Integer group determinants for ${\rm C}_{4}^{2}$
We determine all possible values of the integer group determinant of ${\rm C}_{4}^{2}$, where ${\rm C}_{4}$ is the cyclic group of order $4$.
math.NT↗
arXiv subjects
Naoya Yamaguchi
Publications and source records attributed to Naoya Yamaguchi.
Integer group determinants for ${\rm C}_{2}^{4}$
We determine all possible values of the integer group determinant of ${\rm C}_{2}^{4}$, where ${\rm C}_{2}$ is the cyclic group of order $2$.
math.NT↗
First-principles LCPAO Approach for Insulators under Finite Electric Field
We propose a linear-combination-of-pseudo-atomic-orbitals scheme for a finite electric field method based on the modern theory of polarization. We derive the matrix elements of the effective potential for the field and the corresponding terms of the forces on atoms. In addition, we successfully evaluated the dielectric constants and Born effective charges of typical semiconducting and insulating materials. Our formalism will aid in the study of materials under electric fields.
cond-mat.mtrl-sci↗
Remark on Laquer's theorem for circulant determinants
Olga Taussky-Todd suggested the problem of determining the possible values of integer circulant determinants. To solve a special case of the problem, Laquer gave a factorization of circulant determinants. In this paper, we give a modest generalization of Laquer's theorem. Also, we give an application of the generalization to integer group determinants.
math.RT↗
Integer circulant determinants of order 16
We solve Olga Taussky-Todd's circulant problem in the case of order 16.
math.NT↗
First-principles calculation of anomalous Hall and Nernst conductivity by local Berry phase
In this study, we implemented a finite-difference algorithm for computing anomalous Hall and Nernst conductivity. Based on the expression to evaluate the Berry curvature in an insulating system [J. Phys. Soc. Jpn. 74 1674(2005)], we extended the methods to a metallic system. We calculated anomalous Hall conductivity and Nernst conductivity in a two-dimensional ferromagnetic material FeCl$_2$ and three-dimensional ferromagnetic transition metals bcc-Fe, hcp-Co, and fcc-Ni. Our results are comparable to previously reported results computed by Kubo-formula or Wannier representation. To evaluate anomalous Nernst coefficients, the detailed Fermi-energy dependence of the anomalous Hall conductivity is required. Nonetheless, previous methods based on Wannier representation or Kubo-formula have numerical instability due to the ${\boldsymbol k}$-space Dirac monopole. The present method will open an efficient thermoelectric material design based on the high-throughput first-principles screening.
cond-mat.mtrl-sci↗
Generalized group determinant gives a necessary and sufficient condition for a subset of a finite group to be a subgroup
We generalize the concept of the group determinant and prove a necessary and sufficient novel condition for a subset to be a subgroup. This development is based on the group determinant work by Edward Formanek, David Sibley, and Richard Mansfield, where they show that two groups with the same group determinant are isomorphic. The derived condition leads to a generalization of this result.
math.RT↗
Generalization of Frobenius' theorem for group determinants
Frobenius built a representation theory of finite groups in the process of obtaining the irreducible factorization of the group determinant. Here, we give a generalization of Frobenius' theorem. The generalization leads to a corollary on irreducible representations of finite groups.
math.RT↗
Spin splitting with persistent spin textures induced by the line defect in 1T-phase of monolayer transition metal dichalcogenides
The spin splitting driven by spin-orbit coupling in monolayer (ML) transition metal dichalcogenides (TMDCs) family has been widely studied only for the 1H-phase structure, while it is not profound for the 1T-phase structure due to the centrosymmetric of the crystal. Based on first-principles calculations, we show that significant spin splitting can be induced in the ML 1T-TMDCs by introducing the line defect. Taking the ML PtSe2 as a representative example, we considered the most stable form of the line defects, namely Se-vacancy line defect (Se-VLD). We find that large spin splitting is observed in the defect states of the Se-VLD, exhibiting a highly unidirectional spin configuration in the momentum space. This peculiar spin configuration may yield the so-called persistent spin textures (PST), a specific spin structure resulting in protection against spin-decoherence and supporting an extraordinarily long spin lifetime. Moreover, by using k.p perturbation theory supplemented with symmetry analysis, we clarified that the emerging of the spin splitting maintaining the PST in the defect states is originated from the inversion symmetry breaking together with one-dimensional nature of the Se-VLD engineered ML PtSe2. Our findings pave a possible way to induce the significant spin splitting in the ML 1T-TMDCs, which could be highly important for designing spintronic devices.
cond-mat.str-el↗
Study-type determinants and their properties
In this paper, we define the concept of the Study-type determinant, and we present some properties of these determinants. These properties lead to some properties of the Study determinant. The properties of the Study-type determinants are obtained using a commutative diagram. This diagram leads not only to these properties, but also to an inequality for the degrees of representations and to an extension of Dedekind's theorem.
math.RT↗
Minimizing the expected value of the asymmetric loss and an inequality of the variance of the loss
For some estimations and predictions, we solve minimization problems with asymmetric loss functions. Usually, we estimate the coefficient of regression for these problems. In this paper, we do not make such the estimation, but rather give a solution by correcting any predictions so that the prediction error follows a general normal distribution. In our method, we can not only minimize the expected value of the asymmetric loss, but also lower the variance of the loss.
