Anisotropic non-split zero-energy vortex bound states in a conventional superconductor

Vortices in topological superconductors are predicted to host Majorana bound states (MBSs) as exotic quasiparticles. In recent experiments, the spatially non-split zero-energy vortex bound state in topological superconductors has been regarded as an essential spectroscopic signature for the observation of MBSs. Here, we report the observation of anisotropic non-split zero-energy vortex bound states in a conventional elemental superconductor with a topologically trivial band structure using scanning tunneling microscopy and spectroscopy. The experimental results, corroborated by quasi-classical theoretical calculations, indicate that the non-split states directly reflect the quasiparticle trajectories governed by the surface electronic structure. Our study implies that non-split zero-energy states are not a conclusive signature of MBSs in vortex cores, stimulating a revision of the current understanding of such states.

Whole brain Probabilistic Generative Model toward Realizing Cognitive Architecture for Developmental Robots

Building a humanlike integrative artificial cognitive system, that is, an artificial general intelligence, is one of the goals in artificial intelligence and developmental robotics. Furthermore, a computational model that enables an artificial cognitive system to achieve cognitive development will be an excellent reference for brain and cognitive science. This paper describes the development of a cognitive architecture using probabilistic generative models (PGMs) to fully mirror the human cognitive system. The integrative model is called a whole-brain PGM (WB-PGM). It is both brain-inspired and PGMbased. In this paper, the process of building the WB-PGM and learning from the human brain to build cognitive architectures is described.

Sparse modeling of large-scale quantum impurity models with low symmetries

Quantum embedding theories provide a feasible route for obtaining quantitative descriptions of correlated materials. However, a critical challenge is solving an effective impurity model of correlated orbitals embedded in an electron bath. Many advanced impurity solvers require the approximation of a bath continuum using a finite number of bath levels, producing a highly nonconvex, ill-conditioned inverse problem. To address this drawback, this study proposes an efficient fitting algorithm for matrix-valued hybridization functions based on a data-science approach, sparse modeling, and a compact representation of Matsubara Greens functions. The efficiency of the proposed method is demonstrated by fitting random hybridization functions with large off-diagonal elements as well as those of a 20-orbital impurity model for a high-Tc compound, LaAsFeO, at low temperatures (T). The results set quantitative goals for the future development of impurity solvers toward quantum embedding simulations of complex correlated materials.

Sparse modeling approach to obtaining the shear viscosity from smeared correlation functions

We propose the sparse modeling method to estimate the spectral function from the smeared correlation functions. We give a description of how to obtain the shear viscosity from the correlation function of the renormalized energy-momentum tensor (EMT) measured by the gradient flow method ($C(t,tau)$) for the quenched QCD at finite temperature. The measurement of the renormalized EMT in the gradient flow method reduces a statistical uncertainty thanks to its property of the smearing. However, the smearing breaks the sum rule of the spectral function and the over-smeared data in the correlation function may have to be eliminated from the analyzing process of physical observables. In this work, we demonstrate that the sparse modeling analysis in the intermediate-representation basis (IR basis), which connects between the Matsubara frequency data and real frequency data. It works well even using very limited data of $C(t,tau)$ only in the fiducial window of the gradient flow. We utilize the ADMM algorithm which is useful to solve the LASSO problem under some constraints. We show that the obtained spectral function reproduces the input smeared correlation function at finite flow-time. Several systematic and statistical errors and the flow-time dependence are also discussed.

Weak Ferroelectricity in n = 2 pseudo Ruddlesden-Popper-type niobate Li2SrNb2O7

Li2SrNb2O7 (LSNO) crystallizes in a structure closely related to n = 2 Ruddlesden-Popper-type compounds, which is gen-erally formed by intergrowth of 2-dimensional perovskite-type blocks and rocksalt-type layers. The present study demonstrates a coexistence of spontaneous polarization and anti-ferroelectric-like nonlinear response in LSNO at 80 K, suggesting a weak ferroelectricity below the phase transition temperature of 217 K. A combination of first-principles cal-culations and single crystal x-ray diffractions clarifies a polar P21cn structure for the ground state of LSNO, where an in-plane anti-ferroelectric displacement and an out-of-plane polar shift simultaneously take place. The present study offers a new perspective to design ferroelectric and antiferroelectric materials with Ruddlesden-Popper-type compounds.

