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Gate-tunable superconducting weak link and quantum point contact spectroscopy on a strontium titanate surface

Nature Physics volume 10, pages 748752 (2014) | Download Citation

Abstract

Two-dimensional electron systems in gallium arsenide and graphene have enabled ground-breaking discoveries in condensed-matter physics, in part because they are easily modulated by voltages on nanopatterned gate electrodes. Electron systems at oxide interfaces hold a similarly large potential for fundamental studies of correlated electrons and novel device technologies1,2,3, but typically have carrier densities too large to control by conventional gating techniques. Here we present a quantum transport study of a superconducting strontium titanate (STO) interface, enabled by a combination of electrolyte4,5,6,7 and metal-oxide gating. Our structure consists of two superconducting STO banks flanking a nanoscale STO weak link, which is tunable at low temperatures from insulating to superconducting behaviour by a local metallic gate. At low gate voltages, our device behaves as a quantum point contact that exhibits a minimum conductance plateau of e2/h in zero applied magnetic field, half the expected value for spin-degenerate electrons, but consistent with predictions8,9,10,11,12 and experimental signatures13,14,15,16,17,18 of a magnetically ordered ground state. The quantum point contact mediates tunnelling between normal and superconducting regions, enabling lateral tunnelling spectroscopy of the local superconducting state. Our work provides a generic scheme for quantum transport studies of STO and other surface electron liquids.

Main

Transition metal oxides exhibit electronic ground states not seen in conventional semiconductors2,3. For instance, the interface between lanthanum aluminate and strontium titanate19—two non-magnetic band insulators—hosts superconductivity20 and magnetism13,14,15,16,17,18. Rashba spin–orbit coupling at conductive STO interfaces21 has led to predictions of unconventional superconducting states10, and of helical wires and Majorana fermions in nanoscale STO channels11. Furthermore, nanoscale lateral control of carriers could allow fabrication of gate-tunable, single-material Josephson junctions and superconducting quantum interference devices, as well as mesoscopic devices. However, few experiments on nanostructures in STO systems exist: superconductivity has been demonstrated in submicron regions tunable with a global back gate22, and channels sketched by a nanoscale tip show superconducting features23. In this work, we demonstrate the first realization of an all-STO, gate-tunable superconducting weak link. We tune our device to the ballistic 1D limit and perform superconducting spectroscopy that agrees with BCS weak-coupling expectations and previous work24.

Undoped STO is a band insulator. Inducing a two-dimensional (2D) electron density near 1013 cm−2 creates a metal, and several times that density creates an optimally doped superconducting state4. To modulate the density on this scale, we use the electric double-layer transistor technique4,5,6,7. A schematic of our sample is shown in Fig. 1a. A single crystal of TiO2-terminated (100) SrTiO3 is patterned with ohmic contacts and a narrow metal top gate separated from the STO surface by a 5 nm alumina layer (Fig. 1b and Methods). The sample is covered in ionic liquid, which is polarized by an electrode (not shown) to induce a 2D electron layer at the exposed STO surface; the area below the top gate remains insulating, because the gate screens the ions. The polarized sample is cooled to base temperature in a dilution refrigerator, freezing the ionic liquid and thus fixing the electron density in the exposed STO regions. The voltage on the top gate is then modulated to control transmission across the device, and conductance measurements are carried out with standard lock-in techniques in a four-terminal geometry (see Supplementary Information for filtering details).

Figure 1: Device properties.
Figure 1

a, Schematic of the device, which is submerged in ionic liquid. Cations are drawn to the sample by a positively charged electrode (not shown) that is also immersed in the liquid, accumulating electrons at the exposed superconducting strontium titanate (STO) surface (lavender shading). The top gate defines a channel of low 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 the text has length 50 nm). The scale bar is 100 nm. The alumina dielectric laterally protrudes 5–10 nm (faint edge around top gate). c, Electronic properties versus top gate voltage VTG at 14 mK. Main panel: differential conductance at zero source–drain bias. Insets: IV curves from the insulating, tunnelling, and superconducting regimes.

The data reported in this Letter originate from a single cooldown of an STO channel 2 μm in width spanned by a top gate of length 50 nm (other devices with similar behaviour are described in the Supplementary Information). The electron density in the STO regions exposed to the liquid was fixed near 5 × 1013 cm−2, corresponding to TC ≈ 300 mK (Supplementary Information). At 14 mK and top gate voltage VTG = 0, the device is insulating for source–drain bias voltage VSD up to 1 mV (left inset, Fig. 1c). At intermediate VTG, the IV curve resembles that of an opaque tunnel junction, in which current flows only above a threshold VSD (middle inset, Fig. 1c). This threshold decreases with increasing VTG until a non-zero conductance appears at VSD = 0. At the highest applied voltages VTG ≈ 3 V, the IV curve resembles that of a superconductor with critical current IC (right inset, Fig. 1c). We observe a normal-state resistance RN > 1 kΩ and a non-zero resistance dV/dI below IC, similar to other weak links with high normal-state resistance25.

