Dr. Jun Goryo (Department of Physics, Nagoya University)
"Superconductivity and current confinement in Z2 topological insulator"
We investigates dissipationless electronic transport in a time-reversal invariant
Z2 topological insulator [1,2]. The edge states, which is established as
the characteristics of Z2 topological order, has been investigated extensively.
In this talk, on the other hand, the electronic transport in the bulk state is focused on.
The bulk state of Z2 topological insulators are also investigated by the
recent excellent argument in Ref. [3], which shows unique electromagnetic properties.
In contrast to Ref. [3], which takes into account only topologically robust quantities
protected by Z2 invariants, we reveal the role of quantized spin Hall conductivity (SHC) [4].
SHC is a ``weakly topological" number, since it is quantized topologically
in higher-symmetric system (the structure of symmetry would be clear in the next paragraph),
while loses topological meaning by a symmetry-breaking perturbation.
It is found that SHC also plays important and unexpected roles in electronic
transport in the bulk state of Z2 topological insulator.
Time-reversal invariant quantized spin Hall (QSH) insulator (higher-symmetric state of Z2 insulator) include,
in general, U(1) x Uz(1) (electromagnetic gauge, and a part of spin-rotation)-symmetric structures.
We show that the system shows superconductivity after integrating out Fermions and Uz(1) spin gauge field.
The mechanism of this superconductivity is analogous to that of anyon superconductivity.
Remarkably, it is found that the QSHE effect results in/from this superconductivity.
We also show that, in the more generic Z2 system with perturbations
which break the spin-rotation symmetry Uz(1), like the Rashba term in
Kane-Mele model for graphene [1,2], the total electric charge current tends to be
absent (like a usual insulator), whereas circulating current can exist locally,
namely, current is confined. Topology of the possible current loops on
a torus geometry plays a role of the ''order parameter" and definitely
classifies both of the superconducting and current-confining phases.
A net charge transfer can be finite in the superconducting phase obviously, on the other hand, is
absent in confining phase as is mentioned before. It would be interesting if the transition driven by
the Rashba term can be applied to the development of switching devices for dissipationless
electric transfer.
References:
[1] C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95, 146802 (2005).
[2] C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
[3] X.-L. Qi, T.L. Hughes, and S.-C. Zhang, Phys. Rev. B 78 (2008).
[4] J. Goryo, N. Maeda, and K.-I. Imura, arXiv:0905.2296