Charge Fractionalization in the Integer Quantum Hall Effect

Hiroyuki Inoue, Anna Grivnin, Nissim Ofek, Izhar Neder, Moty Heiblum, Vladimir Umansky, and Diana Mahalu

Phys. Rev. Lett. 112, 166801 – Published 25 April 2014; Erratum Phys. Rev. Lett. 112, 189902 (2014)

Abstract

We report an observation, via sensitive shot noise measurements, of charge fractionalization of chiral edge electrons in the integer quantum Hall effect regime. Such fractionalization results solely from interchannel Coulomb interaction, leading electrons to decompose to excitations carrying fractional charges. The experiment was performed by guiding a partitioned current carrying edge channel in proximity to another unbiased edge channel, leading to shot noise in the unbiased edge channel without net current, which exhibited an unconventional dependence on the partitioning. The determination of the fractional excitations, as well as the relative velocities of the two original (prior to the interaction) channels, relied on a recent theory pertaining to this measurement. Our result exemplifies the correlated nature of multiple chiral edge channels in the integer quantum Hall effect regime.

Received 14 January 2014
Corrected 29 April 2014

DOI:https://doi.org/10.1103/PhysRevLett.112.166801

Corrections

29 April 2014

Erratum

Publisher’s Note: Charge Fractionalization in the Integer Quantum Hall Effect [Phys. Rev. Lett. 112, 166801 (2014)]

Hiroyuki Inoue, Anna Grivnin, Nissim Ofek, Izhar Neder, Moty Heiblum, Vladimir Umansky, and Diana Mahalu

Phys. Rev. Lett. 112, 189902 (2014)

Authors & Affiliations

Hiroyuki Inoue¹, Anna Grivnin¹, Nissim Ofek², Izhar Neder³, Moty Heiblum¹, Vladimir Umansky¹, and Diana Mahalu¹

¹Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, 79100 Rehovot, Israel
²Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
³Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, 69978 Tel Aviv, Israel

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Vol. 112, Iss. 16 — 25 April 2014

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Images

Figure 1
(a) An ordered train of electrons driven from the source (S) transmit the QPC1 with a probability $T_{1}$ and decompose into fast and slow modes. The fast mode consists of fractional charges $α e (β e)$ on channel 1 (2) and the slow mode consists of fractional charges $(1 - α) e$ , ( $- β e$ ) on channel 1 (2). The pairs of $\pm β e$ are partitioned at QPC2 with a transmission probability $T_{2}$ , generating a low-frequency shot noise to be detected at the amplifier (A). (b) A SEM image of the employed device. Below, a magnified view of the core part. The region between the QPCs is the interaction region ( $l = 8 μ m$ ). (c) Configuration 1 ( $C 1$ ). S1 and A1 were employed. The red and the blue arrows are the hot and cold channels. The biased outer channel is the channel 1 (hot channel) here. QPC1 fully reflects the inner channel while partitions the outer channel (dotted heavy red line). Two cold edge channels, emanating from the G contacts, also impinge at QPC1 (thin blue lines), where the outer is fully transmitted and the inner fully reflected. The reflected cold channel (thick blue line) flows in close proximity to the partitioned outer channel, with both reaching QPC2. There, the outer channel is fully transmitted and inner one is being partitioned by half (dotted thick blue line), with its excess current noise (spectral density, $S_{i}$ ) monitored at A1. (d) Configuration 2 ( $C 2$ ). S2 and A2 were employed. The biased inner channel is the hot channel here. $T_{1}$ was set to half-transmitting for the inner channel and the reflected part was directed to QPC2 with various $T_{2}$ to partition the fluctuating cold outer channel.
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Figure 2
(a) Reproduced figure of Ref. [33]. The Fano factor $F = S_{i} / S_{r e f}$ ( $S_{r e f} = 4 e I T_{1} R_{1} R_{2}$ with $R_{2} \to 0$ ) representing the fractional charge in the cold channel ( $e^{*} = F e$ ), plotted as function of the mixing angle. The black dots are values evaluated by the theory ( $T_{1} = 0.5$ , $R_{2} ≪ 1$ ) and the solid curve depicts $β = (\sin θ) / 2$ based on the simple model in the present paper. (b) The exponent $γ_{1}$ plotted as function of the mixing angle $θ$ based on the numerical computation. The experimentally obtained $γ_{1} = 0.71 \pm 0.01$ yields $θ = π / 3.2 - π / 3.7$ , the ratio $u / Δ v = 1.1 - 1.5$ , and a Fano factor $F = 0.41 - 0.46$ . Applying it to the simple model, are $β = 0.38 - 0.41$ and $α = 0.78 - 0.83$ . The blue blurred lines represents the best fit with the error of $1.2 σ$ based on obtained exponent $γ_{1}$ .
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Figure 3
(a) The excess noise traces (in $C 1$ ) as a function of $I$ for various $T_{1}$ with fixed $T_{2} = 0.5$ and selected traces are shown. (b) Relative magnitude of the excess noise as a function of $T_{1}$ , normalized to the one at $T_{1} = 0.5$ . The excess noise is proportional to $[T_{1} (1 - T_{1})]^{γ_{1}}$ , where $γ_{1} = 0.71 \pm 0.08$ with the error of $2 σ$ , which reduces to $γ_{1} = 0.71 \pm 0.01$ for $1.2 σ$ . Curves with $γ_{1} = 0.5$ and 1.0 are also plotted.
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Figure 4
(a) The excess noise traces (in $C 2$ ) as a function of $I$ for selected $T_{2}$ (with $T_{1} = 0.5$ ) are shown. The linear part of the trace of $T_{2} = 0.90$ was exploited to extract the Fano factor $F = 0.38 \pm 0.02$ . (b) Relative magnitude of the excess noise as a function of $T_{2}$ , normalized to the one at $T_{2} = 0.5$ , is plotted. The excess noise is proportional to $[T_{1} (1 - T_{1})]^{γ_{1}}$ , where $γ_{2} = 0.97 \pm 0.02$ for the error of $1.2 σ$ . A dashed curve with $γ_{2} = 0.5$ is plotted. The inset depicts the Fano factor evaluated with the extended reference noise $S_{r e f} = 4 e T_{1} R_{1} T_{2} R_{2}$ at all the employed $T_{2}$ .
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