Absence of magnetic long range order in Ba$_3$ZnRu$_2$O$_9$: A spin-liquid candidate in the $S=3/2$ dimer lattice

We have discovered a novel candidate for a spin liquid state in a ruthenium oxide composed of dimers of $S = $ 3/2 spins of Ru$^{5+}$,Ba$_3$ZnRu$_2$O$_9$. This compound lacks a long range order down to 37 mK, which is a temperature 5000-times lower than the magnetic interaction scale of around 200 K. Partial substitution for Zn can continuously vary the magnetic ground state from an antiferromagnetic order to a spin-gapped state through the liquid state. This indicates that the spin-liquid state emerges from a delicate balance of inter- and intra-dimer interactions, and the spin state of the dimer plays a vital role. This unique feature should realize a new type of quantum magnetism.

Self-consistent study of Abelian and non-Abelian order in a two-dimensional topological superconductor

We perform self-consistent studies of two-dimensional (2D) $s$-wave topological superconductivity (TSC) with Rashba spin-orbit coupling and Zeeman field by solving the Bogoliubov-de Gennes equations. In particular, we examine the effects of a nonmagnetic impurity in detail and show that the nature of the spin-polarised midgap bound state varies significantly depending on the material parameters. Most notably, a nonmagnetic impurity in a 2D $s$-wave topological superconductor can act like a magnetic impurity in a conventional $s$-wave superconductor, leading to phase transitions of the ground state as the impurity potential is varied. Furthermore, by solving for the spin-dependent Hartree potential self-consistently along with the superconducting order parameter, we demonstrate that topological charge density waves can coexist with TSC at half filling just as in a conventional $s$-wave superconductor.

Excitation spectra and wave functions of quasiparticle bound states in bilayer Rashba superconductors

We study the excitation spectra and the wave functions of quasiparticle bound states at a vortex and an edge in bilayer Rashba superconductors under a magnetic field. In particular, we focus on the quasiparticle states at the zero energy in the pair-density wave state in a topologically non-trivial phase. We numerically demonstrate that the quasiparticle wave functions with zero energy are localized at both the edge and the vortex core if the magnetic field exceed the critical value.

Robust zero-energy bound states around a pair-density-wave vortex core in locally noncentrosymmetric superconductors

We numerically investigate the electronic structures around a vortex core in a bilayer superconducting system, with s-wave pairing, Rashba spin-orbit coupling and Zeeman magnetic field, with use of the quasiclassical Greens function method. The Bardeen-Cooper-Schrieffer (BCS) phase and the so-called pair-density wave (PDW) phase appear in the temperature-magnetic-field phase diagram in a bulk uniform system [Phys. Rev. B 86, 134514 (2012)]. In the low magnetic field perpendicular to the layers, the zero-energy vortex bound states in the BCS phase are split by the Zeeman magnetic field. On the other hand, the PDW state appears in the high magnetic field, and sign of the order parameter is opposite between the layers. We find that the vortex core suddenly shrinks and the zero-energy bound states appear by increasing the magnetic field through the BCS-PDW transition. We discuss the origin of the change in vortex core structure between the BCS and PDW states by clarifying the relation between the vortex bound states and the bulk energy spectra. In the high magnetic field region, the PDW state and vortex bound states are protected by the spin-orbit coupling. These characteristic behaviors in the PDW state can be observed by scanning tunneling microscopy/spectroscopy.

Orbital angular momentum in a topological superconductor with Chern number higher than $1$

We investigate the bulk orbital angular momentum (AM) in a two-dimensional hole-doped topological superconductor (SC) which is composed of a hole-doped semiconductor thin film, a magnetic insulator, and an $s$-wave SC and is characterized by the Chern number $C = -3$. In the topological phase, $L_z/N$ is strongly reduced from the intrinsic value by the non-particle-hole-symmetric edge states as in the corresponding chiral $f$-wave SCs when the spin-orbit interactions (SOIs) are small, while this reduction of $L_z/N$ does not work for the large SOIs. Here $L_z$ and $N$ are the bulk orbital AM and the total number of particles at zero temperature, respectively. As a result, $L_z/N$ is discontinuous or continuous at the topological phase transition depending on the strengths of the SOIs. We also discuss the effects of the edge states by calculating the radial distributions of the orbital AM.