Indium-contacted van der Waals gap tunneling spectroscopy for van der Waals layered materials

The electrical phase transition in van der Waals (vdW) layered materials such as transition-metal dichalcogenides and Bi2Sr2CaCu2O8+x (Bi-2212) high-temperature superconductor has been explored using various techniques, including scanning tunneling and photoemission spectroscopies, and measurements of electrical resistance as a function of temperature. In this study, we develop one useful method to elucidate the electrical phases in vdW layered materials: indium (In)-contacted vdW tunneling spectroscopy for 1T-TaS2, Bi-2212 and 2H-MoS2. We utilized the vdW gap formed at an In/vdW material interface as a tunnel barrier for tunneling spectroscopy. For strongly correlated electron systems such as 1T-TaS2 and Bi-2212, pronounced gap features corresponding to the Mott and superconducting gaps were respectively observed at T = 4 K. We observed a gate dependence of the amplitude of the superconducting gap, which has potential applications in a gate-tunable superconducting device with a SiO2/Si substrate. For In/10 nm-thick 2H-MoS2 devices, differential conductance shoulders at bias voltages of approximately ± 0.45 V were observed, which were attributed to the semiconducting gap. These results show that In-contacted vdW gap tunneling spectroscopy in a fashion of field-effect transistor provides feasible and reliable ways to investigate electronic structures of vdW materials.

Van der Waals (vdW) layered materials such as two-dimensional (2D) transition-metal dichalcogenides (TMDCs) and Bi 2 Sr 2 CaCu 2 O 8+x (Bi-2212) have shown various electronic phases that emerge from many-body features such as a charge density wave (CDW) or superconductivity, depending on the temperature and carrier density [1][2][3][4][5][6][7][8][9] . The vdW interface between dissimilar vdW materials have allowed to investigate the electronic structures of such strongly correlated electron systems. For instance, transport spectroscopy in TMDC/Bi-2212 vdW junctions has revealed gap natures due to the many-body features via the formation of a metal/superconductor proximity junction with a low vdW contact resistance 10,11 . For tunneling spectroscopy, on the other hand, a graphite/Bi-2212 interface provided a vdW gap tunnel junction, enabling tunneling spectroscopy for the Bi-2212 superconductor 11,12 . However, it could be hard to apply the graphite to TMDCs for vdW tunneling spectroscopy because graphene/TMDC contacts have been used to form an Ohmic contact 13 . Thus, for feasible and reliable tunneling spectroscopy for vdW materials, it is crucial to seek a material to form a vdW tunneling gap with any vdW materials. With this purpose, we focus on indium (In) metal in this study.
For evaporated-metal/TMDC contacts, only indium (In) metal has shown vdW contact for TMDCs 14,15 , owing to its low evaporation temperature of ~ 500 °C. In this case, the In vdW contact provides an Ohmic contact for a few-layer TMDCs. However, the vdW contact at a cryogenic temperature could provide a vacuum tunneling gap with a high contact resistance that makes the flow of current sensitive to the electronic DOS at the interface. Indeed, vdW gap tunneling spectroscopy based on a field-effect transistor (FET) design with carbon nanotubes (CNTs) with In metal contacts was demonstrated, recently 16,17 . In this previous work, the local conductance peaks observed in the conductance vs bias voltage plot were shown to originate from the van Hove singularities corresponding to the sub-band structures of semiconducting and metallic CNTs.
In the present study, we apply a type of FET with In contacts for various vdW layered materials (i.e., 1T-TaS 2 , Bi-2212, and 2H-MoS 2 ) to demonstrate that In-contacted vdW gap tunneling spectroscopy is a feasible method to investigate the electrical DOS of vdW layered materials. For the experiments with 1T-TaS 2 , the zero-bias resistivity showed a sudden increase at T ~ 180 K as the temperature was lowered. At T = 4 K, a plot of the differential www.nature.com/scientificreports/ conductance for various bias voltages revealed the emergence of an energy gap, i.e., the Mott gap edge, which has been observed in the same material only using scanning tunneling and photoemission spectroscopies [18][19][20][21] . The In/Bi-2212 junction also showed a superconducting gap of ~ 58 meV at T = 4 K. The gap feature slightly decreased with increasing gate voltage, which indicates that the high-temperature superconductivity could be controlled by electric fields 12 . Finally, for ~ 10 nm-thick MoS 2 FETs, we observed gap features at energy levels of ~ 0.9 eV in differential conductance vs bias voltage curves recorded at T = 4 K, corresponding to a semiconducting bandgap. The formation of the tunneling barrier with a high contact resistance for ~ 10 nm-thick MoS 2 is inconsistent with the Ohmic contacts for few-layer (thickness ⪅ 4 nm) MoS 2 flakes with In contacts, which might be related to the location of the Fermi level of an In electrode with respect to the bandgap, depending on the thickness of the MoS 2 layer. The naturally formed vdW tunnel gap without any artificial insulating barrier is very robust under varying temperature. Our work provides simple and reliable identification of electronic DOS using the simple FET geometry for the vdW materials without sophisticated tools such as scanning tunneling microscope.

