$0\text{\ensuremath{-}}\ensuremath{\pi}$ phase transition in hybrid superconductor--InSb nanowire quantum dot devices

$0 − π$ phase transition in hybrid superconductor–InSb nanowire quantum dot devices

Sen Li, N. Kang, P. Caroff, and H. Q. Xu

Phys. Rev. B 95, 014515 – Published 20 January 2017

Abstract

Hybrid superconductor-semiconducting nanowire devices provide an ideal platform to investigating interesting intragap bound states, such as the Andreev bound states (ABSs), Yu-Shiba-Rusinov (YSR) states, and the Majorana bound states. The competition between Kondo correlations and superconductivity in Josephson quantum dot (QD) devices results in two different ground states and the occurrence of a $0 − π$ quantum phase transition. Here we report on transport measurements on hybrid superconductor–InSb nanowire QD devices with different device geometries. We demonstrate a realization of continuous gate-tunable ABSs with both 0-type levels and $π$ -type levels. This allow us to manipulate the transition between the 0 and $π$ junction and explore charge transport and spectrum in the vicinity of the quantum phase transition regime. Furthermore, we find a coexistence of 0-type ABS and $π$ -type ABS in the same charge state. By measuring temperature and magnetic field evolution of the ABSs, the different natures of the two sets of ABSs are verified, being consistent with the scenario of phase transition between the singlet and doublet ground state. Our study provides insight into Andreev transport properties of hybrid superconductor-QD devices and sheds light on the crossover behavior of the subgap spectrum in the vicinity of the $0 − π$ transition.

Received 14 February 2016
Revised 30 November 2016

DOI:https://doi.org/10.1103/PhysRevB.95.014515

Physics Subject Headings (PhySH)

Proximity effect Transport phenomena

Quantum dots Superconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Sen Li¹, N. Kang^1,*, P. Caroff^2,†, and H. Q. Xu^1,3,‡

¹Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics, Peking University, Beijing 100871, China
²I.E.M.N., UMR CNRS 8520, Avenue Poincaré, BP 60069, F-59652 Villeneuve d'Ascq, France
³Division of Solid State Physics, Lund University, Box 118, S-221 00 Lund, Sweden

^*Corresponding author: nkang@pku.edu.cn
^†Present address: Department of Electronic Materials Engineering, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia.
^‡Corresponding author: hqxu@pku.edu.cn

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Vol. 95, Iss. 1 — 1 January 2017

