The spin Hall effect is a phenomenon of inducing spin current by an external electric field. We recently proposed that this effect can occur in p-type semiconductors without relying upon any disorder scattering [S. Murakami et al., Science 301, 1348 (2003)]. This intrinsic effect is due to the “Berry phase in momentum space”, representing topological structure of the Bloch band structure. We ex...

Finding new phase of matter is a fundamental task in physics. Generally, various phases or states of matter (for instance solid/liquid/gas phases) have different symmetries, the phase transitions among them can be explained by Landau's symmetry breaking theory. The topological phases discovered in recent years show that different phases may have the same symmetry. The different topological phas...

We investigate the equilibrium property of a mesoscopic ring with a spin-orbit interaction. It is well known that, for a normal mesoscopic ring threaded by a magnetic flux, the electron acquires a Berry phase that induces the persistent (charge) current. Similarly, the spin of an electron acquires a spin Berry phase traversing a ring with a spin-orbit interaction. It is this spin Berry phase th...

We study a simple quantum mechanical model of a spinning particle moving on a sphere in the presence of a magnetic field. The system has two ground states. As the magnetic field is varied, the ground states mix through a non-Abelian Berry phase. We show that this Berry phase is the path ordered exponential of the smooth SU(2) ’t Hooft-Polyakov monopole. We further show that, by adjusting a pote...

We study quasiparticle dynamics in a Bose-Einstein condensate with a vortex by following the center of mass motion of a Bogoliubov wave packet, and find important Berry-phase effects due to the background flow. We show that the Berry phase invalidates the usual canonical relation between the mechanical momentum and position variables, leading to important modifications of quasiparticle statisti...