Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0705.2474

The Nonperiodic Anyon Model and the Fractional Quantum Hall Effect

Stefan Mashkevich·Stéphane Ouvry
View original source ↗Read source document ↗Export metadata ↓

Abstract

The lowest-Landau-level anyon model becomes nonperiodic in the statistics parameter when the finite size of the attached flux tubes is taken into account. The finite-size effects cause the inverse proportional relation between the critical filling factor and the statistics parameter to be nonperiodically continued in the screening regime, where the fluxes are anti-parallel to the external magnetic field -- at critical filling, the external magnetic field is entirely screened by the mean magnetic field associated with the flux tubes. A clustering argument is proposed to select particular values of the statistics parameter. In this way, IQHE and FQHE fillings are obtained in terms of gapped nondegenerate LLL-anyonic wave functions. Jain's series are reproduced without the need to populate higher Landau levels. New FQHE series are proposed, like, in particular, the particle-hole complementary series of the Laughlin one. For fast-rotating Bose-Einstein condensates, a corresponding clustering argument yields particular fractional filling series.

Explore related subjects

cond-mat.mes-hallcond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Stefan Mashkevich, Stéphane Ouvry. 2007-05-17. The Nonperiodic Anyon Model and the Fractional Quantum Hall Effect. https://arxiv.org/abs/0705.2474

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Density-matrix quantum kinetics of spin-mode crossover and ac Edelstein response in spin--orbit-coupled chiral metals

To clarify spin relaxation and precession across the weak-to-strong SOC crossover in chiral conductors, we formulate a density-matrix quantum kinetic theory for a three-dimensional isotropic chiral metal with hedgehog SOC and nonmagnetic impurity scattering. The formulation retains interband coherence, and its collision integral conserves charge, energy, and spin during impurity scattering. We identify three spin modes that evolve continuously from a long-lived D'yakonov--Perel' relaxation mode and two strongly damped precessional modes at weak SOC to one relaxational and two coherent precessional modes at strong SOC. A closed multipole decomposition maps the spin dynamics onto an effective Bloch equation, providing a unified interpretation of relaxation and precession across the crossover. We further derive the ac Edelstein susceptibility and the reciprocal current response to a time-dependent Zeeman field, show that their poles coincide with the spin modes, and verify Onsager reciprocity. The theory thus provides a unified analytic description of spin relaxation, precession, and spin--charge conversion across the weak-to-strong SOC crossover.

cond-mat.mes-hall↗
arXiv2026

Incipient superconductivity and tunable Chern insulators in twisted bilayer-trilayer graphene

Moiré superlattices assembled by twisting Bernal and rhombohedral multilayer graphene host a rich set of interaction-driven magnetic and topological states, yet superconductivity has not been observed in these systems except in proximity to a transition-metal dichalcogenide. Here we report incipient superconductivity and tunable Chern insulators in twisted bilayer-trilayer graphene encapsulated by hexagonal boron nitride. Across twist angles from $θ= 1.05^\circ$ to $1.50^\circ$, Chern insulators form at integer and fractional moiré fillings for electron doping, with Chern numbers up to |C| = 3 set by twist angle and tuned by doping. At $θ= 1.18^\circ$, a symmetry-broken metallic region forms for hole doping and hosts a trivial insulator at band filling $ν= -2$. Displacement field alone drives this insulator into a pocket of incipient superconductivity with a sharp transition, a well-defined critical current, and a critical temperature that peaks near the insulating boundary, although the resistance does not fall to zero. In-plane magnetic field expands the pocket, which persists to more than four times the weak-coupling Pauli limit, and stabilizes a second pocket in which Fraunhofer-like modulation of the critical current signals phase-coherent pairing. Twisted bilayer-trilayer graphene thus offers a single gate-tunable system in which pairing can be interfaced with Chern insulators whose topology is itself an adjustable parameter.

cond-mat.mes-hall↗
arXiv2026

Electrically switchable one-dimensional quadrupolar excitons in lateral double heterojunctions

Two neighboring lateral interfaces provide a spatial degree of freedom for controlling one-dimensional charge-transfer excitons within a single semiconductor monolayer. We investigate a type-II WS2-MoS2-WS2 double heterojunction using an effective-mass two-particle Hamiltonian with a screened Coulomb interaction. For equivalent left and right interfaces at zero electric field,inter-interface coupling produces energetically split even- and odd-parity exciton states, each with zero permanent dipole. An electric field perpendicular to the interfaces continuously converts the lower state from a quadrupolar superposition with a quadratic Stark shift into a predominantly single-interface dipolar exciton with an approximately linear shift. The spatially resolved calculation gives binding energies of approximately 104 and 100 meV, a doublet splitting of 4.6 meV, and a crossover field of 0.87 V/um for a representative 1.5-nm MoS2 strip. Projection tests show that the lowest doublet controls the response near this crossover. Strip width tunes the coupling much more strongly than the binding energy, providing geometric control of the low-field Stark sensitivity. These results establish a continuum-model route to electrically reconfigurable one-dimensional quadrupolar excitons.

cond-mat.mes-hall↗