35 research outputs found
Electronic Properties and Persistent Spin Currents of Nanospring under Static Magnetic Field
Relativistic electronic properties of a nanospring under a static magnetic
field are theoretically investigated in the present study. The wave equation
accounting for the spin-orbit interaction is derived for the nanospring as a
special case of the Pauli equation for a spin-1/2 particle confined to a curved
surface under an electromagnetic field. We define the helical momentum operator
and show that it commutes with the Hamiltonian owing to the helical geometry of
the nanospring. The energy eigenstates are hence also the eigenstates of the
helical momentum. We solve the equation numerically to obtain the surface wave
functions and the energy spectra. The electronic properties are systematically
examined by varying the parameters that characterize the system. It is
demonstrated that either the nonzero spin-orbit interaction or the nonzero
external magnetic field suffices for the occurrence of the persistent spin
current on the nanospring. Two different mechanisms are shown to generate the
persistent spin current. One employs the spin-orbit interaction coming from the
local inversion asymmetry on the surface, while the other employs the curvature
coupling with the external magnetic field.Comment: 10 figure
Pauli Equation on a Curved Surface and Rashba Splitting on a Corrugated Surface
The Schroedinger equation for a spinless charged particle on a curved surface
under an electromagnetic field has been obtained by adopting a proper gauge
which allows the separation of the on-surface and transverse dynamics. [Phys.
Rev. Lett. 100 (2008) 230403] As its extension, I provide the Pauli equation
for a charged spin-1/2 particle confined to a curved surface under an
electromagnetic field. Energy spectra of a sphere and a corrugated surface to
which a particle is confined are given as simple applications of the equation.
The energy levels obtained exhibit splittings due to the relativistic effect
known as the Rashba effect
Quantum Singwi-Tosi-Land-Sjoelander approach for interacting inhomogeneous systems under electromagnetic fields: Comparison with exact results
For inhomogeneous interacting electronic systems under a time-dependent
electromagnetic perturbation, we derive the linear equation for response
functions in a quantum mechanical manner. It is a natural extension of the
original semi-classical Singwi-Tosi-Land-Sjoelander (STLS) approach for an
electron gas. The factorization ansatz for the two-particle distribution is an
indispensable ingredient in the STLS approaches for determination of the
response function and the pair correlation function. In this study, we choose
an analytically solvable interacting two-electron system as the target for
which we examine the validity of the approximation. It is demonstrated that the
STLS response function reproduces well the exact one for low-energy
excitations. The interaction energy contributed from the STLS response function
is also discussed.Comment: 5 figure
Second-order Perturbation Formula for Magnetocrystalline Anisotropy using Orbital Angular Momentum Matrix
We derive a second-order perturbation formula for an electronic system
subject to spin-orbit interactions (SOI). The energy correction originates in
the spin-conserving and the spin-flip transitions. The former are represented
by the orbital angular momentum (OAM) acquired via the SOI. The latter come
from the quantum fluctuation effect. By using our formula, we examine the
relativistic electronic structures of a d orbital chain and L1_0 alloys. The
appearance of OAM in the chain is understood by using a parabolic-bands model
and the exact expressions of the single-particle states. The total energy is
found to be accurately reproduced by the formula. The self-consistent fully
relativistic first-principles calculations based on the density functional
theory are performed for five L1_0 alloys. It is found that the formula
reproduces qualitatively the behavior of their exact magnetocrystalline
anisotropy (MCA) energies. While the MCA of FePt, CoPt, and FePd originates in
the spin-conserving transitions, that in MnAl and MnGa originates in the
spin-flip contributions. For FePt, CoPt, and FePd, the tendency of the MCA
energy with the variation in the lattice constant obeys basically that of the
spin-flip contributions. These results indicate that not only the anisotropy of
OAM, but also that of spin-flip contributions must be taken into account for
the understanding of the MCA of the L1_0 alloys.Comment: 9 figure
Implementation of quantum imaginary-time evolution method on NISQ devices: Nonlocal approximation
The imaginary-time evolution method is widely known to be efficient for
obtaining the ground state in quantum many-body problems on a classical
computer. A recently proposed quantum imaginary-time evolution method (QITE)
faces problems of deep circuit depth and difficulty in the implementation on
noisy intermediate-scale quantum (NISQ) devices. In this study, a nonlocal
approximation is developed to tackle this difficulty. We found that by removing
the locality condition or local approximation (LA), which was imposed when the
imaginary-time evolution operator is converted to a unitary operator, the
quantum circuit depth is significantly reduced. We propose two-step
approximation methods based on a nonlocality condition: extended LA (eLA) and
nonlocal approximation (NLA). To confirm the validity of eLA and NLA, we apply
them to the max-cut problem of an unweighted 3-regular graph and a weighted
fully connected graph; we comparatively evaluate the performances of LA, eLA,
and NLA. The eLA and NLA methods require far fewer circuit depths than LA to
maintain the same level of computational accuracy. Further, we developed a
``compression'' method of the quantum circuit for the imaginary-time steps as a
method to further reduce the circuit depth in the QITE method. The eLA, NLA,
