Time-resolved charge fractionalization in inhomogeneous Luttinger liquids

Rapid Communication

Time-resolved charge fractionalization in inhomogeneous Luttinger liquids

E. Perfetto, G. Stefanucci, H. Kamata, and T. Fujisawa

Phys. Rev. B 89, 201413(R) – Published 29 May 2014

Abstract

The recent observation of charge fractionalization in single Tomanga-Luttinger liquids (TLLs) [H. Kamata et al., Nat. Nanotechnol. 9, 177 (2014)] opens new routes for a systematic investigation of this exotic quantum phenomenon. In this Rapid Communication we perform measurements on two adjacent TLLs and put forward an accurate theoretical framework to address the experiments. The theory is based on the plasmon scattering approach and can deal with injected charge pulses of arbitrary shape in TLL regions. We accurately reproduce and interpret the time-resolved multiple fractionalization events in both single and double TLLs. The effect of intercorrelations between the two TLLs is also discussed.

Received 12 March 2014

DOI:https://doi.org/10.1103/PhysRevB.89.201413

Authors & Affiliations

E. Perfetto and G. Stefanucci

Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Rome, Italy; INFN, Laboratori Nazionali di Frascati, Via E. Fermi 40, 00044 Frascati, Italy; and European Theoretical Spectroscopy Facility (ETSF)

H. Kamata and T. Fujisawa

Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo 152-8551, Japan

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Issue

Vol. 89, Iss. 20 — 15 May 2014

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Images

Figure 1
Optical micrograph of the sample (the horizontal white line indicates that unused parts are not shown). Metal gate electrodes (gold regions) are patterned on a 2DES (light-gray region) and etched insulating GaAs (dark-gray regions). The 2DES located $90 nm$ below the surface has a density of $1.45 \times 10^{11} {cm}^{- 2}$ and a low-temperature mobility of $4.0 \times 10^{5} {cm}^{2} V^{- 1} s^{- 1}$ . Chiral one-dimensional edge channels are formed along the edge of the 2DES in a strong perpendicular magnetic field $B = 4.0 T$ , which corresponds to a bulk filling factor $ν = 1.5$ . Type-I and type-II TLL regions have an effective length of $ℓ_{1} = 68$ and $ℓ_{2} = 80 μ m$ , respectively, and a width of $1 μ m$ . The charge wave packet is injected at the falling edge of a voltage step $5 mV$ in amplitude applied to an injection gate $V_{inj}$ . The QPC detector is set at the pinched-off regime, and one of the gate voltages is modulated by a voltage pulse $V_{\det}$ of height $0.2 V$ for a period of $80 ps$ to temporally enhance the transmission probability of the QPC. The average current $I$ through the QPC as a function of time interval $t$ between two voltage pulses is measured at the detection Ohmic contact $Ω_{\det}$ under the pulse pattern repeated at $25 MHz$ . All measurements were carried out at $\sim 300 mK$ .
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Figure 2
Model of the experimental setup. The wave packet is injected from the $R$ edge (dashed circle). The figure shows a snapshot of the fractionalized charge when the injected wave packet has passed the TLL region. Transmitted packets are dark (blue) and reflected packets are light (red). Type-I geometry (a): $R$ and $L$ edges with NI regions for $x < 0$ and $x > ℓ$ , and activated TLL region for $0 < x < ℓ$ . Type-II geometry (b): A single bent edge with NI regions for $x < 0$ , and activated TLL region for $0 < x < ℓ$ .
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Figure 3
Type-I geometry: Calculated current (black curve) from Eqs. (8) and (9) versus measured current (dotted-red curve) from Ref. [22]. The inset shows the incident wave form $v ρ^{(inc)}$ .
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Figure 4
Type-II geometry: Calculated current (black curve) from Eqs. (8) and (11) versus measured current (dotted-red curve) from Ref. [22].
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Figure 5
Measured current (dotted-red curve) from TLL-I when both TLL-I and TLL-II are activated versus calculated current with $g = 0.92$ (black dashed curve) and $g = 0.87$ (black solid curve). The inset shows a cartoon of the fractionalization process. The velocities in TLL-I and TLL-II are different (with $V_{G 1} = - 0.19 V$ and $V_{G 2} = - 1.4 V$ ) in order to isolate four fractionalized wave packets.
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