Strontium titanate [SrTiO3 (STO)], a perovskite oxide with an extremely high gate-tunable dielectric constant (ε) due to quantum paraelectric phases, is attracting considerable attention for yielding various physical phenomena when two-dimensional (2D) layers are integrated. Superconductivity is such a typical phenomenon. However, the influence of the STO substrates on enhancing transition temperatures (Tc) for (atomically) thin 2D flakes attached to them has been rarely investigated. Here, we report gate-tunable and gradual four-terminal resistance drops with critical onset T (TCR) and scanning tunneling spectroscopy (STS) spectra in devices comprising thin TaS2 flakes attached on monolayer hexagonal boron nitride (hBN) spacer/STO substrates. Observation of STS spectra confirms the presence of local superconducting gaps Δ (∼1.5 meV) with transition T (TΔC) three-times higher than previous reports of Tc under absent pressure and strong position dependence of Δ. Depending on Δ on back gate voltages (Vbg) and magnetic fields, there is a strong correlation between TCR and the onset Tc of superconductivity, implying an enhancement of approximately five times compared with the previous highest-onset Tc values without pressure as the applied Vbg increases. The high onset Tc and Δ are discussed based on screening of the long-range Coulomb interaction (CI) due to the high-ε of SrTiO3, while the short-ranged CI remains strong in the 2D limit, causing the superconductivity. Using a monolayer hBN/SrTiO3 substrate with Vbg opens doors to Tc enhancement in thin superconducting layers integrated on it and wide application due to the solid-state high-ε substrates.
Strontium titanate [SrTiO3 (STO)],1–8 a perovskite oxide with quantum paraelectric phases at low temperature (T), is attracting considerable attention because of (1) an anomalously large and back gate-voltage (Vbg) tunable dielectric constant (e.g., ε ∼ 104 at T = 2 K) through all T regimes due to strong quantum fluctuation1–3 and (2) specified surface states.5,6 These create abundant high-T physical phenomena, such as high transition temperatures (Tc) superconductivity, novel quantum Hall states (quantum Hall topological insulators), and Majorana zero-bias states1–8 (the supplementary material, 1), which arise from the introduction of (1) the high charge carrier density nD and (2) the unique two-dimensional (2D) electronic states into the interfaced materials, respectively. Among those, high-Tc superconductivity is of great interest because of the discovery of Tc [owing to (2)] as high as ∼100 K in mono-atom layer FeSe directly grown on the STO substrate.5 However, the influence of the STO substrates on enhancing Tc for (atomically) thin 2D flakes, which are mechanically exfoliated and attached to the substrates, has been rarely investigated.
On the other hand, superconductivity in various (atomically) thin 2D layers, which were mechanically exfoliated and attached to a silicon oxide (SiO2)/silicon substrate, has been widely researched from many perspectives.9–20 Enhancement of Tc depends on a number of physical factors, such as nD, layer number (the thickness d), and in-plane or interlayer Coulomb interaction (CI).
The thin transition metal dichalcogenide (TMDC), titanium disulfide (TaS2), exhibits such superconducting characteristics in both its 1T- and 2H-phases, indirectly competing with charge density wave (CDW) states depending on nD.9–13 For instance, Tc increased up to 2 K as d decreased to ∼3 nm from ∼15 nm (bulk with Tc ∼ 0.7 K) in conventional non-doped 2H structures without applying Vbg.9 Because the interlayer CI is weak, the Tc was enhanced by increasing the 2D electronic density of states (EDOS), which is caused by the growth of a van Hove singularity (vHS) driven by in-plane strong repulsive CI [i.e., Luttinger liquid (LL) states] and the alignment of the Fermi level (EF) with the vHS.19,21,31–33 Moreover, a significant increase in Tc up to 8.5 K was observed in 2H–TaS2 when a pressure of 9.5 GPa was applied.34
In contrast, gate-controlled Li-ion heavy intercalation into the 1T structure demonstrated contradictory results, i.e., Tc (∼2 K) decreased with decreasing d and the superconducting phase finally disappeared at d ∼ 3 nm, whereas nearly commensurate CDW and Mott insulating phases became dominant.20 This situation is analogous to the case of Bardeen–Cooper–Shriffer (BCS) superconductivity in systems with strong interlayer coupling, such as NbSe214–16 and heavily doped MoS2 (Ising superconductivity).17,18
Without applying pressure, in all cases, the maximum (onset) Tc in TaS2 flakes attached to SiO2/Si substrates was limited below ∼2 K, except for some specified cases.11,12 In particular, the influence of the substrates on enhancing Tc has been rarely investigated, even for the STO substrate.
