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Divergent density of states (DOS) can induce extraordinary phenomena such as significant enhancement of superconductivity and unexpected phase transitions. Moreover, van Hove singularities (VHSs) are known to lead to divergent DOS in two-dimensional (2D) systems. Despite the recent interest in VHSs, only a few controllable cases have been reported to date. In this work, we investigate the electronic band structures of a 2D VHS with angle-resolved photoemission spectroscopy and control transport properties by utilizing an atomically ultrathin SrRuO$_3$ film. By applying electric fields with alkali metal deposition and ionic-liquid gating methods, we precisely control the 2D VHS, and the sign of the charge carrier. Use of a tunable 2D VHS in an atomically flat oxide film could serve as a new strategy to realize infinite DOS near the Fermi level, thereby allowing efficient tuning of electric properties., Comment: 7 pages, 4 figures

Based on the interface polarization model, the two-dimensional electron gas (2DEG) at $LaInO_{3}$(LIO)/$BaSnO_{3}$(BSO) interfaces is understood to originate from a polarization discontinuity at the interface and the conduction band offset between LIO and BSO. In this scenario, the direction of polarization at the interface is determined by whether the first atomic LIO layer at the interface is LaO$^{+}$ or InO$_{2}^{-}$. We investigate the role of the terminating layer at the LIO/BSO interface in creating the 2DEG. Based on conductance measurements of our in-situ grown LIO/BSO heterostructures, we report in this work that the 2DEG only forms when the BSO surface is terminated with a SnO$_{2}$ layer. We controlled the terminating layer by additional SnO$_{2}$ deposition on the BSO surface. We show that the as-grown BSO surface has a mixed terminating layer of BaO and SnO$_{2}$ while the BSO surfaces prepared with additional SnO$_{2}$ deposition are terminated mainly with the SnO$_{2}$ layer. The terminating layer was confirmed by coaxial impact collision ion scattering spectroscopy (CAICISS). Our finding is consistent with the interface polarization model for 2DEG formation at LIO/BSO interfaces, in which the direction of the interfacial polarization in LIO is determined by the terminating layer of the BSO surface., Comment: 22 pages

A novel 2-dimensional electron gas (2DEG) system with high-mobility was discovered at the interface of two perovskite oxides, a polar orthorhombic perovskite LaScO3 (LSO) and a nonpolar cubic perovskite BaSnO3 (BSO). Upon depositing the LSO film on the BSO film, the conductance enhancement and the resulting 2DEG density (n2D) was measured. Comparing the results with the previously reported LaInO3/BaSnO3 (LIO/BSO) polar interface, we applied the interface polarization model to the LSO/BSO system, in which the polarization exists only over 4 pseudocubic unit cells in LSO from the interface and vanishes afterward like the LIO/BSO interface. Based on the calculations of the self-consistent Poisson-Schrodinger equations, the LSO thickness dependence of n2D of LSO/BSO heterointerface is consistent with this model. Furthermore, a single subband in the quantum well is predicted. Using the conductive interface and the LSO as a gate dielectric, a 2DEG transistor composed of only perovskite oxides with high field-effect mobility (uFE) close to 100 cm2 V-1 s-1 is demonstrated., Comment: 36 pages

In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations of quantum mechanics had been established in around 1930, by von Neumann. The formulation uses functional analysis, linear algebra and probability theory. The knowledge of the mathematical formulation of QM is enough quantum mechanical knowledge for approaching to quantum algorithm and it might be efficient way for mathematicians that starting with mathematical formulations of QM. We explain the mathematical formulations of quantum mechanics briefly, quantum bits, quantum gates, quantum discrete Fourier transformation, Deutsch's algorithm and Shor's algorithm.

We introduce a scheme for the membership verification, a scheme for a secret ballot, a scheme for the unanimity rule which can hide the number of voter using some partition number identities.

