2007 Fiscal Year Final Research Report Summary
Study of topological excitations in gauge theories and quantum transport phenomena
| Project/Area Number |
17540253
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Particle/Nuclear/Cosmic ray/Astro physics
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| Research Institution | Kyoto University |
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Principal Investigator |
SHIZUYA Ken-ichi Kyoto University, Yukawa Institute for Theoretical Physics, Professor (50154216)
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| Project Period (FY) |
2005 – 2007
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| Keywords | topological excitation / anomalies / supersymmetry / gauge theory / quantum transport phenomena / quantum Hall effect / graphene |
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| Research Abstract |
Topological excitations play an important role in quantum transport phenomena, as seen from observations of Skyrmion (spin) excitations in quantum Hall systems, as well as in gauge and (super) string theories where one considers topological excitations in various dimensions. Under a Grant-in-Aid over the past three years we have studied quantum features of topological excitations in supersymmetric theories and, as a new subject, electromagnetic characteristics of a novel carbon material, graphene, for which an exotic half-integer quantum Hall effect was observed.
1. We had earlier studied, with focus on the central-charge anomaly in the superalgebra, the quantum features of (BPS) topological excitations in supersymmetric theories. In academic year 2005 we organized such early studies and developed, by combined use of dilatation and superfield formalism, a unified description of quantum spectra of topological excitations of various kinds and dimensions.
2. A great deal of attention has recently been directed to graphene, a monolayer graphite, which supports charge carriers that behave like massless Dirac fermions. Graphene is thus a 'relativistic' condensed-matter system and is of prime interest to particle physicists as well. (1) We first examined the electromagnetic response of graphene in a magnetic field and showed that graphene is an exotic dielectric medium as a consequence of the particle-hole picture of the ground state. (2) We then examined the static structure factor of graphene and showed that graphene is substantially different in electronic correlations at short distances from conventional 2D systems. (3) A subsequent look into bilayer graphene revealed that it supports, for topologoical reasons, some nearly-degenerate quasi-zero-mode Landau levels and that their energy gap, remarkably, is controllable by an applied electric field or by an injected Hall current.
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