A. Sample preparation and characterization
In the present experiment, thin 1T–TaS2 flakes were attached to a mono-layer hexagonal boron nitride (hBN) spacer atop an STO substrate [Figs. 1(a)–1(c)] (Methods and the supplementary material, 2). The thickness d of TaS2 flakes was confirmed by Raman spectroscopy [via E2g and A1g peaks in Fig. 1(c)] and atomic force microscopy (AFM) (the supplementary material, 2). The STO substrates used here have large surface roughness at some points, which may lead to non-zero resistance (R) at T = 2 K, as shown later (the supplementary material, 2). Four-terminal Au/Ti electrodes with 500 nm space between two electrodes for R observation [e.g., white arrow in Fig. 1(a)] were formed on the flakes using conventional electron-beam lithography methods to detect the small superconducting area [Fig. 1(b)] (the supplementary material, 3). Before electrode evaporation, the surface of TaS2 was slightly etched by the Ar ion to avoid the influence of oxidation. Four-terminal R as functions of T, Vbg, and out-of-plane magnetic fields (B) were measured by Dyna Cool (Quantum Design) using a lock-in amplifier, applying Vbg from the back side of the STO substrate [Fig. 1(b)], without applying pressure. Positions used for observation of scanning tunneling spectroscopy (STS) spectra are shown in the numbers ①–⑤.
B. Observation of four-terminal resistance drops
Figure 2(a) shows the four-terminal R of a sample with d ∼ 8 nm (sample A) as a function of T (i.e., from a T of 300–2 K) with Vbg = +30 V and B = 0. As T decreases, R monotonically decreases and abruptly drops below critical T (TCR) ∼ 10 K (shown in the red arrow). Figure 2(b) presents the Vbg dependence of the R–T feature shown in Fig. 2(a). This figure reveals an accurate TCR of ∼ 3.8 K at Vbg = 0 V (shown in the red arrow) and its shift to a higher T with increasing Vbg (i.e., to a TCR of ∼ 6 K at Vbg = +40 V).
In contrast, Fig. 2(c) demonstrates a similar dependence in sample B with a smaller thickness (d ∼ 3 nm). It also implies the evident TCR ∼ 5.8 K at Vbg = 0 V (red arrow) with the second abrupt R drop at TCR ∼ 4 K (blue arrow), which increases as Vbg increases, resulting in the highest TCR ∼ 9 K at Vbg = +30 V. The TCR values are higher than those in Fig. 2(b) at individual values of Vbg. The normalized R value drops by a factor of four from the TCR to T = 2 K at Vbg = +30 V. The TCR as a function of d, including the results in Figs. 2(c) and 2(d) at Vbg = +30 V, is demonstrated in Fig. 2(d). It is clear that the TCR monotonically increases with decreasing d. When the TCR values are compared with the onset Tc for superconductivity in (atomically)thin TaS2, the highest TCR values of ∼ 6 K (sample A) and ∼9 K (sample B) are approximately three and five times higher than the highest onset Tc of 2 K without pressure.9,10 They are also larger than those even in highly disordered (∼4 K) or oxygenated (∼3 K) TaS2.11,12
C. STS spectra confirming local superconducting gaps
Here, the R drops are gradual below the TCR, with non-zero R values at T = 2 K. In order to confirm the origin, STS spectra have been measured at seven local points of flake B [Fig. 1(a) and the supplementary material, 4]. The results are shown in Fig. 3. The T-dependence of dI/dV vs V is shown for Vbg = +30 V at the local position ①, which is one of the positions exhibiting Δ [①, ①′, ③–⑤ in Fig. 1(a)], in Fig. 3(a). The dI/dV gap Δ starts to appear at T = 10 K and increases as T decreases, resulting in the entire Δ reaching 0 Ω at TΔC = 6 K and the Δ ∼ 0.4 mV with smearing at T = 2 K. Vbg and position dependence of Δ at T = 2 K are shown in Fig. 3(c). Δ ∼ 1 and ∼0.1 mV for Vbg = +30 and 0 V, respectively, can be confirmed at the local position ①. The dependence of Δ at T = 2 K on perpendicular magnetic fields (B⊥) is shown in Fig. 3(d). The magnitude of Δ decreases with increasing B⊥ (particularly from 2 T) and disappears around B⊥ = 4 T. These behaviors are in qualitatively good agreement with those in previous reports of superconductivity in TaS2, and, thus, suggest that the observed Δ corresponds to the local superconducting gaps.
