Magnus Force in High Temperature Superconductivity and Berry Phase

This is the text of a talk which is to be published in the proceedings of the Joint APCTP-ICTP conference (Seoul National University Korea, May 26th-30th 1997).

We have discussed here the Magnus force acting on the vortices and skyrmions in the quantum Hall systems. We have found that it is generated by the chirality of the system which is associated with the Berry phase and is same for both the cases.

We propose a mechanism of high temperature superconductivity from the viewpoint of chirality and Berry phase. It is observed that spin pairing and charge pairing is caused by a gauge force generated by magnetic flux quanta attached to them. From the renormalization group equation involving the Berry phase factor $\mu$ it is found that there are two crossovers above the superconducting temperature $T_c$, one corresponds to the glass phase and the other represents the spin gap ...

The effective action for the Josephson junction arrays should contain the topological term, which violates the particle-hole symmetry. This term is responsible for the nonzero Magnus force acting on the vortex. The Magnus force is however small because the parameter of the particle-hole asymmetry in superconductors is small.

The topological approach to the understanding of pairing mechanism in high $T_c$ superconductors analyses the relevance of the Berry phase factor in this context. This also gives the evidence for the pairing mechanism to be of magnetic origin.

We present a new derivation of the Berry phase picked up during exchange of parallel vortices. This derivation is based on the Bogolubov - de Gennes formalism. The origin of the Magnus force is also critically reanalised. The Magnus force can be interpreted as interaction with effective magnetic field. The efective magnetic field may be even of the order $10^{6} T/\AA$. We discuss a possibility of the FQHE in vortex systems. As the real magnetic field is varied to drive chang...

A microscopic analysis of the non-dissipative force ${\bf F}_{nd}$ acting on a line vortex in a type-II superconductor at $T=0$ is given. We first examine the Berry phase induced in the true superconducting ground state by movement of the vortex and show how this induces a Wess-Zumino term in the hydrodynamic action $S_{hyd}$ of the superconducting condensate. Appropriate variation of $S_{hyd}$ gives ${\bf F}_{nd}$ and variation of the Wess-Zumino term is seen to contribute t...

From topological viewpoint we have analysed the role of Berry phase in spin pairing mechanism of high $T_c$ superconducting state.

The paper addresses the problem of the transverse force (Magnus force) on a vortex in a Galilean invariant quantum Bose liquid. Interaction of quasiparticles (phonons) with a vortex produces an additional transverse force (Iordanskii force). The Iordanskii force is related to the acoustic Aharonov--Bohm effect.Connection of the effective Magnus force with the Berry phase is also discussed.

We give a general review of recent developments in the theory of vortices in superfluids and superconductors, discussing why the dynamics of vortices is important, and why some key results are still controversial. We discuss work that we have done on the dynamics of quantized vortices in a superfluid. Despite the fact that this problem has been recognized as important for forty years, there is still a lot of controversy about the forces on and masses of quantized vortices. We...