We studied the electronic band structure of pulsed laser deposition (PLD) grown (111)-oriented SrRuO$_3$ (SRO) thin films using \textit{in situ} angle-resolved photoemission spectroscopy (ARPES) technique. We observed previously unreported, light bands with a renormalized quasiparticle effective mass of about 0.8$m_{e}$. The electron-phonon coupling underlying this mass renormalization yields a characteristic "kink" in the band dispersion. The self-energy analysis using the Einstein model suggests five optical phonon modes covering an energy range 44 to 90 meV contribute to the coupling. Besides, we show that the quasiparticle spectral intensity at the Fermi level is considerably suppressed, and two prominent peaks appear in the valance band spectrum at binding energies of 0.8 eV and 1.4 eV, respectively. We discuss the possible implications of these observations. Overall, our work demonstrates that high-quality thin films of oxides with large spin-orbit coupling can be grown along the polar (111) orientation by the PLD technique, enabling \textit{in situ} electronic band structure study. This could allow for characterizing the thickness-dependent evolution of band structure of (111) heterostructures$-$a prerequisite for exploring possible topological quantum states in the bilayer limit.

Magnetism and spin-orbit coupling (SOC) are two quintessential ingredients underlying novel topological transport phenomena in itinerant ferromagnets. When spin-polarized bands support nodal points/lines with band degeneracy that can be lifted by SOC, the nodal structures become a source of Berry curvature; this leads to a large anomalous Hall effect (AHE). Contrary to three-dimensional systems that naturally host nodal points/lines, two-dimensional (2D) systems can possess stable nodal structures only when proper crystalline symmetry exists. Here we show that 2D spin-polarized band structures of perovskite oxides generally support symmetry-protected nodal lines and points that govern both the sign and the magnitude of the AHE. To demonstrate this, we performed angle-resolved photoemission studies of ultrathin films of SrRuO$_3$, a representative metallic ferromagnet with SOC. We show that the sign-changing AHE upon variation in the film thickness, magnetization, and chemical potential can be well explained by theoretical models. Our study is the first to directly characterize the topological band structure of 2D spin-polarized bands and the corresponding AHE, which could facilitate new switchable devices based on ferromagnetic ultrathin films.

We studied surface and electronic structures of barium stannate (BaSnO$_3$) thin-film by low energy electron diffraction (LEED), and angle-resolved photoemission spectroscopy (ARPES) techniques. BaSnO$_3$/Ba$_{0.96}$La$_{0.04}$SnO$_3$/SrTiO$_3$ (10 nm/100 nm/0.5 mm) samples were grown using pulsed-laser deposition (PLD) method and were \emph{ex-situ} transferred from PLD chamber to ultra-high vacuum (UHV) chambers for annealing, LEED and ARPES studies. UHV annealing starting from 300$^{\circ}$C up to 550$^{\circ}$C, followed by LEED and ARPES measurements show 1$\times$1 surfaces with non-dispersive energy-momentum bands. The 1$\times$1 surface reconstructs into a $\sqrt{2}$$\times$$\sqrt{2}R45^\circ$ one at the annealing temperature of 700$^{\circ}$C where the ARPES data shows clear dispersive bands with valence band maximum located around 3.3 eV below Fermi level. While the $\sqrt{2}$$\times$$\sqrt{2}R45^\circ$ surface reconstruction is stable under further UHV annealing, it is reversed to 1$\times$1 surface by annealing the sample in 400 mTorr oxygen at 600$^{\circ}$C. Another UHV annealing at 600$^{\circ}$C followed by LEED and ARPES measurements, suggests that LEED $\sqrt{2}$$\times$$\sqrt{2}R45^\circ$ surface reconstruction and ARPES dispersive bands are reproduced. Our results provide a better picture of electronic structure of BaSnO$_3$ surface and are suggestive of role of oxygen vacancies in the reversible $\sqrt{2}$$\times$$\sqrt{2}R45^\circ$ surface reconstruction., Comment: 7 pages, 4 figures, Journal

