LETTERS PUBLISHED ONLINE: 31 AUGUST 2014 | DOI: 10.1038/NPHYS3049 Gate-tunable superconducting weak link and quantum point contact spectroscopy on a strontium titanate surface Patrick Gallagher, Menyoung Lee, James R. Williams and David Goldhaber-Gordon* Two-dimensional electron systems in gallium arsenide and state4. To modulate the density on this scale, we use the electric graphene have enabled ground-breaking discoveries in double-layer transistor technique4–7. A schematic of our sample is condensed-matter physics, in part because they are easily shown in Fig.1 a. A single crystal of TiO2-terminated (100) SrTiO3 modulated by voltages on nanopatterned gate electrodes. is patterned with ohmic contacts and a narrow metal top gate Electron systems at oxide interfaces hold a similarly large separated from the STO surface by a 5 nm alumina layer (Fig.1 b potential for fundamental studies of correlated electrons and and Methods). The sample is covered in ionic liquid, which is novel device technologies1–3, but typically have carrier densities polarized by an electrode (not shown) to induce a 2D electron too large to control by conventional gating techniques. Here layer at the exposed STO surface; the area below the top gate we present a quantum transport study of a superconducting remains insulating, because the gate screens the ions. The polarized strontium titanate (STO) interface, enabled by a combination sample is cooled to base temperature in a dilution refrigerator, of electrolyte4–7 and metal-oxide gating. Our structure consists freezing the ionic liquid and thus fixing the electron density in the of two superconducting STO banks flanking a nanoscale STO exposed STO regions. The voltage on the top gate is then modulated weak link, which is tunable at low temperatures from insulating to control transmission across the device, and conductance to superconducting behaviour by a local metallic gate. At low measurements are carried out with standard lock-in techniques gate voltages, our device behaves as a quantum point contact in a four-terminal geometry (see Supplementary Information for that exhibits a minimum conductance plateau of e2=h in filtering details). zero applied magnetic field, half the expected value for The data reported in this Letter originate from a single cooldown spin-degenerate electrons, but consistent with predictions8–12 of an STO channel 2 µm in width spanned by a top gate of and experimental signatures13–18 of a magnetically ordered length 50 nm (other devices with similar behaviour are described ground state. The quantum point contact mediates tunnelling in the Supplementary Information). The electron density in the between normal and superconducting regions, enabling lateral STO regions exposed to the liquid was fixed near 5 × 1013 cm−2, tunnelling spectroscopy of the local superconducting state. corresponding to TC ≈ 300 mK (Supplementary Information). At Our work provides a generic scheme for quantum transport 14 mK and top gate voltage VTG D 0, the device is insulating for studies of STO and other surface electron liquids. source–drain bias voltage VSD up to 1 mV (left inset, Fig.1 c). Transition metal oxides exhibit electronic ground states At intermediate VTG, the IV curve resembles that of an opaque 2,3 not seen in conventional semiconductors . For instance, the tunnel junction, in which current flows only above a threshold VSD interface between lanthanum aluminate and strontium titanate19— (middle inset, Fig.1 c). This threshold decreases with increasing 20 two non-magnetic band insulators—hosts superconductivity VTG until a non-zero conductance appears at VSD D 0. At the 13–18 and magnetism . Rashba spin–orbit coupling at conductive highest applied voltages VTG ≈ 3 V, the IV curve resembles that 21 STO interfaces has led to predictions of unconventional of a superconductor with critical current IC (right inset, Fig.1 c). 10 > superconducting states , and of helical wires and Majorana We observe a normal-state resistance RN 1 k and a non-zero 11 = fermions in nanoscale STO channels . Furthermore, nanoscale resistance dV dI below IC, similar to other weak links with high lateral control of carriers could allow fabrication of gate-tunable, normal-state resistance25. single-material Josephson junctions and superconducting quantum Current-biased differential resistance measurements reveal that interference devices, as well as mesoscopic devices. However, IC is a strong function of VTG (Fig.2 a). IC can first be few experiments on nanostructures in STO systems exist: resolved around VTG D 2.1 V, and increases to over 100 nA by superconductivity has been demonstrated in submicron regions VTG D3.2 V (IC is defined as the lowest current at which the device 22 tunable with a global back gate , and channels sketched by a reaches its normal-state resistance