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T. Shiota

Publications and source records attributed to T. Shiota.

15 recordsLinked to original sources
arXiv2019

High-$T_c$ Iron-phosphide Superconductivity Enhanced by Reemergent Antiferromagnetic Spin Fluctuations in (Sr$_4$Sc$_2$O$_6$)Fe$_2$(As$_{1-x}$P$_{x}$)$_2$ probed by NMR

We report a systematic NMR study on [Sr$_4$Sc$_2$O$_6$]Fe$_2$(As$_{1-x}$P$_x$)$_2$, for which the local lattice parameters of the iron-pnictogen (Fe$Pn$) layer are similar to those of the series LaFe(As$_{1-x'}$P$_{x'}$)O, which exhibit two segregated antiferromagnetic (AFM) order phases, AFM1 at $x'$=0-0.2 and AFM2 at $x'$=0.4-0.7. Our results revealed that the parent AFM1 phase at $x$=0 disappears at $x$=0.3-0.4, corresponding to a pnictogen height ($h_{pn}$) from the Fe-plane of 1.3-1.32 Å, which is similar to that of LaFe(As$_{1-x'}$P$_{x'}$)O and various parent Fe-pnictides. By contrast, the AFM2 order reported for LaFe(As$_{0.4}$P$_{0.6}$)O does not appear at $x\sim$0.8, although the local lattice parameters of the Fe$Pn$ layer and the microscopic electronic states are quite similar. Despite the absence of the {\it static} AFM2 order, reemergent {\it dynamical} AFM spin fluctuations were observed at approximately $x\sim$0.8, which can be attributed to the instability of the AFM2 phase. We suggest this re-enhancement of AFM spin fluctuations to play a significant role in enhancing the $T_c$ to 17 K for $x$=0.8-1. Finally, we discuss the universality and diversity of the complicated magnetic ground states from a microscopic point of view, including the difference in the origins of the AFM1 and AFM2 phases, and their relations with the high superconducting transitions in Fe-pnictides.

cond-mat.supr-con↗
arXiv2017

Three superconducting phases with different categories of pairing in hole- and electron-doped LaFeAs$_{1-x}$P$_x$O

The phase diagram of LaFeAs$_{1-x}$P$_x$O system has been extensively studied through hole- and electron-doping as well as As/P-substitution. It has been revealed that there are three different superconducting phases with different Fermi surface (FS) topologies and thus with possibly different pairing glues. One of them is well understood as spin fluctuation-mediated superconductivity within a FS nesting scenario. Another one with the FSs in a bad nesting condition must be explained in a different context such as orbital or spin fluctuation in strongly correlated electronic system. In both phases, $T$-linear resistivity was commonly observed when the superconducting transition temperature $T_{\rm c}$ becomes the highest value, indicating that the strength of bosonic fluctuation determines $T_{\rm c}$. In the last superconducting phase, the nesting condition of FSs and the related bosonic fluctuation are moderate. Variety of phase diagram characterizes the multiple orbital nature of the iron-based superconductors which are just near the boundary between weak and strong correlation regimes.

cond-mat.supr-con↗
arXiv2016

Pfaffian structures and certain solutions to BKP hierarchies II. Multiple integrals

We introduce a useful and rather simple classes of BKP tau functions which which we shall shall call "easy tau functions". We consider the "large BKP hiearchy" related to $O(2\infty +1)$ which was introduced in \cite{KvdLbispec} (which is closely related to the DKP $O(2\infty) $hierarchy introduced in \cite{JM}). Actually "easy tau functions" of the small BKP was already considered in \cite{HLO}, here we are more interested in the large BKP and also the mixed small-large BKP tau functions \cite{KvdLbispec}. Tau functions under consideration are equal to sums over partitions and to multi-integrals. In this way they may be appliciable in models of random partitions and models of random matrices. Here in the part II we consider multi-intergals and series of $N$-ply integrals in $N$. Relations to matrix models is explained. This paper may be viewed as a developement of the the paper by J.van de Leur \cite{L1} related to orthogonal and symplectic ensembles of random matrices.

nlin.SI↗
arXiv2016

Multiple Antiferromagnetic Spin Fluctuations and Novel Evolution of Tc in Iron-based superconductors LaFe(As1-xPx)(O1-yFy) revealed by 31P-NMR Studies