Current-biased differential resistance measurements reveal that IC is a strong function of VTG (Fig. 2a). IC can first be resolved around VTG = 2.1 V, and increases to over 100 nA byVTG = 3.2 V (IC is defined as the lowest current at which the device reaches its normal-state resistance RN). VTG is limited to 3.5 V by the breakdown of the alumina dielectric; for all data shown, gate leakage is below experimental sensitivity. The product ICRN, which is a measure of the superconducting gap Δ in the banks surrounding the weak link26, saturates near 150 μV whereas IC steadily rises with increasing VTG (lower panel, Fig. 2a). For a short superconductor–normal–superconductor (SNS) junction in the dirty limit, Kulik–Omelyanchuk theory (KO-1; ref. 26) predicts that eICRN/Δ 2, giving Δ 75 μeV in our sample. As described below, we measure Δ 80 μeV by tunnelling spectroscopy, in agreement with KO-1. Furthermore, the saturating behaviour of ICRN is expected: the top gate modulates the density in the weak link, which is largely independent of Δ in the banks. The above results are qualitatively insensitive to the exact definition of IC.

Figure 2: Tunable superconducting weak link.
Figure 2

a, Differential resistance versus top gate voltage and d.c. bias current Id.c.. A critical current IC is clearly observed, and grows with increasing VTG. Right panel: VTG = 3.2 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.. ICRN saturates whereas IC continues to grow with increasing VTG. b, Differential resistance versus applied perpendicular magnetic field and Id.c.. IC is suppressed with increasing magnetic field, but without a magnetic diffraction pattern.

IC decreases smoothly to zero in a magnetic field perpendicular to the plane (Fig. 2b). Were supercurrent flowing uniformly beneath the top gate, we would expect a Fraunhofer diffraction pattern27 for IC(H), with zeros every 20 mT. Instead, the magnetic field response mirrors the diminishing superconductivity in the bulk. We suggest that only a small fraction of the area under our top gate becomes conductive, even at high VTG.

We next focus on the transition from tunnelling to superconducting behaviour. Figure 3a shows a waterfall plot of differential conductance versus source–drain voltage VSD at intermediate VTG, measured in a voltage-biased configuration with μ0H = 0.25 T to suppress superconductivity. The traces cluster slightly below 1 and 2 e2/h for zero bias, and near 1/2 and 3/2 e2/h for VSD ≈ 200 μV. We estimate a series resistance 2 kΩ h/e2 (Supplementary Information), which would make the 1 and 2 e2/h quantization quite accurate. This quantization appears as plateaux in dI/dV as a function of VTG for VSD = 0 (Fig. 3d), and the plateau features form a crossing structure in VSDVTG space (Fig. 3b). These data strongly resemble measurements on ballistic quantum point contacts (QPCs) in clean 2D systems, where the zero-bias conductance is quantized to integer multiples of G0 = ge2/h for subband degeneracy g. The high-bias plateaux at half-integer multiples of G0 are well documented28, and arise when the number of subbands below the Fermi level differs by one between the two leads.

Figure 3: Quantum point contact.
Figure 3

a, Two-terminal differential conductance versus source–drain bias voltage VSD for top gate voltages from 1.76 V (violet) to 2.24 V (red), with no adjustments for contact resistance. A magnetic field of 0.25 T is applied to suppress superconductivity. The curves cluster near e2/h and 2e2/h, as well as at the half-integers e2/2h and 3e2/2h for higher VSD. b, Same data as in a but the VTG range is offset by 60 mV to correct for hysteresis and align features with c. The crossing resonances track the subband minima. c, Two-terminal dI/dV as in a and b but with H = 0 so that the banks are superconducting. Split peaks emerge around zero bias, merging into one strong superconducting peak at the highest VTG. Right panel: VTG = 2.02 V (red dashed line in left panel). The dashed black curve is a fit of the double peak region to BTK theory (Rint = 1.87 e2/h, Δ = 71 μeV, Γ = 15 μeV and Z = 0.48; standard deviations from the genetic fitting algorithm are smaller than 1%). d, Differential conductance from b and c at VSD = 0, showing the plateau structure. e, Cartoon of the electron distribution that gives rise to the quantum point contacts (QPC) behaviour. A normal channel (blue) beneath the top gate forms two superconductor–normal (SN) interfaces, but owing to sample inhomogeneity only one interface is narrow enough to create a QPC in this gate voltage window. For VTG < 1.8 V, the narrowest end of the channel completely closes, leading to a tunnelling IV curve (Fig. 1c); for VTG > 2.2 V, the channel widens, yielding a superconducting IV curve.

