Critical Majorana Fermion at a Topological Quantum Hall Bilayer Transition

Area of Science:

• Condensed Matter Physics
• Quantum Hall Effect
• Topological Phases of Matter

Background:

• Quantum Hall bilayers offer a tunable platform for studying topological phases.
• The transition between Halperin and Moore-Read Pfaffian states is predicted to host Majorana fermions but lacks experimental verification.
• Unbiased microscopic simulations are crucial for validating theoretical predictions.

Purpose of the Study:

• To investigate the topological phase transition between the Halperin state and the Moore-Read Pfaffian in quantum Hall bilayers.
• To verify the existence of a critical theory of Majorana fermions at this transition.
• To understand the underlying mechanisms and operator content driving the transition.

Main Methods:

• Utilizing fuzzy-sphere regularization to analyze the low-energy spectrum.
• Identifying the system's behavior with a 3D gauged Majorana conformal field theory.
• Analyzing the closing of the neutral fermion gap as the transition driver.

Main Results:

• The low-energy spectrum at the transition is identified with the 3D gauged Majorana conformal field theory.
• The transition is confirmed to be driven by the closing of the neutral fermion gap.
• Operator content in both integer and half-integer spin sectors was directly extracted.

Conclusions:

• The study resolves a long-standing question regarding the nature of topological phase transitions in quantum Hall systems.
• Provides experimental relevance for the theoretical understanding of Majorana fermions.
• Demonstrates a realization of emergent fermionic fields on the fuzzy sphere, extending previous findings for bosonic fields.