Gate-tunable resistance drops related to local superconducting gaps in thin TaS₂ layers on SrTiO₃ 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 (V_bg) tunable dielectric constant (e.g., ε ∼ 10⁴ at T = 2 K) through all T regimes due to strong quantum fluctuation^1–3 and (2) specified surface states.^5,6 These create abundant high-T physical phenomena, such as high transition temperatures (T_c) superconductivity, novel quantum Hall states (quantum Hall topological insulators), and Majorana zero-bias states^1–8 (the supplementary material, 1), which arise from the introduction of (1) the high charge carrier density n_D and (2) the unique two-dimensional (2D) electronic states into the interfaced materials, respectively. Among those, high-T_c superconductivity is of great interest because of the discovery of T_c [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 T_c 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 T_c depends on a number of physical factors, such as n_D, 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 n_D.^9–13 For instance, T_c increased up to 2 K as d decreased to ∼3 nm from ∼15 nm (bulk with T_c ∼ 0.7 K) in conventional non-doped 2H structures without applying V_bg.⁹ Because the interlayer CI is weak, the T_c 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 (E_F) with the vHS.^{19,21,31–33} Moreover, a significant increase in T_c 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., T_c (∼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 NbSe₂^14–16 and heavily doped MoS₂ (Ising superconductivity).^17,18

Without applying pressure, in all cases, the maximum (onset) T_c 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 T_c has been rarely investigated, even for the STO substrate.

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 E_2g and A_1g 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, V_bg, and out-of-plane magnetic fields (B) were measured by Dyna Cool (Quantum Design) using a lock-in amplifier, applying V_bg 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.

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 V_bg = +30 V and B = 0. As T decreases, R monotonically decreases and abruptly drops below critical T (T_CR) ∼ 10 K (shown in the red arrow). Figure 2(b) presents the V_bg dependence of the R–T feature shown in Fig. 2(a). This figure reveals an accurate T_CR of ∼ 3.8 K at V_bg = 0 V (shown in the red arrow) and its shift to a higher T with increasing V_bg (i.e., to a T_CR of ∼ 6 K at V_bg = +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 T_CR ∼ 5.8 K at V_bg = 0 V (red arrow) with the second abrupt R drop at T_CR ∼ 4 K (blue arrow), which increases as V_bg increases, resulting in the highest T_CR ∼ 9 K at V_bg = +30 V. The T_CR values are higher than those in Fig. 2(b) at individual values of V_bg. The normalized R value drops by a factor of four from the T_CR to T = 2 K at V_bg = +30 V. The T_CR as a function of d, including the results in Figs. 2(c) and 2(d) at V_bg = +30 V, is demonstrated in Fig. 2(d). It is clear that the T_CR monotonically increases with decreasing d. When the T_CR values are compared with the onset T_c for superconductivity in (atomically)thin TaS₂, the highest T_CR values of ∼ 6 K (sample A) and ∼9 K (sample B) are approximately three and five times higher than the highest onset T_c 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

Here, the R drops are gradual below the T_CR, 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 V_bg = +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 T_ΔC = 6 K and the Δ ∼ 0.4 mV with smearing at T = 2 K. V_bg and position dependence of Δ at T = 2 K are shown in Fig. 3(c). Δ ∼ 1 and ∼0.1 mV for V_bg = +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 T_ΔC = 6 K in Fig. 3(a) is also at least three times higher than previous reports of the T_c in TaS₂ under no pressure. Reduction of the Δ values from V_bg = 30–0 V qualitatively agrees with those in the T_CR [Fig. 3(e)]. This also implies the strong correlation of the T_CR with the onset T_c.

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.

Figures 4(a) and 4(b) show R vs V_bg relationships for different T at B = 0 T in sample B (the supplementary material, 5). R increases as V_bg decreases in the +V_bg region for all T regions in Fig. 4(b). For +V_bg > ∼3 V, R monotonically decreases with a decrease in T, whereas for +V_bg < ∼3 V, R becomes insensitive to T change at T > 4 K as +V_bg 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 T_c in the lower V_bg region. In contrast, the T dependence of the R vs V_bg relationships suggests transitions to the possible CDW phase (the supplementary material, 6) in the −V_bg region, particularly at V_bg < ∼−7 V [Fig. 4(a)].