math.ST↗
Electric-field-induced Z2 topological phase transition in strained single bilayer Bi(111)
For controlling the critical electric fields of the topological phase transition in single bilayer Bi(111), we investigated topological phases in a strained system through first-principles calculations. We found a quadratic band touching semimetallic state at tensile strain $ε=0.5$%. Around this strain, the topological phase can be switched to a trivial insulator by an infinitesimal electric field. The positions at which Dirac cones appear in the electric-field-induced topological phase transition changed for the strain $ε>0.5$% and $ε<0.5$%. Our results indicate that this topological phase transition could be applied to novel spintronic devices.
cond-mat.mes-hall↗
Photoinduced Rashba spin to charge conversion via interfacial unoccupied state
At interfaces with inversion symmetry breaking, Rashba effect couples the motion of electrons to their spin; as a result, spin-charge interconversion mechanism can occur. These interconversion mechanisms commonly exploit Rashba spin splitting at the Fermi level by spin pumping or spin torque ferromagnetic resonance. Here, we report evidence of significant photoinduced spin to charge conversion via Rashba spin splitting in an unoccupied state above the Fermi level at the Cu(111)/$α$-Bi$_{2}$O$_{3}$ interface. We predict an average Rashba coefficient of $1.72\times 10^{-10}eV.m$ at 1.98 eV above the Fermi level, by fully relativistic first-principles analysis of the interfacial electronic structure with spin orbit interaction. We find agreement with our observation of helicity dependent photoinduced spin to charge conversion excited at 1.96 eV at room temperature, with spin current generation of $J_{s}=10^{6}A/m^{2}$. The present letter shows evidence of efficient spin-charge conversion exploiting Rashba spin splitting at excited states, harvesting light energy without magnetic materials or external magnetic fields.
cond-mat.mes-hall↗
Compositions of invertibility preserving maps for some monoids and their application to Clifford algebras
For some monoids, we give a method of composing invertibility preserving maps associated to "partial involutions." Also, we define the notion of "determinants for finite dimensional algebras over a field." As examples, we give invertibility preserving maps for Clifford algebras into a field and determinants for Clifford algebras into a field, where we assume that the algebras are generated by less than or equal to 5 generators over the field. On the other hand, "determinant formulas for Clifford algebras" are known. We understand these formulas as an expression that connects invertibility preserving maps for Clifford algebras and determinants for Clifford algebras. As a result, we have a better sense of determinant formulas. In addition, we show that there is not such a determinant formula for Clifford algebras generated by greater than 5 generators.
math.RA↗
First-principles Study of Rashba Spin Splitting at Strained SrTiO3(001) Surfaces
We investigated the Rashba spin splittings in a compressive-strained SrTiO$_3$(001) ultra thin-film using first-principles calculations. The effect of the polarization due to the compressive strain leads to the 2DEG with large Rashba spin splittings, where the sheet carrier density is of the same order of magnitude as that of the heterostructure LaAlO$_3$/SrTiO$_3$ ($\sim10^{14}$ cm$^{-2}$). Some localized surface states (SSs) show the giant Rashba coefficient $α_R$ larger than 100 meV$\cdot$Å.
cond-mat.mtrl-sci↗
Minimising the expectation value of the procurement cost in electricity markets based on the prediction error of energy consumption
In this paper, we formulate a method for minimising the expectation value of the procurement cost of electricity in two popular spot markets: {\it day-ahead} and {\it intra-day}, under the assumption that expectation value of unit prices and the distributions of prediction errors for the electricity demand traded in two markets are known. The expectation value of the total electricity cost is minimised over two parameters that change the amounts of electricity. Two parameters depend only on the expected unit prices of electricity and the distributions of prediction errors for the electricity demand traded in two markets. That is, even if we do not know the predictions for the electricity demand, we can determine the values of two parameters that minimise the expectation value of the procurement cost of electricity in two popular spot markets. We demonstrate numerically that the estimate of two parameters often results in a small variance of the total electricity cost, and illustrate the usefulness of the proposed procurement method through the analysis of actual data.
econ.GN↗
Proof of some properties of transfer using noncommutative determinants
A transfer is a group homomorphism from a finite group to an abelian quotient group of a subgroup of the group. In this paper, we explain some of the properties of transfers by using noncommutative determinants. These properties enable us to understand transfers more naturally.
math.GR↗
Clear variation of spin splitting by changing electron distribution at non-magnetic metal/Bi2O3 interfaces
Large spin splitting at Rashba interface, giving rise to strong spin-momentum locking, is essential for efficient spin-to-charge conversion. Recently, a Cu/Bismuth oxide (Bi2O3) interface has been found to exhibit an efficient spin-to-charge conversion similar to a Ag/Bi interface with large Rashba spin splitting. However, the guiding principle of designing the metal/oxide interface for the efficient conversion has not been clarified yet. Here we report strong non-magnetic (NM) material dependence of spin splitting at NM/Bi2O3 interfaces. We employed spin pumping technique to inject spin current into the interface and evaluated the magnitude of interfacial spin-to-charge conversion. We observed large modulation and sign change in conversion coefficient which corresponds to the variation of spin splitting. Our experimental results together with first-principles calculations indicate that such large variation is caused by material dependent electron distribution near the interface. The results suggest that control of interfacial electron distribution by tuning the difference in work function across the interface may be an effective way to tune the magnitude and sign of spin-to-charge conversion and Rashba parameter at interface.
cond-mat.mtrl-sci↗