Observation of half-integer thermal Hall conductance

Abstract

Topological states of matter are characterized by topological invariant, which are physical quantities whose values are quantized and do not depend on details of the measured system. Of these, the easiest to probe in experiments is the electrical Hall conductance, which is expressed in units of $e^2/h$ ($e$ the electron charge, $h$ the Planck's constant). In the fractional quantum Hall effect (FQHE), fractional quantized values of the electrical Hall conductance attest to topologically ordered states, which are states that carry quasi particles with fractional charge and anyonic statistics. Another topological invariant, which is much harder to measure, is the thermal Hall conductance, expressed in units of ${\kappa }_{0}T=({\pi }^{2}k{B}^2/3h)T$ ($kB$ the Boltzmann constant, $T$ the temperature). For the quantized thermal Hall conductance, a fractional value attests that the probed state of matter is non-abelian. Quasi particles in non-abelian states lead to a ground state degeneracy and perform topological unitary transformations among ground states when braided. As such, they may be useful for topological quantum computation. In this paper, we report our measurements of the thermal Hall conductance for several quantum Hall states in the first excited Landau level. Remarkably, we find the thermal Hall conductance of the $\nu =5/2$ state to be fractional, and to equal $2.5{\kappa }_{0}T$

16 pages, 16 figures

References in corpus (15)

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• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Quantum limit of heat flow across a single electronic channel
• Single-mode heat conduction by photons
• Observation of neutral modes in the fractional quantum Hall regime
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• Experimental probe of topological orders and edge excitations in the second Landau level
• On the Interpretation of Thermal Conductance of the nu=5/2 Edge
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• Experimental constraints and a possible quantum Hall state at $\nu =5/2$
• Gating of high-mobility two-dimensional electron gases in GaAs/AlGaAs heterostructures
• Low-temperature illumination and annealing of ultra-high quality quantum wells

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