Dependence of the tunneling quasiparticle charge determined via shot noise measurements on the tunneling barrier and energetics

Abstract

ABSRACTCharged excitations in the fractional quantum Hall effect are known to carry fractional charges, as theoretically predicted and experimentally verified. Here we report on the dependence of the tunneling quasiparticle charge, as determined via highly sensitive shot noise measurements, on the measurement conditions, in the odd denominators states ν=1/3 and ν=7/3 and in the even denominator state ν=5/2. In particular, for very weak backscattering probability and sufficiently small excitation energies (temperature and applied voltage), tunneling charges across a constriction were found to be significantly higher than the theoretically predicted fundamental quasiparticle charges. 2Odd denominator fractional quantum Hall effect (FQHE) states [1,2], whose quasiparticles are expected to possess fractional statistics, have been already the focus of extensive studies [3].However, more recently, particular attention was devoted to the even denominator fractional state ν=5/2 [4], which is conjectured to be described by a Pfaffian wavefunction [5][6][7], mainly due to the expectation that its quasiparticles carry a charge e/4 and obey non-abelian statistics [5,[8][9][10]. As such, these quasiparticles may be useful for topological quantum computation [11][12][13].An important step in the experimental study of the FQHE states is the determination of the quasiparticle charge. While the fundamental quasiparticle charge in the bulk for a fractional state is expected to be unique, the charge that tunnels between two counter propagating edgeschannels might depend on the measurement conditions. Here we study the uniqueness of the tunneling charge, and search for conditions under which it is equal to the expected fundamental quasiparticle charge.Most charge measurements detect charges that tunnel either across a narrow constriction, via shot noise measurements [14][15][16][17][18], conductance measurements [19] and interference [20,21], or charges that tunnel into localized states in the bulk [22], which, in all cases, are not guaranteed to be equal to the fundamental quasiparticle charge in the bulk. Moreover, the excitation energy (applied voltage and temperature) is also expected to affect the tunneling charge. However, since charges that tunnel between edges can only be integer multiples of the fundamental charge, the smallest measured charge sets an upper bound for the fundamental charge. For example, a measurement in the ν=5/2 state of a charge e/4 rules out e/2 fundamental charges in this state.We present here measurement results of low frequency shot noise generated by partitioning. This work was motivated by our attempt to improve the accuracy of our previous measurements 3 and tighten the data points with more sensitive measurements, thus allowing us to determine the charge in a previously inaccessible low energy and very weak backscattering regimes -where shot noise is excessively small. Our new measurements revealed an interesting dependence of the conductance and the tunneling charge on the energy and the transmi...

Anomalous Charge Tunneling in Fractional Quantum Hall Edge States at a Filling Factorν=5/2

“…This fact has been experimentally supported by bulk measurements [7] and with current noise experiments through a quantum point contact geometry [8], successfully applied for other FQH states [9,10]. Very recently, measurements were reported [11] for ¼ 5=2 where the e=4 charge value is observed at high temperatures, while at low temperatures the measured charge reaches the unexpected value e=2. Analogous enhancement of the carrier charge has been already observed [10,12] and theoretically explained [13] in other composite FQH states belonging to the Jain sequence.…”

“…5 of Ref. [11], with courtesy of Dolev. Different styles indicate different temperatures: T ¼ 27 mK (asterisks, short-dashed blue line), T ¼ 41 mK (triangles, dashed-dotted cyan line), T ¼ 57 mK (crosses, longdashed green line), T ¼ 76 mK (squares, dotted magenta line), and T ¼ 86 mK (circles, solid red line).…”

“…2, we compare the effective charge e eff (triangles), calculated from our theoretical curves by using a single parameter fitting procedure, with the results of Ref. [11] (circles with error bars). This result reinforces the idea that the evolution of the effective charge, as a function of the temperature, is essentially due to the crossover between the single-qp and the 2-agglomerate contributions.…”

“…We acknowledge the support of the CNR STM 2010 program and the EU-FP7 via ITN-2008-234970 NANOCTM. [11], with courtesy of Heiblum. Triangles are the effective charges obtained from the theoretical curves of excess noise in Fig.…”

Condensation of achiral simple currents in topological lattice models: Hamiltonian study of topological symmetry breaking

“…The vertex projectors of the Levin-Wen model, based on these fusion rules, have eigenvalue 1 if the edges incident on a vertex are in one of the following 3 combinations (here the order in which they appear is not important): (27) and the vertex projector gives zero for any other combination of edge labels.…”