Coulomb Blockade Effects in a Topological Insulator Grown on a High-Tc Cuprate Superconductor

Using high-Tc superconductors to proximitize topological materials could give rise to new phenomena with enhanced metrics. However, the evidence for proximity-induced superconductivity in heterostructures of topological insulators and high-Tc cuprates has been intensely debated. We use molecular beam epitaxy to grow ultrathin films of topological insulator Bi2Te3 on a cuprate Bi2Sr2CaCu2O8+x, and study the surface using low-temperature scanning tunneling microscopy and spectroscopy. In ~few unit-cell thick Bi2Te3 films, we find a V-shaped gap-like feature at the Fermi energy in dI/dV spectra. By reducing the coverage of Bi2Te3 films to create nanoscale islands, we discover that this spectral feature dramatically evolves into a much larger hard gap, which can be understood as a Coulomb blockade gap. This conclusion is supported by the evolution of dI/dV spectra with the lateral size of Bi2Te3 islands, as well as by topographic measurements that show an additional barrier separating Bi2Te3 and Bi2Sr2CaCu2O8+x. We conclude that the gap-like feature in dI/dV spectra in Bi2Te3 films can be explained by Coulomb blockade effects, which take into account additional resistive and capacitive coupling at the interface. Our experiments provide a fresh insight into the tunneling measurements of complex heterostructures with buried interfaces.

40 meV, has been primarily used in this effort due to the ease of cleaving to expose a large, clean and flat surface. However, the experiments have given conflicting results [13][14][15][16][17][18] . Angle-resolved photoemission spectroscopy (ARPES) measurements reported the absence of an induced gap in the TI band structure, attributed to the very short coherence length of Bi-2212 along the c-axis 13 , and the mismatch between the Fermi surfaces of the TI and Bi-2212 13,14 . On the other hand, tunneling measurements have observed a gap-like feature in dI/dV spectra in both Bi 18 and Bi2Te3 17 grown on Bi-2212, interpreted as a strong evidence of proximity-induced superconductivity in the topological material. Here we shed light on this controversy by using high-resolution scanning tunneling microscopy and spectroscopy (STM/S) to explore Bi2Te3 ultrathin films and nano-islands grown on Bi-2212.

