Probing Fractional Topological Insulators with Magnetic Edge Perturbations

We discuss detection strategies for fractional topological insulators (FTIs) realizing time-reversal invariant analogues of fractional quantum Hall systems in the Laughlin universality class. Focusing on transport measurements, we study the effect of magnetic perturbations on the edge modes. We find that the modes show unexpected robustness against magnetic backscattering for moderate couplings and edge interactions, allowing for various phase transitions signaling the FTI phase. We also describe protocols for extracting the universal integer $m$ characterizing the phase and the edge interaction parameter from the conductance of setups with magnets and a quantum point contact.

Figure 1

FTI (shaded region) with a magnetic edge perturbation (hatched region). The solid and dashed arrows indicate the pair of counterpropagating edge modes between the source (voltage $V$) and drain (grounded) terminals. Inset: QPC setup near the pinched off limit.

Figure 2

The Kosterlitz-Thouless flow in the regime $L_M\gg L_T$ with conducting ($C$) and insulating ($I$) phases (separated by the dashed line).