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Singular behavior at the edge of Laughlin states
- Source :
- Physical Review B. 89
- Publication Year :
- 2014
- Publisher :
- American Physical Society (APS), 2014.
-
Abstract
- A distinguishing feature of fractional quantum Hall (FQH) states is a singular behavior of equilibrium densities at boundaries. In contrast to states at integer filling fraction, such quantum liquids posses an additional dipole moment localized near edges. It enters observable quantities such as universal dispersion of edge states and Lorentz shear stress. For a Laughlin state, this behavior is seen as a peak, or overshoot, in the single particle density near the edge, reflecting a general tendency of electrons in FQH states to cluster near edges. We compute the singular edge behavior of the one particle density by a perturbative expansion carried out around a completely filled Landau level. This correction is shown to fully capture the dipole moment and the major features of the overshoot observed numerically. Furthermore, it exhibits the Stokes phenomenon with the Stokes line at the boundary of the droplet, decaying like a Gaussian inside and outside the liquid with different decay lengths. In the limit of vanishing magnetic length the shape the overshoot is a singular double layer with a capacity that is a universal function of the filling fraction. Finally, we derive the edge dipole moment of Pfaffian FQH states. The result suggests an explicit connection between the magnitude of the dipole moment and the bulk odd viscosity.<br />Comment: v1: 5 pages, 2 figures; v2: 7 pages, 2 figures, includes an expanded discussion of the singular double layer, and two new sections discussing the edge dipole moment of Pfaffian states. Otherwise, only minor changes to improve clarity
- Subjects :
- Physics
Strongly Correlated Electrons (cond-mat.str-el)
Condensed matter physics
Transition dipole moment
FOS: Physical sciences
Stokes line
Observable
Electron
Landau quantization
Quantum Hall effect
Condensed Matter::Mesoscopic Systems and Quantum Hall Effect
Condensed Matter Physics
Electronic, Optical and Magnetic Materials
Moment (mathematics)
Condensed Matter - Strongly Correlated Electrons
Dipole
Quantum mechanics
Subjects
Details
- ISSN :
- 1550235X and 10980121
- Volume :
- 89
- Database :
- OpenAIRE
- Journal :
- Physical Review B
- Accession number :
- edsair.doi.dedup.....76022b9b76891b152e81bf31a2149ede