Ken Matsuba

Anti-phase modulation of electron-and hole-like states in vortex core of Bi2Sr2CaCu2Ox probed by scanning tunneling spectroscopy

In the vortex core of slightly overdoped Bi 2 Sr 2 CaCu 2 O x , the electron- and hole-like states have been found to exhibit spatial modulations in anti-phase with each other along the Cu–O bonding direction. Some kind of one-dimensionality has been observed in the vortex core, and it is more clearly seen in differential conductance maps at lower biases below ±9 mV.

Quantum Limiting Behaviors of a Vortex Core in an Anisotropic Gap Superconductor

Quantized bound states at a vortex core are discretized in YNi 2 B 2 C. By using scanning tunneling spectroscopy with an unprecedented 0.1 nm spatial resolution, we find and identify the localized spectral structure, where in addition to the first main peak with a positive low energy, a second subpeak coming from the fourfold symmetric gap structure is seen inside the energy gap. Those spectral features are understood solving the Bogoliubov–de Gennes equation for a fully three-dimensional gap structure. A particle–hole asymmetric spectrum at the core site and quantum oscillation in the spectra are clearly observed.

Ordered Vortex Lattice and Intrinsic Vortex Core States in Bi2Sr2CaCu2Ox Studied by Scanning Tunneling Microscopy and Spectroscopy

The ordered vortex lattice in Bi 2 Sr 2 CaCu 2 O x (overdoped, T c =83 K) has been observed for the first time at 4.2 K in 8 T by scanning tunneling spectroscopy (STS). The vortex lattice is short-range ordered in the length scale of 100 nm. The vortices form an almost square lattice with the sides parallel to the diagonal direction of the CuO 2 square lattice, that is, the nodal direction of the d x 2 - y 2 superconductor. In all of the vortex cores of the ordered lattice, the localized states are observed at ±9 meV symmetrically in the superconducting gap and are clearly determined to be intrinsic to the vortex in Bi 2 Sr 2 CaCu 2 O x . The intensity is found to be electron–hole asymmetric.

Influence of disorder on superconductivity in Bi2Sr2CaCu2Ox studied by low temperature scanning tunneling spectroscopy

Abstract The spatial distributions of superconducting energy gap 2 Δ p have been measured at 6 K in underdoped Bi 2 Sr 2 CaCu 2 O x by scanning tunneling spectroscopy. The 2 Δ p has been found to vary in the length scale of about 3 nm. In different regions of the cleaved surface, the average values of 2 Δ p are equal to each other, while the variances are different. This means that the superconducting properties in Bi 2 Sr 2 CaCu 2 O x are not determined only by the carrier concentration. To characterize the superconductivity of Bi 2 Sr 2 CaCu 2 O x , it is necessary to introduce a new parameter of microscopic degree of disorder, which is defined as a ratio of the variance to the average for the distribution of 2 Δ p .

High-Resolution Scanning Tunneling Spectroscopy of Vortex Cores in Inhomogeneous Electronic States of Bi2Sr2CaCu2Ox

We studied electronic states in vortex cores of slightly overdoped Bi2Sr2CaCu2Ox by scanning tunneling spectroscopy. We have found that they have stripe structures with a \(4a_{0}\) width extending along the Cu–O bond directions. Vortex core states are observed as two peaks at particle–hole symmetric positions in the energy gap. Along a stripe, the peak positions of vortex core states are constant and not influenced by the spatial variation of the energy gap Δ. Outer stripes have a larger energy than inner stripes. A mazelike pattern in the electronic states at \(E = \pm\Delta\) has been observed all over the surface both inside and outside the vortex core. The orientation of stripes of vortex core states was found to be related to the mazelike pattern in the vortex core region. A short-range order of the mazelike pattern spatially coexists with the superconductivity and locally breaks the symmetry of the two Cu–O bond directions. We propose that the vortex core bound states are formed by Bogoliubov quasi...

Exact Solutions of the Davey-Stewartson Equation with Complex Coefficients

We give three types of exact solutions (a hole, a solitary wave and a shock) of the Davey-Stewartson equation with complex coefficients, which is a kind of 2+1 dimensional generalization of the 1+1 dimensional complex Ginzburg-Landau equation.

Imaging of vortex lattice in single crystal YNi2B2C by STM

Abstract The vortex lattice in YNi 2 B 2 C has been observed through the measurements of the local quasi-particle density of states with low temperature scanning tunneling microscopy and spectroscopy. The vortex lattice has shown the hexagonal to the square lattice transition around 0.1T under the magnetic field applied along the c-axis. On the other hands, under the magnetic field along the a-axis, the transition has occurred at much higher magnetic field of 1.0T. We have also observed that the vortex lattice gets disordered above 2.0T.

Observation of the vortex lattice near the step edge in YNi2B2C by scanning tunneling spectroscopy

Abstract The vortex lattice in YNi 2 B 2 C has been observed on the c -surface by low temperature scanning tunneling spectroscopy at 4.2 K under a magnetic field of 0.5 T parallel to the c -axis. The c -surface which is prepared by cracking or cutting the single crystal at 4.2 K in helium gas is rather flat and shows a step structure whose height is about 1.5 nm. We have found that the quasiparticle density of states at the Fermi energy on the step edge has increased when the vortices are near the step edge.

Renormalization Group Method and Reductive Perturbation Method

It is shown that the renormalization group method does not necessarily eliminate all secular terms in the perturbation series to partial differential equations. Also, choosing a subspace of renormalizable secular solutions corresponds with setting scales of independent variables in the reductive perturbation method.