Observation of half-integer thermal Hall conductance

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Topological states of matter

Background:

• Topological states are defined by quantized invariants, unaffected by system imperfections.
• Electrical Hall conductance measurements reveal topologically ordered states with fractional quasiparticles.
• Thermal Hall conductance, though harder to measure, provides distinct topological information.

Purpose of the Study:

• To investigate the thermal Hall conductance of quantum Hall states in the first excited Landau level.
• To determine if the 5/2 quantum Hall state exhibits non-Abelian properties.

Main Methods:

• Measurement of thermal Hall conductance.
• Analysis of quantum Hall states in the first excited Landau level.
• Comparison of experimental results with theoretical predictions for topological invariants.

Main Results:

• The thermal Hall conductance of the 5/2 state was measured to be 2.5κ₀.
• This fractional value is compatible with theoretical expectations for a non-Abelian topological state.
• Other measured quantum Hall states showed different thermal Hall conductance values.

Conclusions:

• The 5/2 quantum Hall state is demonstrated to be non-Abelian.
• This finding supports the potential application of this state in topological quantum computation.
• The study highlights the importance of thermal Hall conductance as a probe for exotic quantum matter.