$h/e$ Superconducting Quantum Interference through Trivial Edge States in InAs

$h / e$ Superconducting Quantum Interference through Trivial Edge States in InAs

Folkert K. de Vries, Tom Timmerman, Viacheslav P. Ostroukh, Jasper van Veen, Arjan J. A. Beukman, Fanming Qu, Michael Wimmer, Binh-Minh Nguyen, Andrey A. Kiselev, Wei Yi, Marko Sokolich, Michael J. Manfra, Charles M. Marcus, and Leo P. Kouwenhoven

Phys. Rev. Lett. 120, 047702 – Published 26 January 2018

Abstract

Josephson junctions defined in strong spin orbit semiconductors are highly interesting for the search for topological systems. However, next to topological edge states that emerge in a sufficient magnetic field, trivial edge states can also occur. We study the trivial edge states with superconducting quantum interference measurements on nontopological InAs Josephson junctions. We observe a SQUID pattern, an indication of superconducting edge transport. Also, a remarkable $h / e$ SQUID signal is observed that, as we find, stems from crossed Andreev states.

Received 12 September 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.047702

Physics Subject Headings (PhySH)

Andreev reflection Ballistic transport Edge states Josephson effect Mesoscopics Quantum interference effects Semiconductors Superconductivity

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Folkert K. de Vries¹, Tom Timmerman¹, Viacheslav P. Ostroukh², Jasper van Veen¹, Arjan J. A. Beukman¹, Fanming Qu¹, Michael Wimmer¹, Binh-Minh Nguyen³, Andrey A. Kiselev³, Wei Yi³, Marko Sokolich³, Michael J. Manfra⁴, Charles M. Marcus⁵, and Leo P. Kouwenhoven^1,6,*

¹QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
²Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
³HRL Laboratories, 3011 Malibu Canyon Road, Malibu, California 90265, USA
⁴Department of Physics and Astronomy and Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA
⁵Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
⁶Microsoft Station Q Delft, 2600 GA Delft, The Netherlands

^*l.p.kouwenhoven@tudelft.nl

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Vol. 120, Iss. 4 — 26 January 2018

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Images

Figure 1
(a) Sketch of the conduction band minimum around the edge of a 2DEG with Fermi level pinning at $W / 2$ . The band bending leads to a roughly triangular quantum well in the vicinity of the edge; therefore, one-dimensional subbands form, of which three are drawn, as an example. The orange dashed line indicates the Fermi level corresponding to the current distribution in (e). (b) False colored SEM image of the device with dimensions $W = 4 μ m$ and $L = 500 nm$ , where the quasifour terminal measurement setup is added. Red is the mesa, green the NbTiN contacts, blue ${SiN}_{x}$ dielectric, and yellow the gold top gate. (c) Schematic representation of a Josephson junction of width $W$ and length $L$ . A homogeneously distributed supercurrent $I_{sc}$ is running through the whole junction, resulting in (d) a Fraunhofer SQI pattern. (e) If the supercurrent only flows along the edges of the sample, (f) a SQUID pattern is observed.
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Figure 2
(a) Normal state resistance $R_{n}$ and switching current $I_{s}$ at the respective top gate $V_{tg}$ and bottom gate $V_{bg}$ voltages. The left inset depicts a separate measurement at the indicated gate voltages, where a smaller current bias step size is used for higher resolution. The right inset shows an IV trace at $V_{tg} = 0 V$ and $V_{bg} = - 1.65 V$ , where two dashed lines are added for extraction of the induced superconducting gap $Δ$ and the excess current. (b) The measured voltage as function of the applied current $I_{bias}$ and perpendicular magnetic field $B$ at $V_{tg} = 0 V$ and $V_{bg} = - 1.65 V$ . The inset depicts the calculated supercurrent density along the width of the device that is indicated by the dotted lines.
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Figure 3
(a) The switching current plotted as a function of perpendicular magnetic field and (b) the corresponding current density along the width of the device (see inset), assuming the validity of the Dynes-Fulton approach. The gate values used are from bottom to top: $V_{tg} - 5.4 V$ to $- 3.6 V$ (0.2 V step) and $V_{bg} - 1.270 V$ to $- 1.396 V$ (0.014 V step). The green, blue, and orange traces are Fraunhofer, even-odd, and SQUID patterns, respectively. Since the current is only swept up to 100 nA, the green traces are not suitable for extracting a supercurrent density profile. The traces are offset by 50 nA in (a) and $25 nA / μ m$ in (b).
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Figure 4
(a) Measured voltage as a function of $I_{bias}$ and magnetic field $B$ at $V_{tg} = - 5 V$ and $V_{bg} = - 1.29 V$ . (b) Switching current versus the magnetic field for different temperatures at the same gate voltages as (a). The traces are offset by 5 nA for clarity. (c) Current density profile, calculated from the SQI pattern of (a) (see also Ref. [14]). The blue trace uses Eq. (1), thus correcting the vertical offset in the SQI pattern. The yellow dashed trace is extracted without this correction.
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Figure 5
(a) Schematic representation of two crossed Andreev processes. The black and white lines indicate electron and hole trajectories or vice versa. The solid lines represent a single edge Andreev state and the dotted lines a crossed Andreev state. (b) Detailed sketch of one corner of the junction in our tight binding mode indicating the widths $W_{ns}$ and $W_{e}$ , and tunnel barrier $Γ$ . (c) Calculated SQI patterns at overall chemical potential ranging from $- 0.06 e V$ to 0.18 eV (0.04 eV step) at 0.46 K and (d) at temperatures 0.4 K, 0.9 K, 1.4 K, 1.9 K, 2.3 K at a chemical potential of $- 0.2 e V$ . Traces are offset by 10 nA for clarity. In (c) the color represents the type of interference pattern, green for Fraunhofer, blue for even-odd, and orange for SQUID, respectively.
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