Hiroyuki Shima

Observation of Riemannian geometric effects on electronic states

Einstein first applied Riemannian geometry to develop the general theory of relativity almost one hundred years ago and succeeded in understanding astronomical-scale phenomena such as the straining of time-space by a gravitational field. Whether or not Riemannian space affects the electronic properties of condensed matters on a much smaller scale is of great interest. Although Riemannian geometry has been applied to quantum mechanics since the 1950s, nobody has yet answered this question, because the electronic properties of materials with Riemannian geometry have not been examined experimentally. We report here the first observation of Riemannian geometrical effects on the electronic properties of materials such as Tomononaga-Luttinger liquids, which were previously theoretically predicted by our group. We present in situ high-resolution ultraviolet photoemission spectra of a one-dimensional metallic C60 polymer with an uneven periodic peanut-shaped structure.

Multiple radial corrugations in multiwalled carbon nanotubes under pressure

Radial elastic corrugation of multiwalled carbon nanotubes under hydrostatic pressure is demonstrated by using the continuum elastic theory. Various corrugation patterns are observed under a pressure of several GPa, wherein the stable cross-sectional shape depends on the innermost tube diameter D and the total number N of concentric walls. A phase diagram is established to obtain the requisite values of D and N for a desired corrugation pattern among choices. In all corrugation patterns, the cylindrical symmetry of the innermost tube is maintained even under high external pressure.

Tuning the electrical resistivity of semiconductor thin films by nanoscale corrugation

Department of Applied Physics, Graduate School of Engineering, HokkaidoUniversity, Sapporo. 060-8628 JapanE-mail: shota-o@eng.hokudai.ac.jpE-mail: shima@eng.hokudai.ac.jpAbstract. The low-temperature electrical resistivity of corrugated semiconductorfilms is theoretically considered. Nanoscale corrugation enhances the electron-electronscattering contribution to the resistivity, resulting in a stepwise resistivity developmentwith increasing corrugation amplitude. The enhanced electron scattering is attributedto the curvature-induced potential energy that affects the motion of electrons confinedto a thin curved film. Geometric conditions and microscopic mechanism of the stepwiseresistivity are discussed in detail.

Diverse corrugation pattern in radially shrinking carbon nanotubes

Stable cross sections of multiwalled carbon nanotubes subjected to electron-beam irradiation are investigated in the realm of the continuum mechanics approximation. The self-healing nature of sp2 graphitic sheets implies that selective irradiation of the outermost walls causes their radial shrinkage with the remaining inner walls undamaged. The shrinking walls exert high pressure on the interior part of nanotubes, yielding a wide variety of radial-corrugation patterns (i.e. circumferentially wrinkling structures) in the cross section. All corrugation patterns can be classified into two deformation phases for which the corrugation amplitudes of the innermost wall differ significantly.

Pressure-induced structural transitions in multi-walled carbon nanotubes

We demonstrate a novel cross-sectional deformation, called the radial corrugation, of multi-walled carbon nanotubes (MWNTs) under hydrostatic pressure. Theoretical analyses based on the continuum elastic approximation have revealed that MWNTs consisting of more than ten concentric walls undergo elastic deformations at critical pressure

Geometric effects on critical behaviours of the Ising model

p_c \simeq 1

Low-Temperature Resistivity Anomalies in Periodic Curved Surfaces

GPa, above which the circular shape of the cross section becomes radially corrugated. Various corrugation modes have been observed by tuning the innermost tube diameter and the number of constituent walls, which is a direct consequence of the core-shell structure of MWNTs.

The dynamic exponent of the Ising model on negatively curved surfaces

We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic susceptibility and the correlation length deviate from those for the Ising lattice model on a flat plane. Furthermore, when reducing the effects of boundary spins, the values of the critical exponents tend to those derived from the mean field theory. These findings evidence that the underlying geometric character is responsible for the critical properties of the Ising model when the lattice is embedded on negatively curved surfaces.

Curvature-induced frustration in the XY model on hyperbolic surfaces

Effects of periodic curvature on the electrical resistivity of corrugated semiconductor films are theoretically considered. The presence of a curvature-induced potential affects the motion of electrons confined to the thin curved film, resulting in a significant resistivity enhancement at specific values of two geometric parameters: the amplitude and period of the surface corrugation. The maximal values of the two parameters in order to observe the corrugation-induced resistivity enhancement in actual experiments are quantified by employing existing material constants.

Flux-free conductance modulation in a helical Aharonov--Bohm interferometer.

We investigate the dynamic critical exponent of the two-dimensional Ising model defined on a curved surface with constant negative curvature. By using the short-time relaxation method, we find a quantitative alteration of the dynamic exponent from the known value for the planar Ising model. This phenomenon is attributed to the fact that the Ising lattices embedded on negatively curved surfaces act as ones in infinite dimensions, thus yielding the dynamic exponent deduced from mean field theory. We further demonstrate that the static critical exponent for the correlation length exhibits the mean field exponent, which agrees with the existing results obtained from canonical Monte Carlo simulations.