Explore the fascinating world of topological states of matter in this 48-minute lecture on the theory of disorder-induced half-integer thermal Hall conductance. Delve into the fractional quantum Hall effect, examining exchange statistics in 2D and 3D systems, and the rich landscape of quantum states. Learn about the quantization of heat flow in fractional quantum Hall regimes, experimental techniques for measuring thermal conductance, and the intricacies of hole-conjugate states. Investigate the behavior of complex fractions, temperature dependencies, and the implications for non-abelian states at v=5/2. Gain insights into cutting-edge research on topological phases of matter and their potential applications in condensed matter physics.
Theory of Disorder-Induced Half-Integer Thermal Hall Conductance by Mitali Banerjee
International Centre for Theoretical Sciences via YouTube
Overview
Syllabus
Quantization of heat flow in the fractional quantum Hall regime
topological states of matter
The paradigmatic fractional quantum Hall effect - first known topological state
Exchange statistics in 3D
possible Exchange statistics in 2D
Exchange statistics due to ground state degeneracy
Main platform: fractional quantum Hall effect
insulating bulk
quantum Hall effect
quantum Hall effect.....integer
quantum Hall effect......fraction
Laughlin's quasiparticles lowest LL
Rich world of fascinating quantum states
quantum Hall effect..even denominator fraction
with time...
what may happen at v=1/2?
Moore - Read theory
5/2 state
fractional quantum states...
Most of the experimental probes are sensitive to charge
Quantum limit of heat flow for 1D ballistic channel
Experimental evidences
Working principle
we measure only temperature....
measuringTm....Johnson-Nyquist noise
Determining thermal conductance
more complex fractions...
K of hole-states...
v=2/3 ...... why K = 0?
Hole-conjugate states
Temperature dependence
calculating Tx & K ...... V=2/3
Summary
already known for v=5/2
fractional state........ v=5/2; if non-abelian......
increasing equilibration length at lower temperature
PH-Pfaffian for sure?
v=5/2..... non-abelian - measuring thermal conductance
Acknowledgement
Taught by
International Centre for Theoretical Sciences