Figures 4(c) and 4(d) demonstrate the R vs V_bg 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 V_bg, whereas the B_⊥ dependence of R reveals a different tendency around V_bg ∼ 10 V in the +V_bg region. At V_bg > ∼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 V_bg < ∼10 V. For the −V_bg 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 V_bg = 0 V and +V_bg regions in Fig. 4(e), including that for V_bg = +30 V shown in sample A. R values monotonically and gradually increase with increasing B_⊥ and drastically increase above B_⊥ ∼ 2 T for V_bg = 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 V_bg = 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 T_CR 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 T_c ∼ 10 K through 2Δ/k_BT_c = 3.5 for the conventional gap equation for superconductivity. Because this T_c ∼ 10 K value is in good agreement with T_CR ∼ 9 K at V_bg = +30 V in Fig. 3, it implies a strong possibility that T_CR can be the onset T_c. 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 V_bg 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 T_c (i.e., T_CR) 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 E_F with it by decreasing d to the 2D limit^9,19(the supplementary material, 7). This mechanism can qualitatively correspond to the present case because T_c increases with decreasing d. Moreover, the work, which reported the significant increase in T_c 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 T_c despite applying no pressure, the two regimes have been distinctly separated by applying V_bg in the present samples using the STO substrate with a high ε. CDW might be caused only in the −V_bg region via hole doping in this case. Thus, the comparison is difficult.

In addition to this repulsive-CI based model, the much higher onset T_c observed in the present structure can originate from the large ε of the STO substrate, i.e., (1) the large n_D doping by applying V_bg to the high-ε STO substrate and (2) screening of the long-range CI by the high n_D. 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 V_bg to the high-ε STO substrate dopes large n_D into the thin TaS₂. Indeed, the estimated n_2D ∼ 10¹⁴ cm⁻² at V_bg = +30 V and T = 2 K in sample B is almost equivalent to the lowest case of an extremely large n_2D of the Li-ion intercalated 1T–TaS₂. However, the onset T_c was still below 2 K even at n_2D > ∼2 × 10¹⁴ in the Li-doped TaS₂, while the present onset-T_c 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 n_2D, 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 n_D region (>∼1.3 × 10¹⁴ cm⁻²) and did not explain the decrease in T_c 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 NbSe₂^14–16 mentioned in Sec. I), it is more appropriate for the present results, which show the maximum n_D < ∼1 × 10¹⁴ cm⁻² and the increase in T_c 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 ≫ r_s, the usual ∼e²/ɛr CI is replaced by the more quickly decaying ∼$e2rs2/εr3$⁠, where r_s is the screening radius. The value of r_s depends inversely on the EDOS υ, as r_s = 2πɛ/(e²υ), so increasing the υ by V_bg produces an increasingly prominent truncation of the CI. Naively inserting the large ɛ of STO into the formula for r_s yields a very long r_s, 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 r_s 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 $εq=ε(0)/1+qξ2$⁠, 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 V_bg-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 T_ΔC, which is about three-times higher than previous reports of T_c in thin TaS₂ layers under absent pressure, and the strong position dependence of Δ. Its correlation with T_CR for V_bg and B_⊥ changes suggested a strong possibility that the observed R drops could be attributed to superconductivity. When the observed T_RC corresponds to the onset T_c of superconductivity, it is enhanced approximately five times under the applied V_bg, compared with the previous highest-onset T_c values under no pressure. The high onset T_c and Δ were discussed based on screening of the long-range CI due to the high-ε of SrTiO₃ with applying V_bg.

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 T_c. Because of the solid-state and V_bg-tunable high-ε substrates, the present STO method of attaching mechanically exfoliated thin layers offers the promise of wide application of high-T_c 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.

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.