Mahito Kohmoto

Topological invariant and the quantization of the Hall conductance

Abstract The topological aspects of wavefunctions for electrons in a two dimensional periodic potential with a magnetic field are discussed. Special attention is paid to the linear response formula for the Hall conductance σxy. It is shown that the quantized value of σxy is related to the number of zeros of wavefunctions in the magnetic Brillouin zone. A phase of wavefunctions cannot be determined in a unique and smooth way over the entire magnetic Brillouin zone unless the magnetic subband carries no Hall current.

Renormalization group theory of transport properties of polymer solutions. I. Dilute solutions

The (Gell–Mann–Low type) renormalization group theory is applied to frictional properties of dilute polymer solutions for the first time. The universal ratios such as Flory’s intrinsic viscosity constant, the Flory–Scheraga–Mandelkern parameter, etc., are estimated from the first order e‐expansion theory (e=4−d, d being the spatial dimensionality). The results are in satisfactory agreement with experimental results in both the nondraining Gaussian and nondraining self‐avoiding limits. Preaveraging the Oseen tensor makes the value of the intrinsic viscosity about 10% larger according to the first order e‐expansion calculation.

Zero modes of tight-binding electrons on the honeycomb lattice

Tight binding electrons on the honeycomb lattice are studied where nearest neighbor hoppings in the three directions are

Edge states and topological phases in non-Hermitian systems

t_a,t_b

ELECTRONIC SPECTRAL AND WAVEFUNCTION PROPERTIES OF ONE-DIMENSIONAL QUASIPERIODIC SYSTEMS: A SCALING APPROACH

and

Mechanism of Spin-Triplet Superconductivity in Sr2RuO4

t_c

Zero modes and edge states of the honeycomb lattice

, respectively. For the isotropic case, namely for

CRITICAL AND BICRITICAL PROPERTIES OF HARPER'S EQUATION WITH NEXT-NEAREST-NEIGHBOR COUPLING

t_a=t_b=t_c

Quasiparticle Spectra around a Single Vortex in a {ital d} -Wave Superconductor

, two zero modes exist where the energy dispersions at the vanishing points are linear in momentum

Quantum hall effect and the topological number in graphene

k