Sample characteristics

High-quality bulk Bi 2 Se 3 , Bi 2 Te 3 and optimally doped Bi-2212 crystals were cleaved, resulting in atomically flat surfaces over large areas (Fig. 1a and b), and were subsequently mechanically bonded (Fig. 1c-f) in a dry atmosphere. These low-resistance tunnel junctions were then probed by conductance spectroscopy measurements, including the current and differential conductance versus voltage (Fig. 1g). The conductance spectroscopy experiments were performed using four-point probe measurements in a liquid He flow cryostat at different temperatures ranging from 295 to 4.5 K. Our mechanically bonded tunnel junction method was also verified to perform successfully on a Bi-2212/graphite junction (Supplementary Fig. S1), resulting in a typical S–N tunnelling spectra seen previously for Bi-2212, with point contact or scanning tunnelling microscopy35.

Figure 1: Device fabrication and measurement set-up. (a) Atomic force microscope (AFM) image of the crystal surface of Bi 2 Se 3 . The scale bar corresponds to 2 μm. (b) Larger area AFM scan of the Bi 2 Te 3 sample, demonstrating the vertical inhomogeneity of the surface is limited to ±2 unit cells. The scale bar corresponds to 3 μm. Junction fabrication technique: (c) Bi-2212 (BSCCO) crystal is cleaved using scotch tape. (d) Bi 2 Se 3 (or Bi 2 Te 3 ) is sandwiched between glass slides with double-sided tapes and the top glass slide is lifted off, cleaving a flat surface. (e) The Bi 2 Se 3 (or Bi 2 Te 3 ) is transferred to a Cu sample holder, and the cleaved Bi-2212 crystal is applied to Bi 2 Se 3 or Bi 2 Te 3 using GE varnish at the corners. (f) Contacts are made with Ag epoxy or evaporated Au/Ti. (g) Experimental set-up: four-point DC current-voltage and AC differential conductance measurements performed down to 4.5 K, using a liquid He-flow cryostat with lock-in amplifiers. DC bias from the power supply is combined with the AC signal from the voltage lock-in amplifier in a transformer-based adder. Full size image

Bi-2212/Bi 2 Se 3 experiments

The first set of experiments was performed on Bi-2212/Bi 2 Se 3 junctions. DC current along the c axis versus voltage (I–V) characteristics (Fig. 2a) reveal excess current below the Bi-2212 T c (~85 K) due to the Andreev reflection at the S–N interfaces36, consistent with the model developed for anisotropic superconductors34. The observed Andreev reflection indicates that we have achieved a surprisingly low barrier between Bi-2212 and Bi 2 Se 3 . Furthermore, this is the key mechanism for the superconducting proximity effect37, suggesting the existence of a proximity-induced superconducting region at the Bi-2212/Bi 2 Se 3 interface. Just below T c , the excess current, I e , reaches the maximal value similar to the normal–normal (N–N) interface current (measured for T >T c ), resulting in total current nearly twice that of the N–N interface due to the contribution of the Cooper pairs when Andreev reflection occurs. A different measurement—AC differential conductance below T c , (dI/dV) S , divided by the normal state conductance(dI/dV) N measured at 105 K, confirms the DC I–V measurement. Specifically, the AC differential conductance reveals a zero-bias conductance peak due to Andreev reflection below T c (Fig. 2b). At lower temperatures (around 60 K), reduction of higher-bias current was observed, and at the same temperatures, additional higher-bias features appeared in the differential conductance measurement. These features result from the gap reduction in Bi-2212 and the induced gap in Bi 2 Se 3 . However, the detailed structure of these spectral features could be studied only at lower temperatures as discussed in detail below.