Results:
Bi2Te3 films are grown on UHV-cleaved, optimally-doped Bi-2212 (Tc~91 K) using molecular-beam epitaxy (MBE), following a recipe similar to previous related work 13,14 (Methods). As the proximity-induced superconducting gap at the exposed "bare" surface of the normal material is expected to decrease with its thickness 19 , we focus on ultrathin Bi2Te3 films: 2 quintuple layers (QLs), 1 QL and ~0.1 QL coverage. There are two main challenges in growing Bi2Te3 on superconducting Bi-2212. The first one is incompatibility of the in-plane atomic structures of the two materials. Bi-2212 cleaves between two BiO planes to reveal a square lattice of Bi atoms observed in STM topographs [ Fig. 1(b)], which is in contrast to Bi2Te3 that has a hexagonal lattice structure [ Fig. 1(c)]. This structural mismatch leads to the formation of two types of Bi2Te3 domains that are rotated 30 degrees with respect to each other [ Fig. 1(e), Fig. S1] 11 . Despite the domain formation, we are still able to routinely locate large (at the order of ~50 nm squared) single-domain areas using STM in thicker films. Second crucial issue is that the electronic properties of the Bi-2212 surface can change upon heating 20 . At ideal Bi2Te3 growth temperatures of ~350 °C 21 , interstitial oxygen dopants escape from the topmost surface layers of Bi-2212, leading to an effective lowering of the hole density and degradation of superconducting properties 20 . To mitigate this issue, in this work we use much lower Bi2Te3 growth temperatures below 250 °C (Methods).
To characterize the large-scale electronic structure of our Bi2Te3 films, we use quasiparticle interference (QPI) imaging 22,23 , rooted in elastic scattering and interference of electrons on the surface of a material, which can be seen as waves in STM dI/dV maps. For both 1 QL and 2 QL Bi2Te3 films, we acquire a series of dI/dV maps at different biases, and analyze their Fourier transforms (FTs) [ Fig. 2(a-h), Fig S2]. In ideal topological insulators, back-scattering is prohibited 24 , but starting at energies ~50 meV away from the Dirac point 23 , a hexagonal warping of the constant energy contour opens up additional scattering channels along the Γ-M direction 23,25,26 . We indeed observe this characteristic scattering pattern [ Fig. 2(e-h)], which is qualitatively similar to that reported on cleaved bulk Bi2Te3 single crystals 23,25 , as well as Bi2Te3 films 11,26 . By tracking the magnitude of the scattering wave vector as a function of STM bias, we are able to map the QPI dispersion for both films [ Fig. 2(i,j)]. These dispersions match well with ARPES measurements of Bi2Te3 films of the same thickness 27 , thus confirming the expected electronic structure of our films.
Next we look for any evidence of induced superconductivity at the surface of Bi2Te3 films. dI/dV spectra acquired on 1 QL and 2 QL Bi2Te3 films show a small suppression in the local density of states within ± ~5-10 meV around the Fermi level [ Fig. 3(b,e)]. To test if the surface state is gapped within the energy range of the gap-like feature, we acquire dI/dV maps at small bias near the Fermi level energy, well within the observed gap feature [ Fig. 3(a,d)]. If the surface state is indeed fully gapped, we would not expect to see any scattering. However, the FTs of the dI/dV maps in both films show a noticeable QPI signal [insets in Fig. 3(b,e)], which allows us to place an upper bound on the magnitude of the induced gap in the Bi2Te3 surface state, if any, to ~2-3 meV, set by the finite temperature thermal broadening and lock-in excitation used in our experiments. In comparison to the average dI/dV spectrum of optimally-doped Bi-2212 that shows ~40 meV magnitude and prominent coherence peaks Given the fragile nature of the Bi-2212 electronic structure when the material is heated 20 , it is conceivable that superconductivity at the surface of Bi-2212 deteriorates once Bi and Te are coevaporated onto the surface at elevated temperatures. This could potentially explain the lack of a prominent spectral gap observed in Figs. 3(b,e). To investigate this, we grow a Bi2Te3 film with a nominal ~0.1 QL coverage, which effectively results in the formation of nano-islands of Bi2Te3 scattered across the Bi-2212 surface [Figs. 4(a),5(a)]. Importantly, this process exposes the substrate to the growth conductions and allows us to characterize both materials simultaneously using the same STM tip. We focus on a region of the sample spanning one of the Bi2Te3 nano-islands and the substrate [ Fig. 4(a)]. dI/dV measurements of the exposed Bi-2212 surface reveal a V-shaped gap [ Fig. 4(b,c)], nearly identical to that observed on the surface of as-cleaved B-2212 20 , which allows us to conclude that the deposition of Bi2Te3 does not significantly alter superconductivity of the Bi-2212 surface layers.
Importantly, films of reduced coverage below 1 QL enable us to investigate bonding of the two materials at the interface. We analyze STM topographs in more detail to extract their topographic height with respect to the substrate [ Fig. 5(a)]. Interestingly, we find the apparent height of all 1 QL Bi2Te3 islands to be ~1.2 nm with respect to Bi-2212 [ Fig. 5(d)], ~20% taller than the expected ~1 nm height for a single QL of Bi2Te3. The same result is confirmed in a film with a nearly complete 1 QL coverage, where the island height is also found to be ~20% larger than expected [ Fig. 5(b,e)]. To demonstrate that our STM scanner has been properly calibrated, we plot the topographic height profile across a step in the 2 QL thick film with respect to the Bi2Te3 layer below, which shows the expected step height of ~1 nm [ Fig.  5(c,f)]. As STM topographs contain both electronic and structural information, to provide evidence that this height difference is of structural origin, and not purely due to the variation in electronic density of states, we provide the following pieces of evidence. First, the same island height is extracted from topographs acquired at both positive and negative STM bias [ Fig. S3]. Second, 1 QL Bi2Te3 nano-islands grown on a superconductor Fe(Te,Se) and on an insulator SrTiO3(001), two materials that are electronically very different, yield a ~1 nm step height in both cases [ Fig. S4]. To explain the larger height of the first Bi2Te3 layer with respect to the Bi-2212 substrate, we postulate that there may be an inter-growth layer forming at the interface [ Fig. 5(g-i)]. This has occasionally been observed at the interface of other van der Waals heterostructures 28 .
We examine the consequences of this imperfect interface in the context of TI/SC heterostructures. A crucial insight comes from investigating the electronic properties of Bi2Te3 nano-islands themselves [ Fig.  6(a,b)]. The average dI/dV spectrum acquired on a small island with ~10 nm diameter [ Fig. 6(a)] shows a markedly different shape compared to that observed on a much larger flat terrace of 1 QL Bi2Te3 film [ Fig. 3]. We observe a hard gap spanning the Fermi level with ~150 meV magnitude, much larger than 2ΔSC of Bi-2212. A gap as large as several hundred meV can be seen on other islands, thus ruling out the superconducting origin of the gap.
Given the additional barrier at the interface we have discovered and the finite size of the system, a natural explanation for the gap could be understood in terms of a Coulomb blockade (CB) gap 29 , which arises due to single electrons exchanging energy with the environment as they tunnel through a barrier 30,31 . The CB effect has been widely reported in tunneling measurements of finite-size heterostructures when there is an extra barrier at the interface of the two materials sandwiched together [32][33][34][35] . It can be modeled by a double tunnel junction, one being the tip-sample junction and the other one being the sample-substrate junction, each consisting of a capacitor and a resistor connected in parallel [ Fig. 6(d)]. The overall size of the CB gap (ΔCB) is roughly inversely proportional to the capacitance between the film and the substrate (C2) 32,33 . The shape of the gap will change depending on the resistive component at the film-substrate junction (R2), where large R2 would lead to a sharp-cutoff in conductance at the gap edge, while smaller R2 would lead to a gradual suppression of conductance approaching zero energy 32,33 .
In small Bi2Te3 islands, due to large C2 and small R2, we observe a sharp CB gap [ Fig. 6(a)]. As the size of the island increases (C2 should become smaller and R2 larger), ΔCB is expected to evolve into a smaller Vshaped gap 32,33 . This is exactly what we observe in our data [ Fig. 6(b)]. As the islands grow even larger and start to connect, the V-shape gap-feature becomes progressively more subdued [ Fig. 6(c)]. We note that Bi2Te3 films inevitably contain domains due to structural mismatch between Bi2Te3 and Bi-2212, observed in reflection high-energy electron diffraction (RHEED) images [ Fig. S1(b)] and in real space [ Fig.  S1(a)], which lead to the finite size effects as seen in STM/S measurements, even as the islands merge together in one or more QL thick films. Therefore, the CB effect will be present in thicker films [ Fig. 3(e)], and the gap-like feature observed in our measurements in thicker films is most likely a simple consequence of this phenomenon, not proximity-induced superconductivity.

