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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Weakly coupled Pfaffian as a type I quantum Hall liquid.

S A Parameswaran¹, S A Kivelson, S L Sondhi

¹Department of Physics, Princeton University, Princeton, New Jersey 08544, USA. sashok@princeton.edu

Physical Review Letters

|July 21, 2011

Summary

The Pfaffian phase, a p+ip superconductor, exhibits unique vortex behavior in the weak-coupling limit. This leads to Coulomb frustrated phase separation, distinguishing it from type II quantum Hall fluids.

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Area of Science:

Condensed Matter Physics
Quantum Hall Effect
Superconductivity

Background:

The Pfaffian phase near a half-filled Landau level is a p+ip superconductor of composite fermions.
Understanding its properties in the weak-coupling BCS limit is crucial.

Purpose of the Study:

To investigate the properties of the paired quantum Hall phase in the weak-coupling limit.
To analyze vortex behavior and phase separation phenomena.

Main Methods:

Considering the BCS limit where pairing energy is small.
Analyzing the relationship between coherence length and charge screening length.

Main Results:

Vortices attract in the weak-coupling Pfaffian phase, similar to type I superconductors.
Varying magnetic field induces Coulomb frustrated phase separation.

Conclusions:

The weakly and strongly coupled Pfaffians represent a dichotomy between type I and type II quantum Hall fluids.
This study provides insights into exotic states of matter in condensed systems.