Figure 2: Bi-2212/Bi 2 Se 3 junction measurements. (a) DC current–voltage characteristics of the low-resistance Bi-2212/Bi 2 Se 3 junction for different temperatures above and below T c . Below T c , excess current typical of Andreev reflection at an S–N interface is exhibited. The 70 K I–V curve shows the maximal excess current I e ~4.85 μA—similar to the value of the normal junction (above T c ) at the voltage where the superconducting state current becomes linear (black dashed line). The total excess current is smaller for lower temperatures due to additional gap features. (b) AC differential conductance(dI/dV) S , normalized by the normal state conductance (dI/dV) N at 105 K, for the low-resistance Bi-2212/Bi 2 Se 3 junction at different temperatures above and below T c . A zero-bias conductance Andreev peak is clearly seen below T c , with additional features in the spectrum appearing at lower temperatures. The curves are shifted for clarity. (c) DC current–voltage characteristics of the low-resistance Bi-2212/Bi 2 Se 3 junction for different temperatures well below T c . In addition to the excess current, the low-temperature curves exhibit two distinct steps corresponding to the dips in the differential conductance measured for AC bias. The black arrow shows the induced Bi 2 Se 3 gap, Δ i , with a current twice that of the normal state at the same voltage (a), and the red arrow indicates the reduced Bi-2212 gap, Δ r , whereas the intrinsic Bi-2212 gap, Δ 0 , is shown by purple arrows. The inset shows the DC and the AC differential conductance at 4.5 K, indicating the good correspondence between the different measurements of Δ 0 (purple arrow), Δ r (red arrow) and Δ i (black arrow); AU, arbitrary units. (d) AC differential conductance (dI/dV) S , normalized by the normal state conductance (dI/dV) N at 105 K, for a low-resistance Bi-2212/Bi 2 Se 3 junction for different temperatures well below T c . The curves are shifted for clarity. The zero-bias conductance feature is due to the Andreev reflection between the normal and proximity-induced superconducting regions in Bi 2 Se 3 , where the width of the peak is nearly 2Δ i . The two additional peaks indicate the reduced and the intrinsic Bi-2212 gaps. Full size image

To demonstrate the spectral features more clearly, we performed both DC and AC measurements at temperatures well below T c . DC I–V characteristics of the junction (Fig. 2c) show excess current at lower voltages up to about 13 mV with a correspondingly smaller value I S ~2.7 μA. However, two additional step-like features appear near 27 and 45 mV. These features are confirmed by an AC differential conductance measurement (Fig. 2d), showing a wide conductance feature between −13 and +13 mV, as well as peaks at ±27 and ±45 mV, in good quantitative agreement with the DC measurement (Fig. 2c inset). Similar results were obtained with Bi-2212/Bi 2 Te 3 junctions as described below. This conductance spectrum is a clear signature of a proximity-induced superconducting region in the Bi 2 Se 3 .

When the proximity effect occurs (Fig. 3a), a superconducting gap is induced in the normal material, Δ i , and near the interface, the gap in the superconducting material is reduced from the intrinsic value, Δ 0 (Fig. 3b), to a smaller one, Δ r 1,23,24,27,28. Generally, the superconducting gap is position-dependent along the axis normal to the interface plane, Δ(x), and Andreev-scattering probability is finite in the whole proximity region. However, the scattering can be divided into two main energy ranges: electrons (holes) with energy |E|<Δ i will be mainly Andreev-reflected inside the proximity-induced superconducting region of the normal material, whereas electrons (holes) with Δ i <|E|<Δ r will continue to the S–N interface and then Andreev-reflect, mainly near the material interface. Thus, conductance spectrum taken on an interface exhibiting the proximity effect will show Andreev-scattering features corresponding to both gaps23,24,27,28. In our experiments, therefore, the central conductance peak is a manifestation of Andreev reflection from the normal region to the proximity-induced superconducting region of Bi 2 Se 3 with a gap Δ i ~13 mV. The reduced gap in Bi-2212 due to the proximity effect appears as a conductance peak at Δ r ~27 mV. The change in the zero-bias conductance with temperature is an additional manifestation of the Andreev scattering. Indeed, just below T c , the zero-bias conductance increases to nearly twice its value above T c (Fig. 3c). This temperature dependence, as well as the spectral shape of the conductance at various temperatures (Fig. 3c inset), completely rules out any possible heating-related effects, whereas a junction with an increased barrier exhibits no proximity (Fig. 3d). Andreev reflection between Bi-2212 and normal Bi 2 Se 3 (or Bi 2 Te 3 ) with no proximity would have appeared as a single Andreev feature with a width corresponding to the full gap of Bi-2212, which is completely different from our observations. The full gap appears in our experiment as additional peaks at Δ 0 ~45 mV, whose magnitude and temperature dependence are quantitatively consistent with previous tunnelling studies of Bi-2212 (ref. 35) and our high-barrier junctions (Fig. 3d).