The subbands seem to be non-degenerate (g = 1) even for H = 0 (Fig. 3d). Two spin-degenerate QPCs connected in series without phase coherence could mimic broken degeneracy in a single QPC, as their resistances (h/2ne2, integer n) would simply add. But this scenario would require nearly identical Fermi levels and dimensions for both QPCs, as we observe only one set of QPC features (Fig. 3b). The apparent broken degeneracy is more naturally explained by ferromagnetism, which has been observed13,14,15,16,17,18 in LaAlO3/SrTiO3 and is expected by theory: in some models, mobile d-electrons align their spins8,9, whereas in others itinerant electrons move in the Zeeman field of localized, spin-polarized dxy electrons10,11,12. Models that include a strong spin–orbit coupling21 alongside ferromagnetism in a 1D STO system predict a helical wire, again leading to an e2/h plateau11; our data cannot distinguish between helical and spin-polarized pictures. Although we do not observe hysteresis, the coercive field could be below the resolution of our data (5 mT), especially for small ferromagnetic patches9,16,17. Note that zero-field broken degeneracy in a QPC has also been reported in structures with an engineered in-plane electric field29, which is absent in our device.

The QPC structure at H = 0 (Fig. 3c) remains largely unchanged from the μ0H = 0.25 T case, except for a slight splitting and sharpening of resonances. For H = 0, however, two peaks emerge near zero bias between 1.9 and 2.05 V, and evolve into one peak above 2.05 V. We ascribe these peaks to a single superconductor–normal (SN) interface; an SNS junction would give a large superconducting peak at zero bias27. For this gate voltage range, inelastic scattering probably transforms the junction into two SN interfaces in series, with current flow shaped by the higher-resistance interface. The peaks are fitted well by the Blonder–Tinkham–Klapwijk (BTK) theory of SN interfaces, where f(E) is the Fermi function, A(E) and B(E) are probabilities of Andreev and normal reflection, and Γ characterizes lifetime broadening30. The interface barrier strength Z accounts for elastic scattering, including reflections due to Fermi wavevector mismatch27. Rint is the interface resistance in the absence of superconductivity, and equals the geometrical Sharvin resistance for Z = 0. The right panel of Fig. 3c shows the high quality of the fit to equation (1) for a representative VTG (2.02 V). Rint = 0.53 h/e2, which nearly agrees with the normal-state QPC resistance 0.58 h/e2 at VTG = 2.02 V. We thus conclude that the QPC itself is the SN interface that dominates the transport behaviour, as depicted inFig. 3e.

The situation of a single-mode quantum wire in contact with a superconductor has been theoretically analysed31, and results in lineshapes nearly identical to BTK, justifying our use of equation (1). However, the small resonances that track the subband edges (moving diagonally in Fig. 3c) overlap the split peaks at some gate voltages—for example, VTG = 1.98 V. To improve BTK fitting, we therefore divide the data of Fig. 3c by those of Fig. 3b. The resulting normalized dI/dV traces and fits are shown in Fig. 4a. With increasing VTG, split peaks merge into a single zero-bias peak, which reaches the theoretical maximum conductance enhancement of 2 for an SN junction with zero barrier. As VTG increases, the extracted Z remains near 0.5 until the middle of the normal-state 2e2/h plateau (2.03 V), where Z begins to drop to zero (Fig. 4b). The extracted Δ is 60–90 μeV, except near the plateau transitions (1.97 V and 2.05 V): there the normal-state conductance varies significantly at low bias, making both our normalization and our BTK model less accurate. Although statistical errors are small, systematic errors due to background features are significant (Supplementary Information). For VTG > 2.12 V, the normalized conductance at zero bias grows larger than 2 and strong dI/dV dips surround the central peak, signalling the transition to SNS behaviour.

Figure 4: Quantum point contact spectroscopy of the superconductor.
Figure 4

a, Normalized dI/dV for 1.91 V < VTG < 2.12 V, calculated by dividing the data in Fig. 3c by the data in Fig. 3b. Dashed black curves are BTK fits. Traces for VTG < 2.12 V are successively offset downwards by 0.2. b, Extracted barrier strength Z (right axis) and gap Δ (left axis). The voltages corresponding to the 1 and 2 e2/h plateaux at μ0H = 0.25 T are indicated with light and dark grey shading, respectively. The data at 1.98 V did not have well-defined peaks to fit. c, Peaks at top gate voltage VTG = 2.03 V for various temperatures, and BTK fits with Z = 0.5 to the double peaks. Traces for T > 14 mK are successively offset downwards by 0.4 e2/h. d, Extracted values of Δ and the broadening parameter Γ versus temperature. Dashed red curve is a fit of Δ to weak-coupling BCS theory. e, Peaks at VTG = 2.08 V for various perpendicular magnetic fields, and BTK fits with Z = 0.4. Traces for H > 0 are successively offset downwards by 0.2 e2/h. Fits are not possible above 0.14 T owing to the increasingly relevant background features. The VTG values quoted for c and e do not correspond exactly to VTG in a owing to gate hysteresis on the order of 50 mV. f, Extracted values of Δ and Γ versus magnetic field. Statistical error bars for all fits are smaller than the markers; systematic error is discussed in the Supplementary Information.

