basics of edge channels in IQHE doing physics with integer edge channels studies of transport in FQHE regime deviations from the ‘accepted’ picture Moty Heiblum QHE Regime Edge States in QHE Regime …. their nature & use

edge channels in FQHE mirrors of the bulk back to shot noise…

V = 0 ……….. S i (0) = 4k B Tg ……….thermal shot noise T > 0 T = 0 ……….. S i (0) = 2qI (1-t )……..shot V, T > 0 …………………………………….total T=100mK noise of independent scattering EFEF n (E ) EFEF

start with =1/3… a reminder =e / 3 ohmic contact J (r ) 00 r

start with, ubiquitous v =1/3 fractional state conductance is not enough - use shot noise employ partition via weak backscattering  infrequent & independent events - stochastic determination of qp charge

h/eV e e e t g =e 2 / 3h noise  e * = e t e / 3 3h/eV g =e 2 / 3h similar conductance - different shot noise partitioning noise  e * =e/3

extremely weak backscattering T=9mK 1-t ~ 0.01 V g =-0.03V

strong  weak backscattering e/3e/3 e only electrons expected

composite edge channel =2/5

1-t ~ 0.01 = 2/5 bunching of quasiparticles charge = filling factor extremely weak backscattering

1 st excited Landau level

- Rxx x Rxy R ( k  B ( T )      v =5/2 Moore - Read proposed non-abelian state  ~ 30  10 6 cm 2 /V-s

ee composite fermions at B * =0 single spin (high field) p-wave superconductor…. Moore-Read state bulkchiral edge modes predicted Majorana qp’s: localized in the bulk and propagating in chiral edge modes v = 5/2  2 + 1/2 R xx = 0 R xy quantized  energy gap charged quasiparticles v =5/2 FQHE state

v = n +1/2 ee composite fermions at B =0 =5/2 = 2+1/2 2020 2020 metal superconductor exotic phases p-wave superconductor R xx =0

expected charge of excitations JrJr  r Cooper pairs 

partitioning =5/2

particle-like (Laughlin) & hole-conjugate quasiparticles

hole-conjugate states

edge: single charge mode with G=G 0 /3 bulk: single component and gapped (incompressible liquid) ν x expected ν = 1/3 (particle-like)

ν = 2/3 = 1 – 1/3 full LL of electrons – 1/3 holes ν = 2/3 (hole-conjugate-like) upstream e/3 was not found….. upstream e/3 was not found….. Ashoori 1992

naive model 2-probe conductance = 4/3 e 2 /h neasured 2-probe conductance = 2/3 e 2 /h MacDonald’s clean edge

forming upstream neutral mode ν =2/3 ν = 2/3 lack of equilibration downstream downstream charge mode G=(2/3)G 0 + upstream neutral mode Kane et al. 1994

why study neutral modes ? predicted but was not measured before an added source of energy dissipation a possible source of quasiparticle dephasing

envisioning neutral modes… coherent (quantum) dipoles or classical heat wave… impinged at a partitioning barrier ( QPC ; non-ideal ohmic contact ) : dipoles may fragment leading to excess noise temperature may rise

neutral mode  ‘flow of dipoles’ shot noise (electron-hole) without net current

neutral mode  heating a QPC thermal noise without net current

excitation of neutral mode at ohmic contact qp injecting from source #2 looking for shot noise with zero net current 40  m downstream currentupstream current

upstream noise v =2/ A 2 /Hz  7mK t (1-t ) transmission of QPC

charge neutral qp excitation of neutral mode at QPC …

noise due to neutral mode T (1-T ) upstream noise v = 2/3

v = 5/2 ….. a few possible wave functions statestatisticschargeupstream neutral mode Moore-Read (Pfaffian) Moore & Read, Nuclear Phys. B (1991) non-abeliane/4no anti-Pfaffian Lee, PRL (2007); Levin et. al. PRL (2007) non-abeliane/4yes U(1)XSU(2) Wen, PRL (1991) non-abeliane/4no 331 Halperin, Helev. Phys. Acta (1983) abeliane/4no identifying wave function M.Dolev et. al., Nature 452, 829 (2008), P. Iuliana et. al., Science 320, 899(2008), V. Venkatachalam et. al., Nature 469, 182 (2008)

neutral mode at v = 5/2 ~t (1-t ) clear evidence of upstream neutral mode favors anti-Pfaffian wave function

status as of 2014…  upstream neutral modes in hole-conjugate states and in v =5/2  excitation when imbalance of Fermi energy  NO upstream net current  no neutral modes in the integer regime  no neutral modes in particle-like states  neutral modes decay at distance (~100  m)  neutral modes decay at temperature (~100mK)

since no sign of interference of qp’s in v =1/3… are particle-like states supporting also unobserved neutral edge modes?

downstream downstream shot noise 1 x cm -2 ; 5 x 10 6 cm 2 /V-sec upstream upstream noise at non-ideal ohmic contact repeating the experiments: > higher sensitivity noise measurements bulk > shorter distance of neutral mode propagation length > could we also have bulk contributions ?

upstream upstream noise (?) downstream downstream shot noise ~ t(1-t ) bulk edge edge bulk could we also have bulk contributions ?

edgebulk energy also propagates through the incompressible bulk ! however, most energy is carried by chiral upstream edge mode A 2 /Hz  7mK start with v = 2/3 25mK

A 2 /Hz = 1.4mK edgebulk v = 1/3 25mK about ~5 weaker than in v =2/3 qualitatively similar results obtained in v = 2/5, 4/3

x x ν = 1/5? an unexpected reconstruction forms at 1/3…

sharp - smooth edge ν x smoother edge ? ν x do we know the structure of v =2/3 ? Girvin, MacDonaldMeir 1994 PRL v =2/3 v =1/3 or, could it be ? initial evidence of thus reconstruction…

 upstream neutral modes in hole-conjugate states and in v =5/2  excitation when imbalance of Fermi energy  NO upstream net current  no neutral modes in the integer regime  no neutral modes in particle-like states  neutral modes decay fast with distance (~100  m)  neutral modes decay fast with temperature (~100mK)  neutral modes in the bulk nature of the modes is not clear (incoherent heat wave, coherent dipoles,…)

small edge velocity  extended duration in interferometer interaction with uncontrolled environment small edge velocity (small electric field)  level spacing < k B T built-in ‘which path’ detection via the ‘neutral modes’ increasing edge velocity………….sharpening the edge eliminating edge reconstruction somehow ? lack of interference of qp…..

thank you