energy bands of the cluster cause additional oscillation peaks of the magnetization. Also, the energy width of the cluster leads to the reduction of the amplitude of the dHvA oscillations, which can be observed as the pseudo Dingle temperature and/or the overestimation of the curvature of the Fermi surface.

cond-mat.str-el↗

arXiv2015

Basic variables to be reproduced in the first-principles theory for superconductors: Fluctuation of the particle number

We show that the diagonal elements of the second-order reduced density matrix (RDM2) can be chosen as basic variables for describing the superconducting state, instead of the off-diagonal elements of the RDM2 that are usually adopted as basic variables in the density functional scheme. The diagonal elements of the RDM2 are called pair-density (PD), which is explicitly related to the fluctuation of the particle number of the system. In this paper, we argue that the fluctuation of the particle number can become an indication of the superconducting state, and that the density functional scheme in which the PD is chosen as a basic variable would be a promising first-principles theory for superconductors.

cond-mat.supr-con↗

arXiv2011

A correction method for the pair density to get close to the ground state one

We present a correction method for the pair density (PD) to get close to the ground state one. The PD is corrected to be a variationally-best PD within the search region that is extended by adding the uniformly-scaled PDs to its elements. The corrected PD is kept N-representable and satisfies the virial relation rigorously. The validity of the present method is confirmed by numerical calculations of neon atom. It is shown that the root-mean-square error of the electron-electron interaction and external potential energies, which is a good benchmark for the error of the PD, is reduced by 69.7% without additional heavy calculations.

cond-mat.str-el↗

arXiv2009

An Alternative Scheme for Calculating the Unrestricted Hartree-Fock Equation: Application to the Boron and Neon Atoms

We present an alternative scheme for calculating the unrestricted Hartree-Fock equation. The scheme is based on the variational method utilizing the sophisticated basis functions that include no adjustable parameters. The validity and accuracy of the present scheme are confirmed by actual calculations of the boron and neon atoms. It is shown that the present scheme not only gives the reasonably lower total energy but also conserves the virial relation with enough accuracy.

cond-mat.other↗

arXiv2008

$N$-representability of the Jastrow wave function pair density of the lowest-order

We have recently proposed a density functional scheme for calculating the ground-state pair density (PD) within the Jastrow wave function PDs of the lowest-order (LO-Jastrow PDs) [M. Higuchi and K. Higuchi, Phys. Rev. A \textbf{75}, 042510 (2007)]. However, there remained an arguable problem on the $N$-representability of the LO-Jastrow PD. In this paper, the sufficient conditions for the $N$-representability of the LO-Jastrow PD are derived. These conditions are used as the constraints on the correlation function of the Jastrow wave function. A concrete procedure to search the suitable correlation function is also presented.

cond-mat.str-el↗

arXiv2006

Pair density functional theory by means of the correlated wave function

We present a density functional scheme for calculating the pair density (PD) by means of the correlated wave function. This scheme is free from both of problems related to PD functional theory, i.e., (a) the need to constrain the variational principle to $N$-representable PDs and (b) the development of a kinetic energy functional. By using the correlated wave function, the searching region for the ground-state PD is substantially extended as compared with our previous theory[Physica B \textbf{372} (2007), in press]. The variational principle results in the simultaneous equations that yield the best PD beyond the previous theory, not to mention the Hartree-Fock approximation.

cond-mat.str-el↗

arXiv2006

Density functional scheme for calculating the pair density

The density functional scheme for calculating the pair density is presented by means of the constrained-search technique. The resultant single-particle equation takes the form of the modified Hartree-Fock equation which contains the kinetic contribution of the exchange-correlation energy functional as the correlation potential. The practical form of the kinetic contribution is also proposed with the aid of the scaling relations of the kinetic energy functionals.

cond-mat.str-el↗

arXiv2003

Exchange-correlation energy functional constructed from orbital-dependent coupling-constant-averaged pair correlation functions

An exchange-correlation energy functional $ E_{\mathrm xc} $ and the resultant exchange-correlation potential $ v_{\mathrm xc}({\bf r}) $ in density-functional theory are proposed using orbital-dependent coupling-constant-averaged pair correlation functions, $ {\bar{g}}^{σσ'}({\bf r, r'})$ for electronic structure calculations of atoms, molecules, and solids. These orbital-dependent $ {\bar{g}}^{σσ'}({\bf r, r'})$ fulfill the symmetric property, the Pauli principle and the sum rules. In the limit of uniform density $ {\bar{g}}^{σσ'}({\bf r, r'})$ are reduced to the very accurate analogues of the electron liquid that are obtained from an interpolation between long- and short-range correlations involving the exchange corrections. The major contribution of $ v_{\mathrm xc}({\bf r}) $ is given in the form of the Coulomb interaction with the exchange-Coulomb hole around an electron. The present theory not only guarantees local charge neutrality, but also reproduces the exact asymptotic form of the exchange potential, $ v_{\mathrm x}({\bf r}) = - e^2 / r $ for finite systems. The present method of dealing with correlations, if properly applied to finite systems, can give even the asymptotic form of the correlation potential $ v_{\mathrm c}({\bf r}) $ of order $ r^{-4} $ as well as the van der Waals potential of order $ r^{-6} $ for large r.

cond-mat.str-el↗

arXiv2003

A proposal of an orbital-dependent correlation energy functional for energy-band calculations

An explicitly orbital-dependent correlation energy functional is proposed, which is to be used in combination with the orbital-dependent exchange energy functional in energy-band calculations. It bears a close resemblance to the second-order direct and exchange perturbation terms calculated with Kohn-Sham orbitals and Kohn-Sham energies except that one of the two Coulomb interactions entering each term is replaced by an effective interaction which contains information about long-, intermediate-, and short-range correlations beyond second-order perturbation theory. Such an effective interaction can rigorously be defined for the correlation energy of the uniform electron liquid and is evaluated with high accuracy in order to apply to the orbital-dependent correlation energy functional. The coupling-constant-averaged spin-parallel and spin-antiparallel pair correlation functions are also evaluated with high accuracy for the electron liquid. The present orbital-dependent correlation energy functional with the effective interaction borrowed from the electron liquid is valid for tightly-binding electrons as well as for nearly-free electrons in marked contrast with the conventional local density approximation.

cond-mat.str-el↗