Isolated Ballistic Non-Abelian Interface Channel

Abstract

Non-abelian anyons are prospective candidates for fault-tolerant topological quantum computation due to their long-range entanglement. Curiously these quasiparticles are charge-neutral, hence elusive to most conventional measurement techniques. A proposed host of such quasiparticles is the $\nu$=5/2 quantum Hall state. The gapless edge modes can provide the topological order of the state, which in turn identifies the chirality of the non-abelian mode. Since the $\nu$=5/2 state hosts a variety of edge modes (integer, fractional, neutral), a robust technique is needed to isolate the fractional channel while retaining its original non-abelian character. Moreover, a single non-abelian channel can be easily manipulated to interfere, thus revealing the state's immunity to decoherence. In this work, we exploit a novel approach to gap-out the integer modes of the $\nu$=5/2 state by interfacing the state with integer states, $\nu$=2 & $\nu$=3 (1). The electrical conductance of the isolated interface channel was 0.5e${}^2$/h, as expected. More importantly, we find a thermal conductance of 0.5${\kappa }_0$T (with ${\kappa }_0$=${\pi }^2{k}_B^2$/3h), confirming unambiguously the non-abelian nature of the $\nu$=1/2 interface channel and its Particle-Hole Pfaffian topological order. Our result opens new avenues to manipulate and test other exotic QHE states and braid, via interference, the isolated fractional channels.

20 pages, 4 main figures

References in corpus (9)

• 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
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Isolated Ballistic Non-Abelian Interface Channel
• Microscopic Theory of the Reentrant IQHE in the First and Second Excited LLs
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Fractional quantum Hall effect energy gap: role of electron layer thickness

Cited by in corpus (24)

• Isolated Ballistic Non-Abelian Interface Channel
• Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise
• Thermal conductance and noise of Majorana modes along interfaced $\nu =5/2$ fractional quantum Hall states
• Quarter- and half-filled quantum Hall states and their topological orders revealed by daughter states in bilayer graphene
• Fingerprints of anti-Pfaffian topological order in quantum point contact transport
• Identifying the topological order of quantized half-filled Landau levels through their daughter states
• Electron Pairing of Interfering Interface-Based Edge Modes
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Identifying non-Abelian anyons with upstream noise
• Possible restoration of particle-hole symmetry in the 5/2 Quantized Hall State at small magnetic field
• Localization and conductance in fractional quantum Hall edges
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Impact of potential and temperature fluctuations on charge and heat transport in quantum Hall edges in the heat Coulomb blockade regime
• Fractional Quantum Hall States of the $\mathcal{A}$ phase in the Second Landau Level
• Transport Signatures of Fractional Quantum Hall Binding Transitions
• Landscapes of an out-of-equilibrium anyonic sea
• Universal charge conductance at Abelian--non-Abelian quantum Hall interfaces
• Drag conductance induced by neutral-mode localization in fractional quantum Hall junctions
• Large composite fermion effective mass at filling factor 5/2
• Fractional-statistics-induced entanglement from Andreev-like tunneling
• Breakdown of the Wiedemann-Franz law in an interacting quantum Hall metamaterial
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene
• Shot noise signatures of candidate states for the fractional quantum Hall $\nu =12/5$ state