and the compression method introduced in this study allow us to reduce the
circuit depth and the accumulation of error caused by the gate operation
significantly and pave the way for implementing the QITE method on NISQ
devices.Comment: 9 pages, 3figure
Electronic Structure of Novel Superconductor Ca4Al2O6Fe2As2
We have performed the first-principles electronic structure calculation for
the novel superconductor Ca4Al2O6Fe2As2 which has the smallest a lattice
parameter and the largest As height from the Fe plane among the Fe-As
superconductors. We find that one of the hole-like Fermi surfaces is missing
around the Gamma point compared to the case of LaFeAsO. Analysis using the
maximally-localized-Wannier-function technique indicates that the xy orbital
becomes more localized as the As-Fe-As angle decreases. This induces
rearrangement of bands, which results in the change of the Fermi-surface
topology of Ca4Al2O6Fe2As2 from that of LaFeAsO. The strength of electron
correlation is also evaluated using the constraint RPA method, and it turns out
that Ca4Al2O6Fe2As2 is more correlated than LaFeAsO.Comment: 5 pages, 6 figures, 2 table
Periodicity-free unfolding method of electronic energy spectra: Application to twisted bilayer graphene
We propose a novel periodicity-free unfolding method of the electronic energy
spectra. Our new method solves a serious problem that calculated electronic
band structure strongly depends on the choice of the simulation cell, i.e.,
primitive-cell or supercell. The present method projects the electronic states
onto the free-electron states, giving rise to the {\it plane-wave unfolded}
spectra. Using the method, the energy spectra can be calculated as a completely
independent quantity from the choice of the simulation cell. We have examined
the unfolded energy spectra in detail for three models and clarified the
validity of our method: One-dimensional interacting two chain model, monolayer
graphene, and twisted bilayer graphene. Furthermore, we have discussed that our
present method is directly related to the experimental ARPES (Angle-Resolved
Photo-Emission Spectroscopy) spectra.Comment: 10 pages, 5 figure
Comparison of Green's functions for transition metal atoms using self-energy functional theory and coupled-cluster singles and doubles (CCSD)
We demonstrate in the present study that self-consistent calculations based
on the self-energy functional theory (SFT) are possible for the electronic
structure of realistic systems in the context of quantum chemistry. We describe
the procedure of a self-consistent SFT calculation in detail and perform the
calculations for isolated transition metal atoms from V to Cu as a
preliminary study. We compare the one-particle Green's functions (GFs) obtained
in this way and those obtained from the coupled-cluster singles and doubles
(CCSD) method. Although the SFT calculation starts from the spin-unpolarized
Hartree--Fock (HF) state for each of the target systems, the self-consistency
loop correctly leads to degenerate spin-polarized ground states. We examine the
spectral functions in detail to find their commonalities and differences among
the atoms by paying attention to the characteristics of the two approaches. It
is demonstrated via the two approaches that calculations based on the density
functional theory (DFT) can fail in predicting the orbital energy spectra for
spherically symmetric systems. It is found that the two methods are quite
reliable and useful beyond DFT.Comment: 7 figure
Quasiparticle energy spectra of isolated atoms from coupled-cluster singles and doubles (CCSD): Comparison with exact CI calculations
In this study, we have calculated single-electron energy spectra via the
Green's function based on the coupled-cluster singles and doubles (GFCCSD)
method for isolated atoms from H to Ne. In order to check the accuracy of the
GFCCSD method, we compared the results with the exact ones calculated from the
full-configuration interaction (FCI). Consequently, we have found that the
GFCCSD method reproduces not only the correct quasiparticle peaks but also
satellite ones by comparing the exact spectra with the 6-31G basis set. It is
also found that open-shell atoms such as C atom exhibit Mott gaps at the Fermi
level, which the exact density-functional theory (DFT) fails to describe. The
GFCCSD successfully reproduces the Mott HOMO-LUMO (highest-occupied molecular
orbital and lowest-unoccupied molecular orbital) gaps even quantitatively. We
also discussed the origin of satellite peaks as shake-up effects by checking
the components of wave function of the satellite peaks. The GFCCSD is a novel
cutting edge to investigate the electronic states in detail.Comment: 9 pages, 4 figure
One-particle Green's function of interacting two electrons using analytic solutions for a three-body problem: comparison with exact Kohn--Sham system
For a three-electron system with finite-strength interactions confined to a
one-dimensional harmonic trap, we solve the Schroedinger equation analytically
to obtain the exact solutions, from which we construct explicitly the
simultaneous eigenstates of the energy and total spin for the first time. The
solutions for the three-electron system allow us to derive analytic expressions
for the exact one-particle Green's function (GF) for the corresponding
two-electron system. We calculate the GF in frequency domain to examine
systematically its behavior depending on the electronic interactions. We also
compare the pole structure of non-interacting GF using the exact Kohn--Sham
(KS) potential with that of the exact GF to find that the discrepancy of the
energy gap between the KS system and the original system is larger for a
stronger interaction. We perform numerical examination on the behavior of GFs
in real space to demonstrate that the exact and KS GFs can have shapes quite
different from each other. Our simple model will help to understand generic
characteristics of interacting GFs.Comment: to be published in Journal of Physics: Condensed Matte