The quantum Hall effect takes place in a two-dimensional electron gas under a strong magnetic field and involves current flow along the edges of the sample. For some particle–hole conjugate states of the fractional regime (for example, with fillings between 1/2 and 1 of the lowest Landau level), early predictions suggested the presence of counter-propagating edge currents in addition to the expected ones. When this did not agree with the measured conductance, it was suggested that disorder and interactions will lead to counter-propagating modes that carry only energy—the so called neutral modes. In addition, a neutral upstream mode (the Majorana mode) was expected for selected wavefunctions proposed for the even-denominator filling 5/2. Here we report the direct observation of counter-propagating neutral modes for fillings of 2/3, 3/5 and 5/2. The basis of our approach is that, if such modes impinge on a narrow constriction, the neutral quasiparticles will be partly reflected and fragmented into charge carriers, which can be detected through shot noise measurements. We find that the resultant shot noise is proportional to the injected current. Moreover, when we simultaneously inject a charge mode, the presence of the neutral mode was found to significantly affect the Fano factor and the temperature of the backscattered charge mode. In particular, such observations for filling 5/2 may single out the non-Abelian wavefunctions for the state.
Figures at a glance
Figure 1: The experimental set-up for measuring the neutral mode. 
The orange pads are ohmic contacts. The green pads form the split-gate of the QPC constriction, with Vg controlling the transmission probability t (or the reflection r = 1 − t). The grounded contacts are directly connected to the cold finger of the dilution refrigerator. Excitation current is driven to the sources via a d.c. voltage V and a large resistor in series. The a.c. signal, tuned to the LC resonance frequency (f0 = 770 kHz), is used to measure the two-terminal differential conductance. Blue lines describe the downstream charge edge modes, while red lines stand for the upstream neutral edge modes. Note that owing to the multi-terminal configuration the ‘current noise’ of the preamplifier (injected backwards from the preamplifier’s input into the sample) and the measured thermal noise (measured with 10-kHz resolution bandwidth around f0) were both independent of t (ref. 18). The cryogenic preamplifier’s ‘current noise’ was ~13.6 fA Hz−1/2 and its ‘voltage noise’ was 680 pV Hz−1/2, both referred to its input.
Figure 2: Detection of the neutral mode at vb = 2/3. 
Shown is excess noise measured at the voltage probe as a function of driven current In via source 2, for different transmission probabilities t of the QPC constriction. The noise is proportional to In and approximately to t(1 − t), vanishing for t = 1 or t = 0. Horizontal arrows indicate ΔVn = 39 μV for ΔIn = 1 nA; vertical arrows indicate ΔT = 2 mK, calculated via ΔSi = 4kBg2/3ΔT.
Figure 3: The effect of impinging the neutral mode simultaneously with the charge mode on the QPC constriction at vb = 2/3. 
a, The conductance and total noise as a function of source 1 current Is for different In. The change in the nonlinear transmission probability as In increases is negligible. The excess noise increases, the partitioned quasiparticle charge diminishes, and the temperature of the quasiparticles increases as In increases. b, Charge evolution as a function of In. The charge starts at e* = 2e/3 and drops to e* = 0.4e. c, Temperature evolution of the partitioned quasiparticles as a function of In. The temperature, fitted from a, increases by approximately 15–25 mK at In = 2 nA. Error bars show ±1 s.d. ( = ±4 mK). d, The dependence of the quasiparticle charge on temperature28.
Figure 4: Measurements at fractional state vb = 2/5. 
a, Injecting only In, with two different transmissions of the QPC constriction, did not result in any excess shot noise. b, Similarly, injecting both In and Is (and plotting the excess noise as a function of Is at two different transmissions) did not have any effect on the excess noise.
Figure 5: Testing for the existence of the neutral mode at vb = 3/5. 
a, Excess noise as a function of injecting In—direct evidence of an upstream neutral mode. b, The dependence of the nonlinear conductance as a function of Is on the presence of In. The relative change is small, amounting to a fraction of a per cent. c, The dependence of the excess noise as a function of Is on the presence of In. The noise increases, the quasiparticle charge drops, and the temperature of the quasiparticles increases. d, The dependence of the quasiparticle charge on In (extracted from c).
Figure 6: Testing for the existence of the neutral mode at vb = 5/2. 
The 2DEG used for these measurements was embedded in a 30-nm-wide quantum well, which was doped on both sides, buried approximately 160 nm below the surface of the heterostructure. The carrier density was 3 × 1011 cm−2 and the low temperature dark mobility was >3 × 107cm2 V−1 s−1. a, Excess noise as a function of injecting In provides direct evidence of an upstream neutral mode. b, The dependence of the nonlinear conductance as a function of Is on the presence of In. The relative change in the transmission is very small, amounting to
1%. As 80% of the total current flows in the two underlying edge channels (ν = 1 and ν = 2), the effective transmission is about 77%. c, The dependence of the excess noise as a function of Is on the presence of In. d, The dependence of the quasiparticle charge on In (extracted from c). The charge drops from e* ≈ 0.75e to e* ≈ 0.32e. By limiting the temperature to 50 mK while fitting the charge we estimated the error in the charge (error bars, ±1 s.d.).
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