A controversy arose over the interpretation of the recently observed hump features in Hall resistivity $\rho_{xy}$ from ultra-thin SrRuO$_3$ (SRO) film; it was initially interpreted to be due to topological Hall effect but was later proposed to be from existence of regions with different anomalous Hall effect (AHE). In order to settle down the issue, we performed Hall effect as well as magneto-optic Kerr-effect measurements on 4 unit cell SRO films grown on SrTiO$_3$ (001) substrates. Clear hump features are observed in the measured $\rho_{xy}$, whereas neither hump feature nor double hysteresis loop is seen in the Kerr rotation which should be proportional to the magnetization. In addition, magnetization measurement by superconducting quantum interference device shows no sign of multiple coercive fields. These results show that inhomogeneous AHE alone cannot explain the observed hump behavior in $\rho_{xy}$ data from our SRO ultra-thin films. We found that emergence of the hump structure in $\rho_{xy}$ is closely related to the growth condition, high quality films having clear sign of humps., Comment: 6 pages, 4 figures

The electronic structure of SrRuO$_3$ thin film with thickness from 50 to 1 unit cell (u.c.) is investigated via the resonant inelastic x-ray scattering (RIXS) technique at the O K-edge to unravel the intriguing interplay of orbital and charge degrees of freedom. We found that orbital-selective quantum confinement effect (QCE) induces the splitting of Ru $4d$ orbitals. At the same time, we observed a clear suppression of the electron-hole continuum across the metal-to-insulator transition (MIT) occurring at the 4 u.c. sample. From these two clear observations we conclude that QCE gives rise to a Mott insulating phase in ultrathin SrRuO$_3$ films. Our interpretation of the RIXS spectra is supported by the configuration interaction calculations of RuO$_6$ clusters., Comment: 7 pages, 7 figures

We observed a hump-like feature in Hall effects of SrRuO$_3$ ultrathin films, and systematically investigated it with controlling thicknesses, temperatures and magnetic fields. The hump-like feature is extremely stable, even surviving as a magnetic field is tilted by as much as 85$^\circ$. Based on the atomic-level structural analysis of a SrRuO$_3$ ultrathin film with a theoretical calculation, we reveal that atomic rumplings at the thin-film surface enhance Dzyaloshinskii-Moriya interaction, which can generate stable chiral spin textures and a hump-like Hall effect. Moreover, temperature dependent resonant X-ray measurements at Ru L-edge under a magnetic field showed that the intensity modulation of unexpected peaks was correlated with the hump region in the Hall effect. We verify that the two-dimensional property of ultrathin films generates stable non-coplanar spin textures having a magnetic order in a ferromagnetic oxide material.

Ferroic domain walls (DWs) create different symmetries and ordered states compared with those in single-domain bulk materials. In particular, the DWs of an antiferromagnet (AFM) with non-coplanar spin structure have a distinct symmetry that cannot be realized in those of their ferromagnet counterparts. In this paper, we show that an unconventional anomalous Hall effect (AHE) can arise from the DWs of a non-coplanar AFM, Nd2Ir2O7. Bulk Nd2Ir2O7 has a cubic symmetry; thus, its Hall signal should be zero without an applied magnetic field. The DWs generated in this material break the two-fold rotational symmetry, which allows for finite anomalous Hall conductivity. A strong f-d exchange interaction between the Nd and Ir magnetic moments significantly influences antiferromagnetic domain switching. Our epitaxial Nd2Ir2O7 thin film showed a large enhancement of the AHE signal when the AFM domains switched, indicating that the AHE is mainly due to DWs. Our study highlights the symmetry broken interface of AFM materials as a new means of exploring topological effects and their relevant applications.

Let $B$ be an infinite subset of $\mathbf{N}$. When we consider partitions of natural numbers into elements of $B$, a partition number without a restriction of the number of equal parts can be expressed by partition numbers with a restriction $\alpha$ of the number of equal parts. Although there are many way of the expression, we prove that there exists a expression form such that this expression form is true for all possible set $B$. This identities comes from the partition numbers of natural numbers into $\{1,\alpha,\alpha^2,\alpha^3,\cdots\}$. Furthermore, we prove that there exist inverse forms of the expression forms. And we prove other similar identities. The proofs in this paper are constructive., Comment: The theorems of this paper stated and proved in 2012 winter