Novel method distinguishing between competing topological orders

Abstract

Quantum Hall states - the progenitors of the growing family of topological insulators -- are rich source of exotic quantum phases. The nature of these states is reflected in the gapless edge modes, which in turn can be classified as integer - carrying electrons, fractional - carrying fractional charges; and neutral - carrying excitations with zero net charge but a well-defined amount of heat. The latter two may obey anyonic statistics, which can be abelian or non-abelian. The most-studied putative non-abelian state is the spin-polarized filling factor {\nu}=5/2, whose charge e/4 quasiparticles are accompanied by neutral modes. This filling, however, permits different possible topological orders, which can be abelian or non-abelian. While numerical calculations favor the non-abelian anti-Pfaffian (A-Pf) order to have the lowest energy, recent thermal conductance measurements suggested the experimentally realized order to be the particle-hole Pfaffian (PH-Pf) order. It has been suggested that lack of thermal equilibration among the different edge modes of the A-Pf order can account for this discrepancy. The identification of the topological order is crucial for the interpretation of braiding (interference) operations, better understanding of the thermal equilibration process, and the reliability of the numerical studies. We developed a new method that helps identifying the topological order of the {\nu}=5/2 state. By creating an interface between the two 2D half-planes, one hosting the {\nu}=5/2 state and the other an integer {\nu}=3 state, the interface supported a fractional {\nu}=1/2 charge mode with 1/2 quantum conductance and a neutral Majorana mode. The presence of the Majorana mode, probed by measuring noise, propagating in the opposite direction to the charge mode, asserted the presence of the PH-Pf order but not that of the A-Pf order.