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Figure 1
Gate tuned ABSs in the NWQD-SQUID device. (a) SEM image of an InSb NWQD-SQUID device and schematic of the measurement configuration. The diameter of the nanowire is $\sim 80$ nm and the channel length of the nanowire is designed to be around 100 nm. (b) Schematic of tunneling processes in the NWQD-SQUID system. The alignment of the singularity of the hole(electron)like quasiparticle DOS of the probe with the electron (hole)-type Andreev bound states results in the main resonance peaks in the $d I / d V$ spectra. (c) Phase diagram of superconductor coupled QD system. $ξ_{d}$ represents the relative position of the chemical potential of the QD, $U$ is the charging energy of the QD, and $Γ_{s}$ is the coupling strength of the QD with superconducting leads. (d) Top panel: differential conductance $d I / d V$ plot as a function of $V_{s d}$ and $V_{g}$ at base temperature and zero magnetic field. The resonance features are labeled as $\circ$ for the main resonance of high conductance and $⋄$ for the weak conductance resonance. The letters e and o represents the even and odd charge number states, and blue or green arrows denote the ABSs in the charge state is $π$ type or 0 type, respectively. Bottom panel, zero-bias conductance $d I / d V$ over the same $V_{g}$ range. (e)–(g) Traces of the $d I / d V$ taken at $V_{g}$ values indicated by the colored dashed lines in (d), respectively. Inset of (g) is a current bias measurement at the same $V_{g}$ , revealing transport with a supercurrent in the device.
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Figure 2
Temperature evolution of different types of ABSs. (a,b) $d I / d V (V_{s d}, V_{g})$ for the odd charge state at $V_{g} ≃ - 1.0$ V measured at (a) base temperatures $T \sim 10$ mK and (b) $T \sim 700$ mK. (c,d) $d I / d V (V_{s d}, V_{g})$ for the odd charge state at $V_{g} ≃ - 1.35$ V measured at (c) base temperatures $T \sim 10$ mK and (d) $T \sim 700$ mK. The distance labeling in (b) and (d) indicates the energy spacing between the original ABS resonance and the thermally developed ABS is a constant $2 Δ$ , i.e., they are parallel.
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Figure 3
Characterization of the S-NWQD-S device in normal and superconducting state. (a) Normal-state differential conductance $d I / d V (V_{s d}, V_{g})$ measured for a two terminal S-NWQD-S device (D2) with $L \sim 65$ nm in contact separation and $D \sim 90$ nm in nanowire diameter at $T = 10$ mK and $B = 50$ mT. (b) Low-bias differential conductance $d I / d V (V_{s d}, V_{g})$ measured at $B = 0$ of the charge state corresponding to the diamond region around $V_{g} \sim - 1.5$ V shown in (a). The black and green dashed curves are guides for the two different types of ABSs resonances. (c) $d I / d V (V_{s d})$ curves at selected $V_{g}$ . The blue (orange) curve corresponds to the blue (orange) dashed line cut in panel (b). The black (green) arrows refer to the resonances denoting the $π (0)$ -type ABSs. A shoulder structure at around $| V_{s d} | \sim 150 μ eV$ originates from the first-order multiple Andreev reflection. Inset: schematics of the model of our S-NWQD-S system. The red bars represent the weakly coupled QD level (thin) and the strongly coupled QD level (thick) which are both involved in the transport processes. (d) Normal-state $d I / d V (V_{s d})$ trace taken at the grey dashed line cut in panel (a). The broad resonances at low bias are indicated by orange arrows and the sharp resonance at high bias is indicated by the black arrow. (e) Normal-state $d I / d V (V_{g})$ trace for the S-NWQD-S device at $V_{s d} = 0$ . A quick transition of transport from a Coulomb blockade regime to an open regime can be recognized from the curve.
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Figure 4
Temperature evolution of the differential conductance in the Kondo valley. (a) $d I / d V (V_{s d})$ curves measured at increasing temperatures from 10 mK to 1 K at $B = 0$ , taken at $V_{g} = - 1.49$ V denoted by the blue dashed line cut in Fig. 3. A zero-bias conductance peak can be identified from above $T = 400$ mK and vanishes at the critical temperature $T = 1$ K. Curves are successively offset upward by $0.05 e^{2} / h$ for clarity. (b) 2D plot of $d I / d V$ vs $V_{s d}$ and $T$ . (c) Schematic of the formation of the zero-bias conductance peak resulting from the ABS-assisted resonant tunneling of the thermally excited quasiparticles. (d) Normalized zero-bias conductances $G_{0} / G_{N}$ vs $T_{K} / Δ$ obtained from traces in (a), where $G_{0}$ is the zero-bias conductance and $G_{N}$ is the normal-state conductance at high bias. (e) Schematic phase diagram for the singlet-doublet transition as a function of $Δ / Γ$ and $U / Γ$ .
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Figure 5
Magnetic field evolution of the differential conductance in the Kondo valley. (a) 2D plot of $d I / d V (V_{s d}, B)$ measured at $V_{g} = - 1.49$ V denoted by the blue dashed line cut in Fig. 3. A weak splitting in the 0-type ABS resonances is observed at $B \sim 14$ mT, indicated by a pair of black arrows. (b) The $d I / d V (V_{s d})$ trace taken at $B = 14$ mT. A split double peak can be seen on top of each 0-type ABS resonance. The spacing between the double peaks is denoted by $Δ E$ , which is expected to be equal to the Zeeman energy $E_{Z}$ . Upper left inset: schematic of the splitting of the 0-type ABS. For a singlet ( $| S 〉$ ) ground state and a doublet ( $| D 〉$ ) excited state, the ABS will split under a magnetic field due to the Zeeman splitting of the doublet excited state. Lower right inset: schematic of the energy change of the $π$ -type ABS. Due to the Zeeman-splitting of doublet ground state, the energy of the ABS will increase.
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Physical Review B

covering condensed matter and materials physics

$0 − π$ phase transition in hybrid superconductor–InSb nanowire quantum dot devices

Sen Li, N. Kang, P. Caroff, and H. Q. Xu

Phys. Rev. B 95, 014515 – Published 20 January 2017

Abstract

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Physical Review B

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0−π phase transition in hybrid superconductor–InSb nanowire quantum dot devices

Sen Li, N. Kang, P. Caroff, and H. Q. Xu

Phys. Rev. B 95, 014515 – Published 20 January 2017

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$0 − π$ phase transition in hybrid superconductor–InSb nanowire quantum dot devices