PCCO characterization and Raman spectroscopy of SLG/PCCO

The PCCO (200-nm-thick) is grown by pulsed laser deposition on (001) oriented SrTiO 3 (STO) (see ‘Methods’) and has a near-bulk superconducting transition of 20.5 K (see Fig. 1a and Supplementary Fig. 1a). High-angle X-ray diffraction performed on control PCCO films grown in the same conditions as those measured in this study by STM (Fig. 1b and Supplementary Fig. 1b) reveals poor c-axis texturing with strong peaks from the (110) family of planes. In particular, the rocking curves of the (006) diffraction peak of the PCCO films show a spread in the full width at half maximum (FWHM) in the range 0.42°–0.85° (Fig. 1c–f), which are large values for perfect (001) texturing. These values are comparable to the FWHMs of the diffraction peaks of the (110) family of planes (with differences typically of ∼0.3° for neighbouring peaks belonging to the two families of planes) as shown in Supplementary Fig. 1c–f, which confirms that the PCCO surface is a mixture of (100) and (110) planes. This is in agreement with previous studies38,40 which have shown that secondary (110) phases would always form during the PCCO growth.

Figure 1: Characterization of SLG on electron-doped PCCO. (a) Schematic of SLG (hexagonal lattice) on PCCO/STO. (b) High-angle X-ray diffraction data on four control films of 5 mm × 5 mm PCCO/STO deposited using identical growth conditions (curves are vertically offset for clarity). (c–f) Rocking curves (omega scans) of the (006) PCCO diffraction peaks from the same samples investigated in (b) with matching colours showing a FWHM of 0.85° (c), 0.42° (d), 0.51° (e) and 0.61° (f). (g) STM topography map showing SLG on PCCO/STO measured at 4.2 K (scale bar in g has a length of 0.5 nm). (h) Raman spectra at 514.5 nm of PCCO as-grown on STO (grey) and following transfer of SLG (red) at 293 K. (i) Raman spectra at 514.5 nm of SLG as-grown on Cu (grey) and following transfer onto PCCO/STO (red) measured at 293 K. The PCCO/STO background is subtracted to allow identification of D, G and 2D peaks. (j) Raman spectra at 514.5 nm of SLG on PCCO/STO, after background subtraction, at 293 K (red), 150 K (blue) and 4.2 K (light blue). Full size image

SLG is grown on Cu by chemical vapour deposition (CVD), as described in ref. 41, and transferred onto PCCO/STO, following the procedure in ref. 42. The analysis of the Raman spectrum acquired on as-grown graphene on Cu (Fig. 1i, grey curve) shows that the 2D peak can be fitted with a single Lorentzian with a position, Pos (2D), ∼2681, cm−1 and FWHM(2D) ∼37 cm−1, indicating SLG (ref. 43). The G peak position, Pos(G), and FWHM(G) are 1,587 cm−1 and 20 cm−1, respectively; and the intensity ratio, I(2D)/I(G), and area ratio, A(2D)/A(G), are 2.9 and 5.6, respectively. These indicate a doping of ∼200 meV for SLG on Cu at room temperature44,45,46. The spectrum shows a small D peak with I(D)/I(G)=0.15, corresponding to a defect concentration of n D ∼3.8 × 1010 cm−2 (refs 45, 47). A compressive biaxial strain of 0.07% is also estimated from the Raman analysis. To compare the SLG quality before and after transfer, the background signal of PCCO on STO is measured under identical conditions (see Fig. 1h and ‘Methods’ section) and subtracted after normalization to the intensity of the Raman peak of STO at ∼300 cm−1. After transfer, Pos(2D) and FWHM(2D) are ∼2681, cm−1 and 37 cm−1, Pos(G) and FWHM(G) are 1,581 cm−1 and 17 cm−1, while I(2D)/I(G) and A(2D)/A(G) are 3.4 and 7.1, respectively (Fig. 1i, red curve). This implies a reduction in doping to <100 meV (refs 44, 45, 46), with I(D)/I(G) ∼0.09, corresponding to n D ∼2.2 × 1010 cm−2. Similar values of defect concentration and strain for as-grown SLG on Cu and after its transfer onto PCCO imply homogeneous SLG on PCCO.