We report on 31P-NMR studies of LaFe(As_{1-x}P_x)(O_{1-y}F_{y}) over wide compositions for 0<x<1 and 0<y<0.14, which provide clear evidence that antiferromagnetic spin fluctuations (AFMSFs) are one of the indispensable elements for enhancing Tc. Systematic 31P-NMR measurements revealed two types of AFMSFs in the temperature evolution, that is, one is the AFMSFs that develop rapidly down to Tc with low-energy characteristics, and the other, with relatively higher energy than the former, develops gradually upon cooling from high temperature. The low-energy AFMSFs in low y (electron doping) over a wide x (pnictogen height suppression) range are associated with the two orbitals of d_{xz/yz}, whereas the higher-energy ones for a wide y region around low x originate from the three orbitals of d_{xy} and d_{xz/yz}. We remark that the nonmonotonic variation of Tc as a function of x and y in LaFe(As_{1-x}P_x)(O_{1-y}F_y) is attributed to these multiple AFMSFs originating from degenerated multiple 3d orbitals inherent to Fe-pnictide superconductors.

cond-mat.supr-con↗
arXiv2014

Emergence of Novel Antiferromagnetic Order Intervening between Two Superconducting Phases in LaFe(As_1-x_P_x_)O: 31P-NMR Studies

We revealed novel phase deagram of Fe-pnictide high-Tc superconductor LaFe(As_{1-x}P_{x})O in wide doping level (0.3<x<1) by P-NMR. Systematic 31P-NMR studies revealed the emergence of the antiferromagnetic ordered phase (AFM-2) in 0.4 < x < 0.7 that intervenes between two superconductivity (SC-1/SC-2) phases. The 31P-NMR Knight shift points to the appearance of the sharp density of states at the Fermi level that is derived from d_{3Z^2?r^2} orbit, which is less relevant with the onset of the SC-2. On the other hand, we remark that the AFM spin fluctuations arising from the interband nesting on the d_{XZ}/d_{YZ} orbits must be a key ingredient for the occurrence of SC around AFM-2.

cond-mat.supr-con↗
arXiv2012

Pfaffian structures and certain solutions to BKP hierarchies I. Sums over partitions

We introduce a useful and rather simple class of BKP tau functions which which we shall call "easy tau functions". We consider two versions of BKP hierarchy, one we will call "small BKP hierarchy" (sBKP) related to $O(\infty)$ introduced in Date et al and "large BKP hierarchy" (lBKP) related to $O(2\infty +1)$ introduced in Kac and van de Leur (which is closely related to the large $O(2\infty)$ DKP hierarchy (lDKP) introduced in Jimbo and Miwa). Actually "easy tau functions" of the sBKP hierarchy were already considered in Harnad et al, here we are more interested in the lBKP case and also the mixed small-large BKP tau functions (Kac and van de Leur). Tau functions under consideration are equal to certain sums over partitions and to certain multi-integrals over cone domains. In this way they may be applicable in models of random partitions and models of random matrices. Here is the first part of the paper where sums of Schur and projective Schur functions over partitions are considered.

math-ph↗
arXiv2011

Soliton equations and the Riemann-Schottky problem

Novikov's conjecture on the Riemann-Schottky problem: {\it the Jacobians of smooth algebraic curves are precisely those indecomposable principally polarized abelian varieties (ppavs) whose theta-functions provide solutions to the Kadomtsev-Petviashvili (KP) equation}, was the first evidence of nowadays well-established fact: connections between the algebraic geometry and the modern theory of integrable systems is beneficial for both sides. The purpose of this paper is twofold. Our first goal is to present a proof of the strongest known characterization of a Jacobian variety in this direction: {\it an indecomposable ppav $X$ is the Jacobian of a curve if and only if its Kummer variety $K(X)$ has a trisecant line} and the solution of the characterization problem of principally polarized Prym varieties. The latter problem is almost as old and famous as the Riemann-Schottky problem but is much harder. In some sense the Prym varieties may be geometrically the easiest-to-understand ppavs beyond Jacobians, and studying them may be a first step towards understanding the geometry of more general abelian varieties as well. Our second and primary objective is to take this opportunity to elaborate on motivations underlining the proposed solution of the Riemann-Schottky problem, to introduce a certain circle of ideas and methods, developed in the theory of soliton equations, and to convince the reader that they are algebro-geometric in nature, simple and universal enough to be included in the Handbook of moduli.

math.AG↗
arXiv2008

Mechanical properties of Pt monatomic chains

The mechanical properties of platinum monatomic chains were investigated by simultaneous measurement of an effective stiffness and the conductance using our newly developed mechanically controllable break junction (MCBJ) technique with a tuning fork as a force sensor. When stretching a monatomic contact (two-atom chain), the stiffness and conductance increases at the early stage of stretching and then decreases just before breaking, which is attributed to a transition of the chain configuration and bond weakening. A statistical analysis was made to investigate the mechanical properties of monatomic chains. The average stiffness shows minima at the peak positions of the length-histogram. From this result we conclude that the peaks in the length-histogram are a measure of the number of atoms in the chains, and that the chains break from a strained state. Additionally, we find that the smaller the initial stiffness of the chain is, the longer the chain becomes. This shows that softer chains can be stretched longer.

