Tunneling current and current correlations for anyonic quasiparticles of ν = 1/2 chiral Luttinger liquid in multi-edge geometries

Abstract

We consider anyonic quasiparticles with charge e/2 described by the ν = 1/2 chiral Luttinger liquid, which collide in a Hong-Ou-Mandel-like interferometer. These colliding anyonic channels can be formally viewed as hosting Laughlin-like fractional ν = 1/2 quasiparticles. More specifically, two possible geometries are considered: (i) a two-edge-channel setup where anyons originate from equilibrium reservoirs; (ii) a four-edge-channel setup where nonequilibrium anyons arrive at the collider in the form of diluted beams. For both setups, we calculate the tunneling current and the current correlations. For setup (i), our results provide analytically exact expressions for the tunneling current, tunneling-current noise, and cross-correlation noise, The exact relation between conductance and noise is demonstrated. For setup (ii), we show that the tunneling current and the generalized Fano factor [defined in B. Rosenow et al. (2016)] are finite for diluted streams of ν = 1/2 anyons. This is due to the processes where nonequilibrium anyons, supplied via either source edge, directly tunnel at the central QPC. Thus, to obtain meaningful results in this case, one should go beyond the so-called time-domain braiding processes, where nonequilibrium anyons do not tunnel at the collider, but rather indirectly influence the tunneling by braiding with the quasiparticle-quasihole pairs created at the collider. This suggests that the effect of direct tunneling and collisions of diluted anyons in the Hong-Ou-Mandel interferometer can be important for various observables in physical quantum-Hall edges at Laughlin filling fractions.

39 pages, 10 figures

References in corpus (35)

• Non-Abelian Anyons and Topological Quantum Computation
• Fractional statistics in anyon collisions
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Interferometry of non-Abelian Anyons
• The non-Abelian Interferometer
• Transport properties of single channel quantum wires with an impurity: Influence of finite length and temperature on average current and noise
• Chiral Mott Insulators, Meissner Effect, and Laughlin States in Quantum Ladders
• Shot Noise in Anyonic Mach-Zehnder Interferometer
• Non-equilibrium Luttinger liquid: Zero-bias anomaly and dephasing
• Hanbury-Brown and Twiss interference of anyons
• Excitonic topological order in imbalanced electron-hole bilayers
• Impact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers
• Partitioning of Diluted Anyons Reveals their Braiding Statistics
• Topological vacuum bubble by anyon braiding
• Fractionalization and anyonic statistics in the integer quantum Hall collider
• Non-Abelian Anyon Collider
• AC conductance and non-symmetrized noise at finite frequency in quantum wires and carbon nanotubes
• Measuring fractional charge and statistics in fractional quantum Hall fluids through noise experiments
• Emission and absorption noise in the fractional quantum Hall effect
• Mach-Zehnder interferometer in the Fractional Quantum Hall regime
• Why a noninteracting model works for shot noise in fractional charge experiments
• One-channel conductor coupled to a quantum of resistance: exact ac conductance and finite-frequency noise
• Chirality, causality, and fluctuation-dissipation theorems in non-equilibrium steady states
• Identification of 331 quantum Hall states with Mach-Zehnder interferometry
• Effect of interactions on the noise of chiral Luttinger liquid systems
• Anyon statistics through conductance measurements of time-domain interferometry
• Probing the $\nu =\frac{5}{2}$ quantum Hall state with electronic Mach-Zehnder interferometry
• Non-Abelian statistics in the interference noise of the Moore-Read quantum Hall state
• Anyonic Mach-Zehnder interferometer on a single edge of a 2D electron gas
• Finite width of anyons changes their braiding signature
• Finite Soliton Width Matters: Investigating Non-equilibrium Exchange Phases of Anyons
• Conductance of a Dissipative Quantum Dot: Nonequilibrium Crossover Near a Non-Fermi-Liquid Quantum Critical Point
• FQHE interferometers in strong tunneling regime. The role of compactness of edge fields

Cited by in corpus (1)

• Landscapes of an out-of-equilibrium anyonic sea