The TΔC = 6 K in Fig. 3(a) is also at least three times higher than previous reports of the Tc in TaS2 under no pressure. Reduction of the Δ values from Vbg = 30–0 V qualitatively agrees with those in the TCR [Fig. 3(e)]. This also implies the strong correlation of the TCR with the onset Tc.
In contrast, Δ disappears at different positions ② and ②′, where it is located ∼200 nm away from ① [Figs. 1(a) and 3(c)]. We confirmed such strong position dependence of Δ at seven random points as mentioned above. This result suggests that one of the main reasons for the non-zero R drops is a non-uniform and local superconducting transition owing to the large local-roughness of the STO surface (the supplementary material, 2) or strain. It obstructs the appearance of the homogeneous superconducting transition (arising from the screening of CI as discussed later) over entire parts between the two electrodes (within a 500 nm distance) used for the R measurements [Fig. 1(b)].24,25 Because the superconducting regions with Δ only locally emerge such as islands and cannot connect the two electrodes at T = 2 K, the non-superconducting regions obstruct the appearance of the R drop down to 0 Ω.
D. Vbg and B dependence of resistances
Figures 4(a) and 4(b) show R vs Vbg relationships for different T at B = 0 T in sample B (the supplementary material, 5). R increases as Vbg decreases in the +Vbg region for all T regions in Fig. 4(b). For +Vbg > ∼3 V, R monotonically decreases with a decrease in T, whereas for +Vbg < ∼3 V, R becomes insensitive to T change at T > 4 K as +Vbg decreases and becomes almost constant, resulting in the largest R drop between T = 3 and 4 K. These results are in good agreement with those shown in Fig. 2(d), which showed a decrease in the onset Tc in the lower Vbg region. In contrast, the T dependence of the R vs Vbg relationships suggests transitions to the possible CDW phase (the supplementary material, 6) in the −Vbg region, particularly at Vbg < ∼−7 V [Fig. 4(a)].
Figures 4(c) and 4(d) demonstrate the R vs Vbg relationships for different B⊥ at T = 2 K in sample B (the supplementary material, 5). In Fig. 4(c), R values monotonically increase for all B⊥ with decreasing Vbg, whereas the B⊥ dependence of R reveals a different tendency around Vbg ∼ 10 V in the +Vbg region. At Vbg > ∼10 V, R monotonically increases as B⊥ increases, whereas R values at B⊥ = 0 and 2 T become the highest and smallest values, respectively, except for the R at B⊥ = 3 T at Vbg < ∼10 V. For the −Vbg region in Fig. 4(c), these R tendencies are still maintained, although the B⊥ dependence becomes much weaker except for the R value at B⊥ = 2 T (the supplementary material, 6).
R vs B⊥ relationships at T = 2 K in sample B are shown for the Vbg = 0 V and +Vbg regions in Fig. 4(e), including that for Vbg = +30 V shown in sample A. R values monotonically and gradually increase with increasing B⊥ and drastically increase above B⊥ ∼ 2 T for Vbg = 10–30 V. They saturate at B⊥ = ∼4 T. These results are in qualitatively good agreement with those in Fig. 3(b), suggesting a close correlation with superconductivity. On the other hand, R at Vbg = 0 V shows quite different behavior due to the influence of the CDW.
We have shown the observation of the gradual R decrease starting from TCR with decreasing T and resulting in a non-zero value at T = 2 K (Fig. 2) and the corresponding local STS signals Δ (Fig. 3). As shown in Fig. 3(b), the calculation result for Δ using the Dynes model [Eq. (1)] was in good agreement with the observed STS result at T = 0.5 K, with the best fitting values for Δ ∼ 1.5 meV and Γ ∼ 5 × 10−2. The value of Δ ∼ 1.5 meV corresponds to Tc ∼ 10 K through 2Δ/kBTc = 3.5 for the conventional gap equation for superconductivity. Because this Tc ∼ 10 K value is in good agreement with TCR ∼ 9 K at Vbg = +30 V in Fig. 3, it implies a strong possibility that TCR can be the onset Tc. This result means that R cannot abruptly drop to 0 Ω over the entire area between the electrodes, even when the local Δ opens in the present material. The gradual R drops with decreasing T reflect just the gradual R decrease due to the metallic conductivity in the area outside the local points with Δ. The best fitting parameter Γ ∼ 5 × 10−2 also indicates that geometrical factors (e.g., disorder, oxidization), which introduce a large Γ, are not large in some positions of the present TaS2 flakes.