cond-mat.mes-hall↗
arXiv2005

Schur function expansion for normal matrix model and associated discrete matrix models

We consider Schur function expansion for the partition function of the model of normal matrices. We show that this expansion coincides with Takasaki expansion \cite{Tinit} for tau functions of Toda lattice hierarchy. We show that the partition function of the model of normal matrices is, at the same time, a partition function of certain discrete models, which can be solved by the method of orthogonal polynomials. We obtain discrete versions of various known matrix models: models of non-negative matrices, unitary matrices, normal matrices.

math-ph↗
arXiv1999

Pfaff tau-functions

Consider the evolution $$ \frac{\pl m_\iy}{\pl t_n}=\Lb^n m_\iy, \frac{\pl m_\iy}{\pl s_n}=-m_\iy(\Lb^\top)^n, $$ on bi- or semi-infinite matrices $m_\iy=m_\iy(t,s)$, with skew-symmetric initial data $m_{\iy}(0,0)$. Then, $m_\iy(t,-t)$ is skew-symmetric, and so the determinants of the successive "upper-left corners" vanish or are squares of Pfaffians. In this paper, we investigate the rich nature of these Pfaffians, as functions of t. This problem is motivated by questions concerning the spectrum of symmetric and symplectic random matrix ensembles.

solv-int↗
arXiv1998

Random matrices, Virasoro algebras, and noncommutative KP

What is the connection of random matrices with integrable systems? Is this connection really useful? The answer to these questions leads to a new and unifying approach to the theory of random matrices. Introducing an appropriate time t-dependence in the probability distribution of the matrix ensemble, leads to vertex operator expressions for the n-point correlation functions (probabilities of n eigenvalues in infinitesimal intervals) and the corresponding Fredholm determinants (probabilities of no eigenvalue in a Borel subset E); the latter probability is a ratio of tau-functions for the KP-equation, whose numerator satisfy partial differential equations, which decouple into the sum of two parts: a Virasoro-like part depending on time only and a Vect(S^1)-part depending on the boundary points A_i of E. Upon setting t=0, and using the KP-hierarchy to eliminate t-derivatives, these PDE's lead to a hierarchy of non-linear PDE's, purely in terms of the A_i. These PDE's are nothing else but the KP hierarchy for which the t-partials, viewed as commuting operators, are replaced by non-commuting operators in the endpoints A_i of the E under consideration. When the boundary of E consists of one point and for the known kernels, one recovers the Painleve equations, found in prior work on the subject.

solv-int↗
arXiv1996

A Matrix Integral Solution to [P,Q]=P and Matrix Laplace Transforms

In this paper we solve the following problems: (i) find two differential operators P and Q satisfying [P,Q]=P, where P flows according to the KP hierarchy \partial P/\partial t_n = [(P^{n/p})_+,P], with p := \ord P\ge 2; (ii) find a matrix integral representation for the associated $\t au$-function. First we construct an infinite dimensional space {\cal W}=\Span_\BC \{ψ_0(z),ψ_1(z),... \} of functions of z\in\BC invariant under the action of two operators, multiplication by z^p and A_c:= z \partial/\partial z - z + c. This requirement is satisfied, for arbitrary p, if ψ_0 is a certain function generalizing the classical Hänkel function (for p=2); our representation of the generalized Hänkel function as a double Laplace transform of a simple function, which was unknown even for the p=2 case, enables us to represent the τ-function associated with the KP time evolution of the space \cal W as a ``double matrix Laplace transform'' in two different ways. One representation involves an integration over the space of matrices whose spectrum belongs to a wedge-shaped contour γ:= γ^+ + γ^- \subset\BC defined by γ^\pm=\BR_+\E^{\pmπ\I/p}. The new integrals above relate to the matrix Laplace transforms, in contrast with the matrix Fourier transforms, which generalize the Kontsevich integrals and solve the operator equation [P,Q]=1.

hep-th↗
arXiv1996

New matrix model solutions to the Kac-Schwarz problem

We examine the Kac-Schwarz problem of specification of point in Grassmannian in the restricted case of gap-one first-order differential Kac-Schwarz operators. While the pair of constraints satisfying $[{\cal K}_1,W] = 1$ always leads to Kontsevich type models, in the case of $[{\cal K}_1,W] = W$ the corresponding KP $τ$-functions are represented as more sophisticated matrix integrals.

hep-th↗