Loic Herviou
Postdoctoral fellow, EPFL Lausanne

“Possible restoration of particle-hole symmetry in the 5/2 Quantized Hall State at small magnetic field”

The nature of the experimentally-measured fractional conductance plateau at filling 5/2 in Quantum Hall states remains a long standing problem, with several candidate states presenting slightly different topological order. After a decade of debate, the theoretical consensus settled on the non-Abelian Antipfaffian state. Nonetheless, recent experimental results measured a quantized thermal conductance of 5/2, incompatible with the theoretical proposal.
Our work revisits the theoretical approaches by pushing the expansion of the effective Hamiltonian of the 5/2 quantized Hall state to third-order in the Landau level mixing, the parameter controlling the interaction between different Landau levels. I will present the challenges behind this expansion, and our main results: the third-order expansion shows an inversion of the gaps at mixings well below the experimental regime, indicating that either the gaps are much smaller than previously expected, or that a quantum phase transition occurs. Our work also emphasizes the role of frozen spin degrees of freedom.
Finally, I will discuss what is needed to give a definite answer to this long standing problem, if it is at all possible.