As possible origins for the gradual R drops other than superconductivity, charge fluctuation originating from the STO substrate with high dependence on Vbg might be the most probable, because such gradual R drops starting from a high T regime were not observed in our TaS2 flakes attached to a SiO2/Si substrate. Indeed. STO has quantum fluctuations in the low T region, as mentioned in the introduction. However, because it does not lead to the observed local Δ in STS, it is not associated with the gradual R drops. Thus, superconductivity has one of the highest possibilities.
Based on this, we discuss the correlation of superconductivity with the observed onset of Tc (i.e., TCR) enhancement. One of the origins of this TaS2 superconductivity on SiO2/Si substrates could be the growth of a vHS driven by in-plane strong repulsive CI and the alignment of EF with it by decreasing d to the 2D limit9,19(the supplementary material, 7). This mechanism can qualitatively correspond to the present case because Tc increases with decreasing d. Moreover, the work, which reported the significant increase in Tc up to 8.5 K in 2H–TaS2 under a pressure of 9.5 GPa,34 also found that, unexpectedly, CDW and superconductivity could coexist in a large part of the phase diagram when applying pressure. Although observation of such an interaction between CDW and superconductivity is highly interesting in the present system because our samples have a similar onset Tc despite applying no pressure, the two regimes have been distinctly separated by applying Vbg in the present samples using the STO substrate with a high ε. CDW might be caused only in the −Vbg region via hole doping in this case. Thus, the comparison is difficult.
In addition to this repulsive-CI based model, the much higher onset Tc observed in the present structure can originate from the large ε of the STO substrate, i.e., (1) the large nD doping by applying Vbg to the high-ε STO substrate and (2) screening of the long-range CI by the high nD. The first term is analogous to that in the gate-controlled Li-ion heavy intercalation into 1T–TaS2.10 In the present case, applying large Vbg to the high-ε STO substrate dopes large nD into the thin TaS2. Indeed, the estimated n2D ∼ 1014 cm−2 at Vbg = +30 V and T = 2 K in sample B is almost equivalent to the lowest case of an extremely large n2D of the Li-ion intercalated 1T–TaS2. However, the onset Tc was still below 2 K even at n2D > ∼2 × 1014 in the Li-doped TaS2, while the present onset-Tc is much higher than 2 K. Thus, the second term becomes important as follows:
Enhancement of superconductivity by screening of the long-range CI was reported as a model to explain the appearance of the superconductivity in heavily doped MoS2 layers.17 The superconductivity was mediated by the short-range, intermittently repulsive CI. When it is assumed that the long-range CI was strongly screened by the high n2D, which was brought about by heavy doping via the ionic-liquid gate, the effect of the short-range repulsive CI was enhanced, resulting in the emergence of superconductivity. A similar mechanism can work in our devices since the long-ranged part of the CI between electrons in TaS2 is effectively screened by the large ε of the STO substrate.26
Indeed, the long-range CI was screened by the large ε of the STO substrate in the graphene/few-layer hBN/STO substrate, resulting in the appearance of the quantum Hall (QH) topological insulating phase (i.e., a copy of two QH phases)4,25,26 (the supplementary material, 1). Although this model17 was not available for the extremely high nD region (>∼1.3 × 1014 cm−2) and did not explain the decrease in Tc observed in such regions (e.g., decreasing d) in the heavily doped MoS2 layers18 (similar to the cases for the Li-ion intercalated TaS210 and interlayer-coupled NbSe214–16 mentioned in Sec. I), it is more appropriate for the present results, which show the maximum nD < ∼1 × 1014 cm−2 and the increase in Tc with decreasing d.
We show another estimation of this model as follows: In general, in a conducting 2D electron gas, the long-ranged part of the CI is screened by the Fermi sea, such that at distances r ≫ rs, the usual ∼e2/ɛr CI is replaced by the more quickly decaying ∼, where rs is the screening radius. The value of rs depends inversely on the EDOS υ, as rs = 2πɛ/(e2υ), so increasing the υ by Vbg produces an increasingly prominent truncation of the CI. Naively inserting the large ɛ of STO into the formula for rs yields a very long rs, which would be irrelevant at the scale of the electron–electron separation. However, the relevant ɛ is likely to be smaller due to strain and inhomogeneity at the STO surface [Figs. 1(a)–1(c)], which stiffens the transverse optical phonon mode.27–29 In this case, the value of rs may not be too large, so electronic screening of the long-range CI can be relevant.