RN). VTG is limited to 3.5 V nanoscale tip show superconducting features23. In this work, by the breakdown of the alumina dielectric; for all data shown, we demonstrate the first realization of an all-STO, gate-tunable gate leakage is below experimental sensitivity. The product ICRN, superconducting weak link. We tune our device to the ballistic 1D which is a measure of the superconducting gap ∆ in the banks 26 limit and perform superconducting spectroscopy that agrees with surrounding the weak link , saturates near 150 µV whereas IC 24 BCS weak-coupling expectations and previous work . steadily rises with increasing VTG (lower panel, Fig.2 a). For a short Undoped STO is a band insulator. Inducing a two-dimensional superconductor–normal–superconductor (SNS) junction in the (2D) electron density near 1013 cm−2 creates a metal, and several dirty limit, Kulik–Omelyanchuk theory (KO-1; ref. 26) predicts =∆ ∆ times that density creates an optimally doped superconducting that eICRN ∼ 2, giving ∼ 75 µeV in our sample. As described Department of Physics, Stanford University, Stanford, California 94305, USA. *e-mail: [email protected] 748 NATURE PHYSICS | VOL 10 | OCTOBER 2014 | www.nature.com/naturephysics © 2014 Macmillan Publishers Limited. All rights reserved NATURE PHYSICS DOI: 10.1038/NPHYS3049 LETTERS Ω a Ionic liquid cations Top gate b a dV/dI (k ) + 0 2 4 dV/dI (kΩ) + + + + 0 1 2 3 + + + + + + + + + + 14 mK + + + + + 200 + + H = 0 200 + + + + 100 100 STO Ohmic contacts Alumina (nA) 0 0 d.c. I c −100 -100 60 1 10 300 −200 -200 ) 0 0 0 h (nA) (nA) (nA) l l l / 0 V 1.7 V 3 V 2 40 e ( −1 −10 −300 150 ICRN 100 I V) V −500 500 −500 500 −250 250 C μ (nA) /d 100 ( l V (µV) V (µV) V (µV) N d I 50 20 R C C 50 I 0 0 14 mK 2.0 2.5 3.0 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 VTG (V) VTG (V) b Figure 1 | Device properties. a, Schematic of the device, which is 100 14 mK d 3.2 V 2.0 V submerged in ionic liquid. Cations are drawn to the sample by a positively /d 1.5 I (k charged electrode (not shown) that is also immersed in the liquid, (nA) 0 Ω d.c. 1.0 I accumulating electrons at the exposed superconducting strontium titanate ) (STO) surface (lavender shading). The top gate defines a channel of low −100 0.5 electron density by spacing and screening the cations. b, Scanning electron micrograph of a top gate of nominal length 60 nm (the device described in −0.1 0.0 0.1 μ the text has length 50 nm). The scale bar is 100 nm. The alumina dielectric 0H (T) laterally protrudes 5–10 nm (faint edge around top gate). c, Electronic properties versus top gate voltage VTG at 14 mK. Main panel: dierential Figure 2 | Tunable superconducting weak link. a, Dierential resistance conductance at zero source–drain bias. Insets: IV curves from the versus top gate voltage and d.c. bias current Id.c.. A critical current IC is insulating, tunnelling, and superconducting regimes. clearly observed, and grows with increasing VTG. Right panel: VTG D3.2 V (black dashed line in left panel). Lower panel: extracted IC and ICRN product, where RN is the normal-state resistance measured at high Id.c.. below, we measure ∆ ∼ 80 µeV by tunnelling spectroscopy, in ICRN saturates whereas IC continues to grow with increasing VTG. agreement with KO-1. Furthermore, the saturating behaviour of b, Dierential resistance versus applied perpendicular magnetic field and ICRN is expected: the top gate modulates the density in the weak link, ∆ Id.c.. IC is suppressed with increasing magnetic field, but without a magnetic which is largely independent of in the banks. The above results are diraction pattern. qualitatively insensitive to the exact definition of IC. IC decreases smoothly to zero in a magnetic field perpendicular to the plane (Fig.2 b). Were supercurrent flowing uniformly beneath phase coherence could mimic broken degeneracy in a single QPC, the top gate, we would expect a Fraunhofer diffraction pattern27 for as their resistances (h=2ne2, integer n) would simply add. But this . / IC H , with zeros every 20 mT. Instead, the magnetic field response scenario would require nearly identical Fermi levels and dimensions mirrors the diminishing superconductivity in the bulk. We suggest for both QPCs, as we observe only one set of QPC features (Fig.3 b). that only a small fraction of the area under our top gate becomes The apparent broken degeneracy is more naturally explained by 13–18 conductive, even at high VTG. ferromagnetism, which has been observed in LaAlO3/SrTiO3 We next focus on the transition from tunnelling to and is expected by theory: in some models, mobile d-electrons superconducting behaviour. Figure3 a shows a waterfall plot align their spins8,9, whereas in others itinerant electrons move 10–12 of differential conductance versus source–drain voltage VSD at in the Zeeman field of localized, spin-polarized dxy electrons .