Figure 3: Proximity induced superconductivity. A schematic drawing of the junction in two regimes: (a) low-resistance with proximity induced superconductivity in Bi 2 Se 3 (or Bi 2 Te 3 ). Andreev scattering takes place in the whole proximity region with lower energy particles reflected mainly in Bi 2 Se 3 (or Bi 2 Te 3 ), and higher energy ones mainly at the interface with Bi-2212; (b) high-resistance with no proximity-induced superconductivity in Bi 2 Se 3 (or Bi 2 Te 3 )—quasiparticle scattering occurs at the interface. (c) Temperature dependence of the zero-bias differential conductance for Bi-2212/Bi 2 Se 3 . Below T c , the Andreev process enhances the conductance by almost a factor of 2. The inset shows the temperature dependence of the reduced Bi-2212 gap Δ r blue circles), and the intrinsic Bi-2212 gap Δ 0 in the low-resistance junction (green squares) and in the high-resistance junction (red diamonds). (d) Differential conductance (dI/dV) S , normalized by the normal state conductance (dI/dV) N at 105 K, for a high-resistance Bi-2212/Bi 2 Se 3 junction for different temperatures, demonstrating the typical quasiparticle tunnelling differential conductance, resulting in a conductance dip in the gapped region. The curves are shifted for clarity. The arrows indicate the intrinsic superconducting gap of Bi-2212, ±Δ 0 , around 45 mV. (e) Measured (solid red line) and calculated (dashed blue line) 15 K differential conductance (dI/dV) S , normalized by the normal state conductance (dI/dV) N at 105 K, for a low-resistance Bi-2212/Bi 2 Se 3 . Full size image

The zero-bias conductance feature has a number of characteristics consistent with Andreev reflection in a proximity-induced region. The height of the Bi 2 Se 3 Andreev zero-bias conductance feature is nearly twice the normal conductance value due to the Cooper pair contribution (Figs 2d and 3c), whereas the width is determined by the induced superconducting gap, 2Δ i . The width of the Andreev feature is also manifested in the excess current up to a negative bias Δ i in the DC I–V characteristic (Fig. 2c)—nearly twice as high as the current in the normal state (Fig. 2a). The probability of Andreev scattering at the interface with the Bi-2212 is reduced by the scattering in Bi 2 Se 3 , resulting in slightly smaller contribution to the conductance at Δ r . At low temperatures, both the induced gap and the reduced gap features in differential conductance result in a step-like I–V curve (Fig. 2c). With increasing temperature, the features in the differential conductance merge into one wide central peak (Fig. 2b) and the step-like structure in I–V disappears (Fig. 2a). Therefore, at certain higher temperatures, the total excess current can be larger than at lower temperatures.

Theoretical modelling

For the quantitative theoretical modelling of the effect, we calculated the c axis Bi-2212/Bi 2 Se 3 and Bi-2212/Bi 2 Te 3 conductance spectra using the S–N transport formalism developed for anisotropic superconductors34. The differential conductance below T c (dI/dV) S , divided by the normal state conductance (dI/dV) N is given by the half-sphere integration over solid angle38 Ω:

where E is the quasiparticle energy and θ N is the incidence angle (relative to the interface normal) in the normal material, σ N is the conductance from normal to normal material with the same geometry, and

where —electron-like and hole-like quasiparticle effective pair potentials with the corresponding phases iφ±.

In case of c axis tunnelling, the hole-like and the electron-like quasiparticles transmitted into the superconductor experience the same effective pair potentials, which have similar dependence on the azimuthal angle α in the ab plane . The total Andreev reflection spectrum is obtained by calculating the reflection and the transmission in the proximity region, followed by reflection at the interface between the two materials. The calculated spectra in this two-stage scattering model with the modified gaps as fit parameters show good agreement with the experimental conductance measurements (Fig. 3e).

Bi-2212/Bi 2 Te 3 experiments

To demonstrate the wide applicability of our mechanical bonding technique, we have constructed similar S–N junctions combining Bi-2212 from a different batch of crystals and Bi 2 Te 3 grown by a different group (Princeton University) than that producing the Bi 2 Se 3 (Rutgers University). Conductance measurements of low-barrier Bi-2212/Bi 2 Te 3 junctions also clearly show the proximity-induced gap in Bi 2 Te 3 , as well as the reduced gap in Bi-2212 (Fig. 4a). The central Andreev feature due to the induced gap in the spectrum also appears immediately below T c similar to Bi 2 Se 3 , with a conductance increase of nearly twice the normal value (Fig. 4b), and a width consistent with Andreev reflection in the proximity-induced region. We have constructed several Bi-2212/Bi 2 Te 3 junctions with various induced gap sizes, and the measured spectra agree well with the calculations (Fig. 4b inset). One of the Bi-2212/Bi 2 Te 3 junctions exhibited particularly large proximity-induced features in differential conductance (Fig. 4c), and the corresponding current-voltage DC measurement shows excess current as high as 90 μA (Fig. 4d). The proximity-related Andreev features and the excess current were observed repeatedly in several Bi-2212/Bi 2 Se 3 (Fig. 4e) and Bi-2212/Bi 2 Te 3 (Fig. 4f) devices.