To assess doping and sample quality in the same temperature range used for the superconductivity studies, Raman measurements are also performed between 4.2 K and room temperature (Fig. 1j and Supplementary Fig. 2a). The low-temperature Raman data indicate that doping remains below 100 meV and that there are no structural changes compared with room temperature.

Local density of states measurements on SLG/PCCO

Using STM we locally measure dI/dV−V spectra of SLG on PCCO at 4.2 K and correlate these to surface topography (Fig. 1g). The most predominant superconducting-related spectra show either V-shaped gaps (Fig. 2a) or a subgap structure, including ZBPCs and split ZBCPs (Fig. 2b,c). Additional supporting data are shown in Supplementary Fig. 3. V-shaped gaps are observed in about 45% of the scans, while in all the other areas we observe either ZBCPs (∼30%) or split peaks (∼25%). In the normal state none of these spectral features is observed, which rules out the possibility that these are due to electronic inhomogeneity in the sample, since this should give rise to the same features independently of temperature. In some areas, in all of which the SLG local topography cannot be properly resolved, single-electron tunnelling spectra are measured in the superconducting state (Supplementary Fig. 4); such features persist above T c (at least up to 50 K), as also shown in Supplementary Fig. 4.

Figure 2: STM differential conductance versus bias-voltage spectra on SLG/PCCO/STO at 4.2 K. (a–c) Typical proximity-induced V-shaped gaps (a), ZBCPs (b) and split ZBCPs (c). Different colours in a–c are used to distinguish between spectra recorded in different sample areas. Insets in a–c show the typical topography of a sample area where the corresponding spectra in a–c are obtained (the scale bars in the insets have a length of 0.5 nm). Full size image

The evolution of superconducting-related spectral features is also studied as the sample is warmed up above its superconducting transition. All subgap features including ZBCPs and split ZBCPs are suppressed as the sample is warmed up (Supplementary Fig. 5) giving spectra that are either consistent with lightly doped SLG with E F within 100 meV from the Dirac point48, or to structureless (flat) spectra, or single-electron tunnelling effects. The latter two appear in <10% of the total scanned area, where no superconducting-related features are observed below T c and the STM topographic images do not exhibit a clear SLG structure. This shows that the proximity takes place only in regions that structurally and electronically conform to the SLG behaviour. Whilst proving that the V-shaped gaps, ZBCPs or split peaks are related to superconductivity, the absence of such structures (particularly conductance peaks) above the superconducting transition temperature, rules out spurious effects from defects (for example magnetic impurities) or structural inhomogeneity that may cause Kondo scattering and thus enhancements of the DoS, as such features would also be present in the normal state. Further support for this conclusion comes from the fact that ZBCPs are found (below T c ) only in regions where the STM images show clear SLG topography and not in defected regions. We also measure the evolution of ZBCPs in an applied out-of-plane magnetic field (Supplementary Fig. 6), and their magnitude is always found to decrease, with no splitting ever observed, which is also inconsistent with a Kondo effect. This effect of magnetic field is similar to those observed in tunnelling spectroscopy studies of proximity-induced p-wave superconductivity in Bi 2 Se 3 (ref. 9) and odd-parity topological superconductivity in Cu x Bi 2 Se 3 (ref. 49).

Control experiments on bare PCCO and Au/PCCO

Control samples of bare PCCO are also investigated, but no subgap structure or V-shaped gaps are observed (Fig. 3a), even at facets that expose the nodal ab-plane. The only DoS features we can observe are smeared BCS-like gaps, consistent with previous STS experiments on electron-doped PCCO (refs 37, 40). We investigate the effect of substrate choice on the superconductor proximity effect by fabricating SLG/PCCO on (001) LaAlO 3 (LAO) and observe similar results to STO (Supplementary Fig. 7).

