Nanoscale Mach-Zehnder interferometer with spin-resolved quantum Hall edge states

Biswajit Karmakar, Davide Venturelli, Luca Chirolli, Vittorio Giovannetti, Rosario Fazio, Stefano Roddaro, Loren N. Pfeiffer, Ken W. West, Fabio Taddei, and Vittorio Pellegrini

Phys. Rev. B 92, 195303 – Published 3 November 2015

Abstract

We realize a nanoscale-area Mach-Zehnder interferometer with co-propagating quantum Hall spin-resolved edge states and demonstrate the persistence of gate-controlled quantum interference oscillations, as a function of an applied magnetic field, at relatively large temperatures. Arrays of top-gate magnetic nanofingers are used to induce a resonant charge transfer between the pair of spin-resolved edge states. To account for the pattern of oscillations measured as a function of magnetic field and gate voltage, we have developed a simple theoretical model which satisfactorily reproduces the data.

Received 15 September 2015

DOI:https://doi.org/10.1103/PhysRevB.92.195303

Authors & Affiliations

Biswajit Karmakar^1,2, Davide Venturelli^3,4, Luca Chirolli⁵, Vittorio Giovannetti², Rosario Fazio^2,6, Stefano Roddaro⁷, Loren N. Pfeiffer⁸, Ken W. West⁸, Fabio Taddei⁷, and Vittorio Pellegrini^7,9

¹Saha Institute of Nuclear Physics, I/AF Bidhannagar, Kolkata 700 064, India
²NEST, Scuola Normale Superiore, and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
³NASA Ames Research Center Quantum Artificial Intelligence Laboratory (QuAIL), Mail Stop 269-1, Moffett Field, California 94035, USA
⁴USRA Research Institute for Advanced Computer Science (RIACS), 615 National, Mountain View, California 94043, USA
⁵IMDEA Nanoscience, Calle de Faraday 9, E-28049 Madrid, Spain
⁶ICTP, Strada Costiera 11, I-34151 Trieste, Italy
⁷NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56126 Pisa, Italy
⁸School of Engineering and Applied Science, Princeton University, Princeton, New Jersey, USA
⁹Istituto Italiano di Tecnologia, Graphene Labs, Via Morego 30, I-16163 Genova, Italy

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Vol. 92, Iss. 19 — 15 November 2015

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Images

Figure 1
(a) Schematic setup of quantum interference device with separately contacted co-propagating SRESs (red and green lines) at filling factor $ν = 2$ . G1, G2, and G denote gates and F1 and F2 denote magnetic nanofingers. (b) SEM shows the two arrays of magnetic nanofingers F1 and F2 and the metal gate G. Red and green lines schematically represent spin-up and spin-down SRESs at the boundary of the mesa. (c) G1 gate bias dependence of output current shows the working point (black arrow) of 0.1 V, where input edge channels are separately contacted. In this measurement the output edge channels are separately contacted by applying $V_{G2} = 0.1$ V and the mixing of SRESs is deactivated by applying the following voltage biases on the nanofingers $V_{F1} = V_{F2} = - 2$ V. Red, green, and maroon lines represent spin up, spin down channel current, and total current respectively. (d) F1 fringe bias dependence of magnetic coupling of SRESs shows the working point (black arrow) at $V_{F 1} = 0.09$ V, while $V_{F 2}$ is kept at $- 2$ V. (e) F2 fringe bias dependence of magnetic coupling of SRESs shows the working point (black arrow) at $V_{F 2} = 0.09$ V, while $V_{F 1}$ is kept at $- 2$ V.
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Figure 2
(a) Transmitted spin-up current $I_{↑}$ as a function of the magnetic field $B$ within the $ν = 2$ plateau for different temperatures. Gate voltages are set as follows: $V_{G} = 0.35$ V, $V_{F 1} = V_{F 2} = 0.09$ V. Interference oscillations weaken with increasing temperature $T$ . (b) Fast Fourier transform of the oscillations of the current measured at 250 mK: the peak corresponds to the frequency $f = 13.6 \pm 0.6 T^{- 1}$ . (c) The visibility of the oscillations, plotted as a function of temperature, decreases from 10% at 250 mK to 0 at 750 mK.
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Figure 3
(a) Color plot of the measured spin-up current $I_{↑}$ showing the modulation through $V_{G}$ of the interference oscillations in $B$ . (b) Color plot of the transmission probability for spin-up electrons calculated through a model which takes into account the “cross-talk” effect of the voltage $V_{G}$ on the transmission properties of the arrays of nanofingers, and reproduces the discontinuous features. (c) Frequency of AB oscillations (left axis) and AB loop area (right axis) as a function of gate voltage $V_{G}$ .
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Figure 4
Sketch of the MZ interferometer. Electrode I is biased at voltage $V$ , while electrode II is grounded.
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Figure 5
Cross-talk effect: the gates F1 and F2 not only affects locally the strength of the coupling between SRESs, but also change the area $A$ of the interference loop. Spin-up current $I_{↑}$ as a function of the magnetic field $B$ within the $ν = 2$ plateau for fixed $V_{G} = 0.35$ V and different values of gate voltages $V_{F1}$ and $V_{F2}$ . Data are taken at 250 mK.
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