Misc,
Dirac-Maxwell correspondence: Spin-1 bosonic topological insulator
(2017)cite arxiv:1708.08192Comment: 18 pages, 5 figures.
Abstract
Fundamental differences between fermions and bosons are revealed in their
spin statistics as well as the discrete symmetries they obey (charge, parity
and time). While significant progress has been made on fermionic topological
phases with time-reversal symmetry, the bosonic counterpart still remains
elusive. We present here a spin-1 bosonic topological insulator for light by
utilizing a Dirac-Maxwell correspondence. Marking a departure from existing
structural photonic approaches which mimic the pseudo-spin-1/2 behavior of
electrons, we exploit the integer spin and discrete symmetries of the photon to
predict the existence of a distinct bosonic topological phase in continuous
media. We introduce the bosonic equivalent of Kramers theorem and topological
quantum numbers for light as well as the concept of photonic Dirac monopoles,
Dirac strings and skyrmions to underscore the correspondence between Maxwell's
and Dirac's equations. We predict that a unique magneto-electric medium with
anomalous parity and time-reversal symmetries, if found in nature, will exhibit
a gapped Quantum spin-1 Hall bosonic phase. Photons do not possess a
conductivity transport parameter which can be quantized (unlike topological
electronic systems), but we predict that the helical quantization of
symmetry--protected edge states in bosonic topological insulators is amenable
to experimental isolation.
