[speech] Topological Phenomena and Singular Transport in Graphene

Speaker: Prof. Tsuneya Ando CV
Honorary Professor, Department of Physics, Tokyo Institute of Technology
Honorary Director, SKKU Advanced Institute of Nano Technology
Visiting Fellow, Toyota Physical and Chemical Research Institute

Time & Venue: May 20, 2019 (Mon.)16:00~17:00 SC353-2, Science Building III

The electron motion in graphene, first fabricated by mechanical exfoliation method and later by various other methods, is governed by Weyl’s equation for a neutrino or the Dirac equation in the relativistic limit. Various reviews have already been published [1-4]. An electron has a pseudo-spin, which is quantized into the direction of the electron motion. As a result, the wave function exhibits a sign change due to Berry’s phase when the wave vector k is rotated around the origin and therefore has a topological singularity at k=0 or at zero energy. This singularity is likely to be the origin of the peculiar behavior in transport properties of graphene, such as the minimum conductivity at zero energy, the half-integer quantum Hall effect, the dynamical conductivity, crossover between the weak- and anti-localization, the singular diamagnetic response, etc.
In this talk, exotic electronic and transport properties of graphene are reviewed from a theoretical point of view. The subjects include the origin of the diamagnetic susceptibility exhibiting a delta-function singularity at zero energy and the topological valley-Hall conductivity when a gap opens up. The singular behavior also appears in the transport itself. When a weak magnetic field is applied, the singularity is enhanced because of the singular divergence of the classical cyclotron frequency at zero energy. Recently, this has theoretically been demonstrated in the weak-field Hall effect and in the weak-field magnetoresistance. Similar singularities appear in various two-dimensional systems such as those with giant Rashba spin-orbit interaction, phosphorene, and other atomic-layer materials, which will be discussed if the time allows.

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