A QPC with conductance e2/h is a half-metal, which typically gives zero Andreev reflection probability at an s-wave superconductor interface. But, in our sample, introducing superconductivity enhances the zero-bias conductance above e2/h (Fig. 3d), suggesting significant Andreev reflection. This conundrum may be resolved by spin-flip Andreev reflections resulting from spin–orbit coupling in the superconductor32, dephasing33, magnetization gradients34, and/or impurities35. Such processes would restore a BTK-like lineshape for split peaks on the e2/h plateau (Supplementary Information).

The BTK model yields spectroscopic information that agrees with our expectations for the superconducting state. Δ(T) extracted from BTK fits on the 2e2/h plateau (Fig. 4c) follows the BCS prediction27 (Fig. 4d). Γ grows slightly as Δ is suppressed to zero with increasing temperature, in agreement with tunnelling measurements on LaAlO3/SrTiO3 (ref. 24; the upturn in Γ for T < 200 mK probably reflects elevated electron temperature, see Supplementary Information). In contrast, as the applied perpendicular magnetic field H increases, Δ stays constant whereas Γ increases markedly (Fig. 4e, f). This behaviour results from pair-breaking in a magnetic field and is observed in other superconductors such as Nb and Sn (ref. 36).

Our experiment illustrates the feasibility of clean transport measurements in nanostructured 2D oxide systems. Our demonstration of magnetism and tunable superconductivity in a single material with strong spin–orbit coupling lays the foundation for a host of interesting experiments. The gating technique presented here is generic, and can be implemented on other high-density surface electron systems.

Methods

Our samples are fabricated on TiO2-terminated (100) strontium titanate substrates (‘SrTiO3 STEP substrates’ from Shinkosha). Ohmic contacts and a large coplanar electrode are patterned by photolithography, followed by ion milling4 and evaporation of titanium and gold. The nanoscale gate is then defined in PMMA resist by 100 kV electron-beam lithography. Following development and an ultraviolet ozone clean, 5 nm of alumina is grown via atomic layer deposition, a 5 nm titanium/35 nm gold stack is deposited by evaporation, and the sample is immersed in acetone for liftoff. Finally, the mesa structure (Supplementary Information) is defined by a hard-baked photoresist mask.

Before measurement, a small drop of the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethanesulphonyl)amide (EMI-TFSI) is applied to the sample, which is then baked free of water in a tube furnace at 120 °C, under a 0.5 slm flow of argon. The sample is loaded into the vacuum chamber of our dilution refrigerator, which is cryopumped by a surface at 77 K. To minimize sample-degrading electrochemical effects, we cool the sample to 265 K before polarizing the liquid with 3.1 V on the coplanar electrode. We gradually cool the polarized sample to liquid helium temperatures over 36 h, and then activate our dilution unit to reach 14 mK.

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Acknowledgements

We thank J-M. Triscone and J. Mannhart for helpful discussions concerning this work, and S. Ilani for broader discussions concerning the properties of STO. Sample fabrication was supported by the Air Force Office of Science Research, Award No. FA9550-12-1-02520. Sample measurement was supported by the MURI Program of the Army Research Office, Grant No. W911-NF-09-1-0398. Development of the ionic liquid gating technique was supported by the Center on Nanostructuring for Efficient Energy Conversion (CNEEC) at Stanford University, an Energy Frontier Research Center funded by the US Department of Energy, Office of Basic Energy Sciences under Award No. DE-SC0001060. P.G. acknowledges support from the DOE Office of Science Graduate Fellowship Program. M.L. acknowledges support from Samsung and Stanford University. J.R.W. and D.G-G. acknowledge support from the W. M. Keck Foundation.

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  1. Department of Physics, Stanford University, Stanford, California 94305, USA

    • Patrick Gallagher
    • , Menyoung Lee
    • , James R. Williams
    •  & David Goldhaber-Gordon

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Contributions

P.G. designed the experiment, fabricated the sample, and performed the measurements. All authors contributed to data analysis. P.G. prepared the manuscript with input from all authors.

Competing interests

The authors declare no competing financial interests.

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Correspondence to David Goldhaber-Gordon.

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