Behavior of superconductivity in a Pb/Ag heterostructure

Hyoungdo Nam, Chendong Zhang, Woojoo Lee, Siyuan Zhu, Hong-Jun Gao, Qian Niu, Gregory A. Fiete, and Chih-Kang Shih

Phys. Rev. B 100, 094512 – Published 6 September 2019

Abstract

The superconducting proximity effect is a long-standing topic of great importance in condensed matter physics. A crucial but unresolved issue is which interfacial and material details determine the efficiency of the proximity effect. In this paper, we study an epitaxially grown superconductor/normal metal (SC-NM) heterostructure (Pb/Ag) and find a spatially constant superconducting gap determined by local tunneling spectroscopy and magnetoresponse measurements, despite the highly mismatched Fermi surfaces between individual Pb and Ag epitaxial layers and the large differences in the lattice constants and electronic densities of states in the separate components. The uniform superconducting gap is in contrast to the spatially varying pair potential with a discontinuity at the interface theoretically predicted for an ideal SC-NM junction and experimentally observed previously in several lateral SC-NM junctions. We experimentally verify that the transmission of electrons across the interface in the vertical Pb/Ag heterostructure is high enough that a new band structure emerges even at the single-particle level. Our experimental results call for further theoretical work in order to develop predictive power for the proximity effect starting from realistic, materially relevant microscopic models.

Received 12 February 2018
Revised 11 July 2019

DOI:https://doi.org/10.1103/PhysRevB.100.094512

Physics Subject Headings (PhySH)

Proximity effect Superconducting gap Surface & interfacial phenomena

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Hyoungdo Nam¹, Chendong Zhang^1,2, Woojoo Lee¹, Siyuan Zhu¹, Hong-Jun Gao², Qian Niu¹, Gregory A. Fiete¹, and Chih-Kang Shih^1,*

¹Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
²Institute of Physics and University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100190, China

^*Corresponding author: shih@physics.utexas.edu

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Vol. 100, Iss. 9 — 1 September 2019

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Figure 1
Growth of the Pb/Ag heterostructure with an atomically sharp interface. (a, b) STM topography of 9-ML Ag/Si(111) 7 × 7 and 22-ML Pb on top of 7-ML Ag film, taken at 4.3 K with $V_{Sample} = 2 V$ . (c) ARPES spectrum on 14-ML Ag/Si(111) at $h v = 21.2$ eV, showing obvious QWS dispersions. (d) Tunneling spectroscopy on 22- (blue) and 23-ML (pink) Pb films grown on 7-ML Ag/Si. The peak locations of QWS are irrelevant to the thickness of the underlying Ag film. (See Supplemental Material [31] for details.)
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Figure 2
Thickness dependence of superconductor transition temperature. (a) In situ STS on 30-ML Pb/10-ML Ag/Si(111). (b) Temperature dependence of Δ( $T$ ), deduced from BCS QP-DOS fit to tunneling spectra in (a). Here, the BCS curve (dash) is drawn using $2 Δ_{0} / k_{B} T_{c} = 4.8$ . (c) Mutual inductance measurements on 30-ML Pb/10-ML Ag/Si(111). (d) On 10-ML Ag/Si, Pb-thickness dependence of $T_{c}$ . $T_{c, SCG}$ and $T_{c, SFD}$ are obtained by STS and SFD, respectively. (e) Transition temperature as a function of thickness ratio of $d_{Pb} / d_{Ag}$ for different thicknesses of underlying Ag films. The black solid line of $7.2 \times e^{- 0.87 \frac{d_{Ag}}{d_{Pb}}}$ is the fit based on an average pairing model [3].
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Figure 3
Inverse heterostructure and lateral SC-NM junction. (a) Mutual inductance measurement of 7-ML Ag on 21-ML Pb/Si(111). (b) Tunneling spectrum of 7-ML Ag/21-ML Pb (green square) at 2.2 K, compared with that of 30-ML Pb/10-ML Ag (blue rhombus) and BCS QP-DOSs (solid lines). Both heterostructures have the same thickness ratio of $L_{Pb} / L_{Ag} = 3$ . (For clarity, there is 0.5 offset.) $T_{c}$ in (a) is consistent with Fig. 2. Pb/Ag and its inverse heterostructures show the same Δ within the experimental error bar. (c) Comparison of $T_{c}$ as a function of $d_{Pb} / d_{Ag}$ for forward and reverse heterostructures. Here $T_{c}$ is deduced from measurements of $Δ$ vs $T$ . (d) Schematic of SC-NM junction and tunneling gap profile along the $z$ axis perpendicular to the interface. (e) Zero-bias conductance (ZBC) profile showing the discontinuous transition at the boundary between the 5-ML Pb island and the surrounding wetting layer as the theoretical description of (d).
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Figure 4
Single-particle electronic states of the Pb/Ag heterostructure. (a–c) ARPES spectra of a 9-ML Ag film on Si (a), an additional 10-ML Pb on top of 9-ML Ag (b), and a 10-ML Pb film on Si (c). (d) Spectra at $k = 0$ for Ag, Ag/Pb heterostructure, and Pb layers, respectively. (e) Schematic of the Pb/Ag heterostructure as a one-integral single-particle system crossing the Pb/Ag interface. (f) The model calculation of the QWS of (d) by using a 20/20-Å model heterostructure with free-electron-like states of $m_{Ag} = 0.4 m_{0}$ and $m_{Pb} = 1.0 m_{0}$ for Ag and Pb, respectively. This result captures the new QWS formation and pairing feature in (b), which come from the one single-particle electronic state of the Pb/Ag heterostructure. Note that in addition to the QWSs being observed one can see interference fringes between QWSs and downward hole-like dispersive Si states at the interface. Such features have been reported and discussed in detail by Speer et al. [28] for the Ag/Si case. Here we observed such interference fringes in cases of Pb/Ag/Si and Pb/Si. This provides additional evidence that Pb/Ag heterostructures form one coherent electronic system which also experiences the presence of Si states at the interface (just like the Ag QWSs).
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