Observation of quantum Hall interferometer phase jumps due to a change in the number of bulk quasiparticles

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Observation of quantum Hall interferometer phase jumps due to a change in the number of bulk quasiparticles

Marc P. Röösli, Lars Brem, Benedikt Kratochwil, Giorgio Nicolí, Beat A. Braem, Szymon Hennel, Peter Märki, Matthias Berl, Christian Reichl, Werner Wegscheider, Klaus Ensslin, Thomas Ihn, and Bernd Rosenow

Phys. Rev. B 101, 125302 – Published 9 March 2020

Abstract

We measure the magnetoconductance through a micron-sized quantum dot hosting about 500 electrons in the quantum Hall regime. In the Coulomb blockade, when the island is weakly coupled to source and drain contacts, edge reconstruction at filling factors between 1 and 2 in the dot leads to the formation of two compressible regions tunnel coupled via an incompressible region of filling factor $ν = 1$ . We interpret the resulting conductance pattern in terms of a phase diagram of stable charge in the two compressible regions. Increasing the coupling of the dot to source and drain, we realize a Fabry-Pérot quantum Hall interferometer, which shows an interference pattern strikingly similar to the phase diagram in the Coulomb blockade regime. We interpret this experimental finding using an empirical model adapted from the Coulomb-blockaded to the interferometer case. The model allows us to relate the observed abrupt jumps of the Fabry-Pérot interferometer phase to a change in the number of bulk quasiparticles. This opens up an avenue for the investigation of phase shifts due to (fractional) charge redistributions in future experiments on similar devices.

Received 25 October 2019
Revised 28 January 2020
Accepted 12 February 2020

DOI:https://doi.org/10.1103/PhysRevB.101.125302

Physics Subject Headings (PhySH)

Aharonov-Bohm effect Coulomb blockade Electrical conductivity Quantum Hall effect

III-V semiconductors Quantum dots Two-dimensional electron gas

Dilution refrigerator Fabry-Pérot interferometry Hall bar Luttinger liquid model Thomas–Fermi model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Marc P. Röösli ^*, Lars Brem , Benedikt Kratochwil, Giorgio Nicolí , Beat A. Braem , Szymon Hennel, Peter Märki , Matthias Berl, Christian Reichl, Werner Wegscheider, Klaus Ensslin, and Thomas Ihn

Solid State Physics Laboratory, Department of Physics, ETH Zurich, 8093 Zurich, Switzerland

Bernd Rosenow

Institute for Theoretical Physics, Leipzig University, Leipzig D-04103, Germany

^*marcro@phys.ethz.ch

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Vol. 101, Iss. 12 — 15 March 2020

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Images

Figure 1
(a) Scanning electron micrograph of the quantum dot (QD) device before evaporation of the second top gate layer. The top gates appear in light gray, the uncovered AlGaAs/GaAs heterostructure in dark gray. A magnetic field $B$ is applied perpendicular to the sample surface. The added schematic shows compressible edge regions (blue) for a filling factor $ν_{b} \approx 2$ , the arrangement of Ohmic contacts, the applied source-drain voltage $V_{SD}$ , and the measured voltages $V_{x x}, V_{x y}$ (bulk), and $V_{long}, V_{diag}$ (across the QD). In addition, we measure the current $I_{SD}$ . (b) Longitudinal and transverse resistances $R_{x x} = V_{x x} / I_{SD}$ and $R_{x y} = V_{x y} / I_{SD}$ across the bulk (dark blue and dark green) with all gate voltages at zero, compared to $R_{long} = V_{long} / I_{SD}$ and $R_{diag} = V_{diag} / I_{SD}$ measured with all gates energized except RB and LB. (c) Conductance $G_{diag} = I_{SD} / V_{diag}$ as a function of $V_{LB}$ and $V_{RB}$ at $B = 2.8 T$ ( $ν_{b} \approx 1.9$ ). Blue points indicate gate voltage settings, where later measurements in Fig. 6 are taken. (d) and (e): Line cuts of panel (c) with conductance $G_{diag}$ vs $V_{LB}$ or $V_{RB}$ , with the respective other barrier gate transmitting the quantized conductance $e^{2} / h$ .
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Figure 2
(a) Conductance of the QD as a function of the plunger gate voltage and the perpendicular magnetic field. (b) Close-up of (a) for a smaller range in magnetic field interpreted as a charge stability diagram (CSD). The lines separate regions of constant charge $(N_{1}, N_{2})$ , where $N_{1}$ and $N_{2}$ correspond to the electron number in the outer and inner compressible region, respectively. Three different transitions are indicated. (c) Coulomb diamond at $ν_{b} \approx 2$ showing the current through the QD on a logarithmic scale (sign-conserving, cut off at $\pm 10 fA$ ) as a function of the plunger gate voltage and the applied bias voltage.
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Figure 3
(a) Conductance around filling factor $ν_{b} \approx 2$ as a function of the plunger gate voltage converted to energy measured for different electron temperatures $T_{e}$ . Solid lines denote fits according to Eq. (4). (b) Conductance peak height $G_{0}$ as a function of inverse electron temperature $1 / T_{e}$ for two different coupling strengths of the QD to the leads. The lines correspond to least-squares fits of the expected linear dependence yielding the effective dot-lead coupling $Γ_{cl}$ .
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Figure 4
(a)–(e) QD operated in the strong Coulomb blockade regime. Conductance $G$ through the QD plotted as a function of plunger gate voltage and magnetic field for different magnetic field ranges between filling factor $2 > ν_{b} > 1$ . (f)–(k) QD operated as an interferometer with the barriers transmitting one edge channel ( $t_{barrier} \approx 0.9$ ). Conductance $G_{diag}$ measured from the transverse voltage across the QD [ $V_{diag}$ ; see Fig. 1] shown as a function of plunger gate voltage and magnetic field for the same magnetic field ranges as in (a)–(e).
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Figure 5
Logarithm of the conductance through the QD as a function of plunger gate voltage and magnetic field. Dashed lines indicate the trend of the resonances. Around $4.22 T$ the upper Landau level becomes completely depopulated.
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Figure 6
(a)–(f) QD operation continuously changed from interferometer to strongly Coulomb-blockaded QD. Conductance $G_{diag}$ shown as a function of plunger gate voltage and magnetic field for different, decreasing transmission of the left and right barrier ( $t_{L}, t_{R}$ ) corresponding to set points of the barrier voltages $V_{LB}, V_{RB}$ indicated in Figs. 1–1. The classical transmission value $t$ is calculated according to Eq. (6) and the color scale is chosen around the classical value $t$ (white) for each plot.
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