arXiv subjects
Publications and source records attributed to B. Basu.
A new framework for quantum Hall skyrmions in O(4) nonlinear sigma model is studied here. The size and energy of the skyrmions are determined incorporating the quartic stability term in the Lagrangian. Moreover, the introduction of a $θ$-term determines the spin and statistics of these skyrmions.
We have studied here the newly observed families of fractional quantum Hall states in the framework of Berry phase. It has been shown that this approach embraces in a unified way the whole spectrum of quantum Hall states with their various characteristic features. The newly observed states can be well accommodated within the primary sequence of FQH states and need not be considered as second generation FQH states as suggested by some authors.
Taking resort to Haldane's spherical geometry we can visualize fractional quantum Hall effect on the noncommutative manifold $M_4 \times Z_N$ with $N>2$ and odd. The discrete space leads to the deformation of symplectic structure of the continuous manifold such that the symplectic area is given by $\triangle p.\triangle q=2πm \hbar$ with $m$ an odd integer which is related to the Berry phase and the filling factor is given by $\frac{1}{m}$. We here argue that this is equivalent to the noncommutative field theory as prescribed by Susskind and Polychronakos which is characterized by area preserving diffeomorphism. The filling factor $\frac{1}{m}$ is determined from the change in chiral anomaly and hence the Berry phase as envisaged by the star product.
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 $μ$ 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 phase. Actually, in this topological framework each charge carrier is dressed with a magnetic flux quantum and represents a skyrmion. The skyrmion-skyrmion bound state leads to the d-wave Cooper pair formation. We have also discussed the Magnus force acting on the vortices of this system.
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 have discussed here the polarization of quantum Hall states in the framework of the hierarchical analysis of IQHE and FQHE in terms of Berry phase. It is observed that we have fully polarized states for the filling factor $ν=1$ as well as $ν=\frac{1}{2m+1}$, $m$ being an integer. However, for $ν=p$ as well as $ν=\frac{p}{q}$, with $p>1$ and odd, $q$ odd we have partially polarized states and for $ν=\frac{p}{q}$, $p$ even, $q$ odd we have unpolarized states. It has been found that skyrmion excitations exist only for fully polarized states and for partially polarized and unpolarized states skyrmionic excitations do not exist.
In the topological framework of high temperature superconductivity we have discussed the Magnus force acting on its vortices.
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.
From topological viewpoint we have analysed the role of Berry phase in spin pairing mechanism of high $T_c$ superconducting state.
We have analysed here the equivalence of RVB states with $ν=1/2$ FQH states in terms of the Berry Phase which is associated with the chiral anomaly in 3+1 dimensions. It is observed that the 3-dimensional spinons and holons are characterised by the non-Abelian Berry phase and these reduce to 1/2 fractional statistics when the motion is confined to the equatorial planes. The topological mechanism of superconductivity is analogous to the topological aspects of fractional quantum Hall effect with $ν=1/2$.