Figure 3: STM differential conductance versus bias-voltage spectra on control samples of PCCO/STO and Au/PCCO/STO at 4.2 K. (a) Typical STM spectra at 4.2 K for PCCO/STO with schematic of the sample structure (inset i) and STM topography (inset ii; the scale bar has a length of 0.5 nm). (b) Typical STM spectra at 4.2 K for Au/PCCO/STO (Au is 10-nm-thick) with schematic of the sample structure (inset iii) and STM topography (inset iv; the scale bar has a length of 0.5 nm). (c,d) Average ZBCP amplitudes for SLG/PCCO/STO (black shaded curve) and Au (green shaded curve) and Ag (red shaded curve) microislands on SLG/PCCO/STO (c) with corresponding schematics shown in (d) where the hexagonal lattice represents SLG. Full size image

The ZBCPs on SLG/PCCO might be related to the penetration of the anisotropic components of PCCO that are masked in bare PCCO, but which may appear in SLG due to its long electron mean free path (∼100 nm near the Dirac point)50 and spin diffusion length (>1 μm) (ref. 51) being much longer than the coherence length in PCCO of ∼30 nm (ref. 37). These are important parameters to consider, since the superconducting condensate is induced in the entire graphene plane. To check this, we replace SLG with Au and fabricate Au/PCCO/STO films (Fig. 3b), where a 10-nm-thick polycrystalline Au layer is deposited in-situ without breaking vacuum by pulsed laser deposition, and perform STS. Au is chosen since it has an electron mean free path ∼30 nm at room temperature52. The topography maps of Au/PCCO/STO (Fig. 3b) reveal a low surface roughness (∼1 nm over a 1 μm2 area; Supplementary Fig. 8), and the corresponding tunnelling spectra on Au show superconducting gaps with no subgap structure, thus supporting our claim that the subgap structures in SLG/PCCO are related to SLG and not the underlying PCCO. We note that the gapped spectra on Au/PCCO are shallower than those of bare PCCO (Fig. 3a,b), but qualitatively similar, suggesting that Au is fully superconducting.

Tuning the superconducting proximity effect in SLG/PCCO

To further confirm our claim that the spectral features on SLG/PCCO are related to a superconductor proximity effect in SLG and not the underlying PCCO, we also measure spectra on SLG covered with evaporated microislands (10 μm in diameter and 30 nm in height) of either Ag or Au (Fig. 3c,d). Unlike metals, such as Pd, which have a stronger binding interaction with SLG (ref. 34), the low binding energy of Au and Ag (0.04 eV per carbon atom34) results in a reduced modification of the SLG band structure34. Ag (Au) has a work function of 4.4 eV (5.2 eV) which is lower (higher) than the work function of SLG (∼4.6 eV; ref. 34). Therefore, if a superconducting proximity effect occurs on SLG/PCCO, this should be stronger near a Ag microisland than a Au one, since Ag (Au) acts as a donor (acceptor) of electrons in SLG, with a doping profile that can extend up to hundreds nanometre from the microisland step edge53. The tens of dI/dV−V spectra acquired on these samples show that pronounced ZBCPs are observed near and even on the Ag microislands, but no ZBCPs are ever observed near or on Au microislands, despite the well-defined SLG topography (some representative spectra are shown in Fig. 3c and in Supplementary Figs 9 and 10). This implies that the Au islands reduce the SLG electron density to the extent that the superconducting proximity effect for SLG on PCCO is suppressed. We also note that these data indicate that possible doping inhomogeneities can only affect the size of the unconventional superconducting features (even to their suppression, along with the proximity effect altogether), but do not affect the unconventional nature of the proximity-induced superconductivity in SLG.