Moreover, the short-ranged part of the CI itself may still be relatively large in magnitude due to the dependence of the ε on the wave vector q. In particular, the ε of STO varies with q as , where ξ ≈ 2.6 nm (as can be seen by looking at the dispersion of the transverse optical phonon mode in STO30). Consequently, the CI is much larger in magnitude at distances shorter than ξ.
The observed gradual R decreases with the local Δ suggest that this screening of the long-range CI cannot homogeneously emerge between the two electrodes measured, owing to the large surface-roughness of the STO substrate (or strain) (the supplementary material, 2), as T decreases.25 Moreover, the relatively T-independent ε of the STO substrate below T ∼ 10 K, due to the softening of ferroelectricity and quantum fluctuations, partially contributes to this mechanism.1–3 We also reveal that the monolayer BN spacer plays a definitively important role in addition to the simple physical isolation between the STO and TaS2 flakes (the supplementary material, 8).
We reported the Vbg-tunable gradual four-terminal R drops and STS spectra in thin TaS2 flakes/monolayer hBN/STO substrates. Observation of the STS spectra confirmed the presence of the local Δ (∼1.5 meV at T = 0.5 K) with TΔC, which is about three-times higher than previous reports of Tc in thin TaS2 layers under absent pressure, and the strong position dependence of Δ. Its correlation with TCR for Vbg and B⊥ changes suggested a strong possibility that the observed R drops could be attributed to superconductivity. When the observed TRC corresponds to the onset Tc of superconductivity, it is enhanced approximately five times under the applied Vbg, compared with the previous highest-onset Tc values under no pressure. The high onset Tc and Δ were discussed based on screening of the long-range CI due to the high-ε of SrTiO3 with applying Vbg.
Further improvement [e.g., using a thinner STO substrate (≪0.5 mm) with a highly uniform surface and no strain] must lead to a full superconducting transition over a large area with a higher Tc. Because of the solid-state and Vbg-tunable high-ε substrates, the present STO method of attaching mechanically exfoliated thin layers offers the promise of wide application of high-Tc materials.
See the supplementary material for further explanation and experiment details. Fabrication and characterization, STS observation, 3D maps of T vs Vbg for R and B vs Vbg for R, and result without hBN layer.
We thank K. Otsuka, J. Oka, S. Noda, S. Murakami, K. Nomura, T. Yamamoto, S. Tarucha, T. Ando, T. Enoki, R. Wu, J. J. Palacios, and A. H. MacDonald for their fruitful discussions and encouragement. This work performed at Aoyama Gakuin University was supported by the Aoyama Gakuin University Research Institute grant program for the creation of innovative research. The part of work at the University of Tokyo was also supported by JSPS KAKENHI (Grant Nos. JP20H05660, JP19J01737, and JP20K14384 for K.K. and K.H., JP20H02599 for T.K., JP20H00220 for S.M., and JP19H05600 for E.S.), and by JST, CREST (Grant Nos. JPMJCR20B5, Japan for S.M., JP19H05600 and JP20H02599 for E.S.), and the Institute for AI and Beyond of the University of Tokyo for E.S.
Conflict of Interest
The authors have no conflicts to disclose.
M.K., R.O., K.S., and R.I. fabricated the TaS2/hBN/STO heterostructure FET and performed all the measurements. K.K. and S.D. supported FET fabrication. T.K., T.Y., and E.S. supported low-T measurements. M.K. and J.H. analyzed the data. Y.S., S.M., K.H., and J.H. supervised the project. M.K., B.S., and J.H. wrote the paper with the input of all co-authors.
M. Kosugi: Investigation (equal). R. Obata: Investigation (equal). K. Suzuki: Investigation (equal). K. Kuroyama: Supervision (equal). S. Du: Supervision (equal). B. Skinner: Supervision (equal); Writing – original draft (equal). T. Kikkawa: Supervision (equal). T. Yokouchi: Supervision (equal). Y. Shiomi: Supervision (equal). S. Maruyama: Supervision (equal). K. Hirakawa: Supervision (equal). E. Saitoh: Supervision (equal). J. Haruyama: Project administration (lead); Supervision (lead); Writing – original draft (equal); Writing – review & editing (equal).
The data that support the findings of this study are available within article and its supplementary material.