Discussion and outlook:
Our measurements resolve the outstanding controversy between ARPES and STM measurements of MBE-grown heterostructures of topological materials and cuprates, by shedding light on an overlooked aspect of underlying physics in these systems. Due to the additional barrier at the interface between Bi2Te3 and Bi-2212, tunneling measurements of Bi2Te3 exhibit a CB gap, as large as a few hundred meV in the smallest Bi2Te3 islands. As the size of the islands increases, this leads to the mitigation of the CB effect, and a much smaller V-shaped gap in the nearly continuous (but with inevitable domains) Bi2Te3 films of one or more QL thickness. We note that the complex structure of additional peaks in dI/dV spectra outside the gap [ Fig. 6(a)] may be due to quantized bound states within the islands [ Fig. S5], similarly to what had been observed in quantum dots 36 . Another explanation for these peaks may be due to the capacitive coupling between the tip and the island 35 , which could be explored in future experiments and analysis. However, a quantitative understanding of each peak position is beyond the scope of this paper. Finally, our work cautions the interpretation of gap-like features in tunneling measurements of complex heterostructures with inaccessible, buried interfaces.

Methods:
Bulk Bi2Sr2CaCu2O8+x (Bi-2212) single crystals were attached to our sample holder using H20E silver epoxy (EPO-TEK), and heated in ultra-high vacuum (UHV) prior to cleaving in order to minimize the surface contamination during outgassing. After cleaving in UHV, the substrates were brought back to the growth temperature ranging from ~170 to ~250 °C. To grow Bi2Te3 films, high purity Bismuth (99.999%) and Tellurium (99.99%) were co-evaporated from Knudsen cells (Sentys Inc) in a nominal flux ratio of ~1:10 Bi:Te determined by quartz crystal microbalance (QCM). Based on the Bismuth flux rate, the Bi2Te3 growth rate is calculated to be approximately 4 minutes per quintuple layer. RHEED (Sentys Inc) is used to monitor the quality of the surface before, during and after Bi2Te3 deposition. Our RHEED patterns show streaky lines [ Fig. 1(e)], indicating a layer-by layer deposition consistent with previous work 37 . After the sample had been cooled to room-temperature, we transferred it to the STM using a vacuum suitcase held at 10 -11 mbar base pressure. This step ensures that our samples are never exposed to air and that the surface remains pristine, from growth to preforming STM measurements. STM/S data were acquired using a Unisoku USM1300 STM at the base temperature of ~4.5 K. Spectroscopic measurements were acquired using a standard lock-in technique at 915 Hz frequency, with bias excitation ranging from ~1 to 10 mV as detailed in figure captions. The STM tips used were homemade chemically-etched tungsten tips that are annealed in vacuum prior to STM imaging.