arXiv subjects

Piotr Sitko

Publications and source records attributed to Piotr Sitko.

4 recordsLinked to original sources

arXiv2004

Charge and Statistics of Quasiholes in Pfaffian States of Composite Fermion Excitations

The charge of quasiparticles in Pfaffian states of composite fermion excitations (the presence of which is indicated by recent experiments) is found. At the filling fraction of the Pfaffian state $ν=p/q$ (of the lowest Landau level) the charge is $\pm e/(2q)$. As in the case of the Pfaffian state of electrons the statistics of $N_{qh}$ quasiholes in the Pfaffian state corresponds to the spinor representation of $U(1)\times SO(2N_{qh})$ (the continuous extension of the braid group). Here U(1) is given by the phase factor $e^{i({1/8}+\frac{1}{4m})π}$ with $m=1+α$, $α$ -- the exclusion statistics parameter of Jain quasiparticles. The possiblity of Read-Rezayi states of Jain quasiparticles is also discussed.

cond-mat.mes-hall↗

arXiv2003

Exclusion Statistics of Quasiparticles in Condensed States of Composite Fermion Excitations

The exclusion statistics of quasiparticles is found at any level of the hierarchy of condensed states of composite fermion excitations (for which experimental indications have recently been found). The hierarchy of condensed states of excitations in boson Jain states is introduced and the statistics of quasiparticles is found. The quantum Hall states of charged $α$-anyons ($α$ -- the exclusion statistics parameter) can be described as incompressible states of $(α+2p)$-anyons ($2p$ -- an even number).

cond-mat.mes-hall↗

arXiv2003

Quantum Hall Systems: Braid groups, composite fermions, and fractional charge

The book presents the wide range of topics in two-dimensional physics of quantum Hall systems, especially fractional quantum Hall states. It starts with the fundamental problems of quantum statistics in two dimensions and the corresponding braid group formalism. The braid group formalism of anyons (previously known) is developed for composite fermions. The main formalism used in many-body quantum Hall theories -- the Chern-Simons theory is also presented. The Chern-Simons theory of anyons (particles obeying fractional statistics) and composite fermions (related to Hall systems) is given, in detail. Numerical studies, which play the important role in quantum Hall theories, are presented for spherical systems (Haldane sphere). The composite fermion theory is tested in numerical studies. The concept of the hierarchy of condensed states of composite fermion excitations is introduced (in analogy to the Haldane hierarchy)1). The hierarchies of odd-denominator states and even-denominator states are presented. The BCS paired Hall state is also discussed. The introduction into multi-component quantum Hall systems and spin quantum Hall systems is sketched. 1)First condensed states of composite fermion excitations have been very recently confirmed in the experiment (Pan et al. Phys. Rev. Lett. 90 (2003) 016801). a sample of this book is available at http://www.oup.co.uk/isbn/0-19-852870-1

cond-mat.mes-hall↗

arXiv2001

Exclusion Statistics of Composite Fermions

The exclusion statistics parameter of composite fermions is determined as an odd number ($α=3$, 5, ...). The statistics of composite fermion excitations at $ν= \frac{n}{2pn+1}$ is rederived as $α_{qe}^{CF}=1+\frac{2p}{2pn+1}$, $α_{qh}^{CF}=1-\frac{2p}{2pn+1}$. The duality $\frac{1}{α_{qe}(n,2p)}=α_{qh}(n+1,2p)$ is found. The distribution function for $α=3$ is obtained.

cond-mat.mes-hall↗