Casimir effect for lattice fermions

We propose a definition of the Casimir energy for free lattice fermions. From this definition, we study the Casimir effects for the massless or massive naive fermion, Wilson fermion, and (M\"obius) domain-wall fermion in $1+1$ dimensional spacetime with the spatial periodic or antiperiodic boundary condition. For the naive fermion, we find an oscillatory behavior of the Casimir energy, which is caused by the difference between odd and even lattice sizes. For the Wilson fermion, in the small lattice size of $N \geq 3$, the Casimir energy agrees very well with that of the continuum theory, which suggests that we can control the discretization artifacts for the Casimir effect measured in lattice simulations. We also investigate the dependence on the parameters tunable in M\"obius domain-wall fermions. Our findings will be observed both in condensed matter systems and in lattice simulations with a small size.Comment: 8 pages, 5 figures; published versio

Casimir effect in axion electrodynamics with lattice regularizations

The Casimir effect is induced by the interplay between photon fields and boundary conditions, and in particular, photon fields modified in axion electrodynamics may lead to the sign-flipping of the Casimir energy. We propose a theoretical approach to derive the Casimir effect in axion electrodynamics. This approach is based on a lattice regularization and enables us to discuss the dependence on the lattice spacing for the Casimir energy. With this approach, the sign-flipping behavior of the Casimir energy is correctly reproduced. By taking the continuum limit of physical quantity calculated on the lattice, we can obtain the results consistent with the continuum theory. This approach can also be applied to the Casimir effect at nonzero temperature.Comment: 11 pages, 9 figure

Lattice-fermionic Casimir effect and topological insulators

The Casimir effect arises from the zero-point energy of particles in momentum space deformed by the existence of two parallel plates. For degrees of freedom on the lattice, its energy-momentum dispersion is determined so as to keep a periodicity within the Brillouin zone, so that its Casimir effect is modified. We study the properties of Casimir effect for lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion based on the M\"obius domain-wall fermion formulation, in the $1+1$-, $2+1$-, and $3+1$-dimensional space-time with the periodic or antiperiodic boundary condition. An oscillatory behavior of Casimir energy between odd and even lattice size is induced by the contribution of ultraviolet-momentum (doubler) modes, which realizes in the naive fermion, Wilson fermion in a negative mass, and overlap fermions with a large domain-wall height. Our findings can be experimentally observed in condensed matter systems such as topological insulators and also numerically measured in lattice simulations.Comment: 27 pages, 9 figures; published versio

Stabilization of a honeycomb lattice of IrO6_6 octahedra in superlattices with ilmenite-type MnTiO3_3

In the quest for quantum spin liquids, thin films are expected to open the way for the control of intricate magnetic interactions in actual materials by exploiting epitaxial strain and two-dimensionality. However, materials compatible with conventional thin-film growth methods have largely remained undeveloped. As a promising candidate towards the materialization of quantum spin liquids in thin films, we here present a robust ilmenite-type oxide with a honeycomb lattice of edge-sharing IrO$_6$ octahedra artificially stabilized by superlattice formation with an ilmenite-type antiferromagnetic oxide MnTiO$_3$. The stabilized sub-unit-cell-thick Mn-Ir-O layer is isostructural to MnTiO$_3$, having the atomic arrangement corresponding to ilmenite-type MnTiO$_3$ not discovered yet. By spin Hall magnetoresistance measurements, we found that antiferromagnetic ordering in the ilmenite Mn sublattice is suppressed by modified magnetic interactions in the MnO$_6$ planes via the IrO$_6$ planes. These findings lay the foundation for the creation of two-dimensional Kitaev candidate materials, accelerating the discovery of exotic physics and applications specific to quantum spin liquids

Development of teaching materials for improving communication skills in Corona disaster

コロナ禍によって大学のアクティブラーニング型授業は大きな方向転換を余儀なくされた。学生のコミュニケーション力を目指して開講していた岡山大学の教養科目の授業でも、従来の双方向型コミュニケーション実践を軸とした授業内容を大幅に改める必要に迫られた。そこで、コミュニケーション力を下支えするメタ認知力の育成を目的とした、日々の生活のリフレクションを通した考察を行うための教材を開発した。その後、教材を活用した授業を実践し、授業の前後、学生へのアンケート調査を行った結果、本教材を用いた授業を行ったことにより、学生のメタ認知力が向上したことが明らかになった

Synthesis and electrochemistry of dimanganese(II) complexes of phenol-based dinucleating ligands with four methoxyethyl chelating arms

Dimanganese(II) complexes [Mn2(bonp)(PhCO2)2]PF6 (1) and [Mn2(bocp)(PhCO2)2]PF6 (2) were synthesized with p-nitro- and p-chloro-substituted phenol-based dinucleating ligands bonp- [2,6-bis[bis(2-methoxyethyl)aminomethyl]-4-nitrophenolate anion] and bocp- [4-chloro-2,6-bis[bis(2-methoxyethyl)aminomethyl]phenolate anion], respectively, with the aim of controlling the redox potentials of the dimanganese center by changing the p-substituents in the dinucleating ligands. Cyclic voltammograms of 1 and 2 showed quasi-reversible oxidation processes, assigned to MnIIMnII/MnIIMnIII, at 1.17 and 1.00 V vs. Ag/AgCl, respectively. Compared to the previous p-methyl complex [Mn2(bomp)(PhCO2)2]PF6 (3) [bomp–: 2,6-bis[bis(2-methoxyethyl)aminomethyl]-4-methylphenolate anion] (0.96 V vs. Ag/AgCl), the order of the potentials was 1(-NO2) > 2(-Cl) > 3(-CH3). Thus, the redox potentials of the dimanganese centers were controlled by the p-substituents in the dinucleating ligands