Calculation of the superconducting DoS in SLG/PCCO

We now consider the spatial variations in the superconducting DoS that we observe on SLG/PCCO (Fig. 2 and Supplementary Fig. 3). These indicate local variations in the proximity effect due to a combination of PCCO faceting and changes in the PCCO surface that is a mixture of different PCCO planes. Fig. 4 plots the theoretical DoS on SLG as a function of the STM orientation relative the graphene surface, which varies due to the PCCO faceting.

Figure 4: Theoretical proximity-induced superconducting DoS in SLG on PCCO. (a–d) The plots show that the projections of the p-wave induced symmetries in SLG are dependent on the crystal orientation of the underlying PCCO. This is clearest in (d) which illustrates the relationship between the observed DoS on SLG and the plane normal to the underlying PCCO: on flat regions oriented along the [001] crystallographic direction, the DoS corresponds to p y -wave or antinodal -wave with a strong tunnelling barrier (red curve in a); rough areas expose a mixture of normal planes oriented between the [001] and [110] crystallographic directions, where the DoS corresponds to p y -wave with a moderate tunnelling barrier (green curve in b); the DoS corresponding to the p x -wave is projected on the phase oriented along the [110] crystallographic direction (blue curve in c). Full size image

These are calculated by applying the model in refs 22, 54, which predicts an effective p-wave pairing at the Dirac points in SLG on a d-wave superconductor and involves solving a tight-binding Hamiltonian for SLG assuming that the tunnelling between SLG and the STM tip obeys an extended Blonder–Tinkham–Klapwijk (BTK) theory30,55. Following refs 22, 54, we write the Hamiltonian in a band-basis where c q is a Fermion-operator in the conduction band and d q is a Fermion-operator in the valence band:

In equation (1) we define the normal-state band dispersion as ɛ q = where the sum is over nearest-neighbour vectors a, t is the hopping parameter, μ is the chemical potential, while δ q and u q are associated to the superconducting order parameter. The above Hamiltonian can be diagonalized and yields eigen values:

Since the shift in Fermi level (E F ) in SLG (below 100 meV in SLG on PCCO at 4.2 K) is much larger than the superconducting order parameter (Δ∼5 meV for PCCO), u q in equation (2) can be neglected and we are left with an effective superconductor with gap δ q . It is this gap that acquires a p-wave symmetry near the Dirac points when d-wave superconducting correlations are induced in SLG22,54. This is due to the fact that the transport properties of SLG are determined by its behaviour near the Dirac points for doping levels comparable to that in our study (<100 meV) and, as explained in refs 22, 54, a d-wave symmetry in the full Brillouin zone corresponds to a p-wave symmetry in the vicinity of the Dirac points at K and K'.

In this regime, where the shift in E F in SLG is much larger than Δ, a simplified model for tunnelling between SLG and the STM-tip based on BTK theory can be adopted to account for p-wave pairing. This is a commonly used modelling tool for tunnelling measurements with unconventional superconductors56,57,58. The procedure consists in setting up the wavefunctions on SLG and on the normal side of the tunnelling barrier, the strength of the latter being characterized by a dimensionless number Z. The Z parameter describes the strength of the tunnel barrier between SLG and the STM tip, that is, the barrier is effectively the vacuum in between. The Z value affects the DoS spectra as it is related to the ratio between Andreev reflections and quasiparticle tunnelling (Z=0 corresponds to a perfect interface with zero resistance, whereas Z>>1 corresponds to a barrier with high tunnel resistance). The Z value can be controlled in STS via the current and bias-voltage settings (see below), which governs the tip-sample distance in the case of an ideally homogeneous sample. However, in our experiment, it is realistic to expect spatial variations in Z (for a given current-bias setting) since the STM tip approaches the graphene surface at slightly different distances at different locations, due to variations in the surface plane of the underlying PCCO and local variations in graphene-PCCO connectivity, which is hence accounted in our theoretical model.