Measurements and results
Experiments. Single crystals of 1T-TaS 2 and Bi-2212 were grown by the usual iodine transport method and solid-state-reaction methods, respectively. A 2H-MoS 2 single crystal was commercially purchased (HQ Graphene). We fabricated vdW material-based FETs with In contacts for TaS 2 , Bi-2212, and MoS 2 , by carrying out several microfabrication processes. The vdW material flakes on a 500 nm-thick SiO 2 /Si substrate were prepared via mechanical exfoliation from the vdW materials. We deposited 100 nm-thick In electrodes onto a multilayer flake using traditional electron-beam lithography and thermal deposition processes 16 . To investigate the quality of the In/vdW material, we collected cross-sectional transmission electron microscopy (TEM) image of an In/ few-layered MoS 2 junction (Fig. 1a), where the thermally deposited In did not show invasion into the MoS 2 layer, resulting in a well-defined vdW gap. Atomic structures of interfaces between In and two vdW materials of 2H-MoS 2 and 1T-TaS 2 with vdW gaps were prepared by the density functional theory (DFT) calculations as shown in Fig. 1b,c, respectively. The schematic atomic structure for In/Bi-2212 is also plotted in Fig. 1d. Figure 1e shows a schematic of a completed device for the vdW tunneling spectroscopy experiment (Fig. 1f), where the highly doped Si substrate serves as a back-gate electrode. For basic electrical characterizations of the three vdW mate- www.nature.com/scientificreports/ rials such as carrier density (n H ) and Hall mobility (μ H ), we performed independent electrical measurements for 1T-TaS 2 and 2H-MoS 2 . We measured the resistivity of 1T-TaS 2 as a function of T in a four-probe configuration (see Supplementary Fig. 1), where ρ ~ 0.1 Ω cm for 50 < T < 220 K. This is a similar ρ range with a previous report 22 Figure 2b shows dI/dV sd as a function of the sourcedrain voltage (V sd ) and back-gate voltage (V g ) at T = 4 K, which shows a substantial suppression of conductance near zero bias, along with conductance shoulders (indicated by two arrows). In the I-V sd curve corresponding to V g = 30 V in Fig. 2c, a relatively flat current region is observed near zero bias, which corresponds to the conductance dip region at the same V g value in Fig. 2b. The dI/dV sd -V sd curve corresponding to V g = 30 V shows a clear gap feature indicated by the bidirectional arrow, which was also observed at V g = − 30 V in Fig. 2c. We speculated that the observed gap is related to the Mott gap (Δ Mott ), exhibiting a gap size of ~ 0.4 eV. The Mott transition in multilayer 1T-TaS 2 has been previously shown to be developed in the temperature range 180 ≤ T ≤ 210 K, accompanied by a transition from the nearly-commensurate CDW (NCCDW) phase to the commensurate CDW (CCDW) phase, as revealed by scanning tunneling spectroscopy and photoelectron spectroscopy 18,19 . A recent study based on resistance measurements as a function of T conducted by using a gate-controlled Li + -ion intercalation method showed that the CCDW phase changed to the NCCDW phase with increasing gate voltage at T = 10 K 2 . In our case, the width of the conductance dip was nearly constant for V g values spanning 60 V, possibly because of relatively less change in the carrier density in our gating method with a 500 nm-thick dielectric SiO 2 layer. In addition, in Fig. 2d, we displayed already reported dI/dV sd -V sd curves obtained by conventional scanning tunneling spectroscopy with the same crystal used in this study 18 . Both of them showed a similar Δ Mott size of ~ 0.4 eV, thus we believe that In-contacted vdW gap tunneling spectroscopy provides a credible method to study the electronic states in vdW materials.
To investigate the phase transition, we obtained dI/dV sd -V sd curves at V g = 30 V over the temperature range 4 ≤ T ≤ 210 K, as shown in Fig. 3a, where the curves are vertically shifted as much as 20 nS for clarity. The pronounced gap feature at T = 4.2 K was smeared with increasing T up to T ~ 140 K and became featureless at T ≥ 180 K, whereas the conductance dip near zero bias was still observed. Figure 3b shows the zero-bias resistivity as a function of T, as extracted from Fig. 3a at V sd = 0 V. A sudden increase is observed at T ~ 180 K (indicated by an arrow) with decreasing T. This behavior was found to be consistent with previous observations of the Mott transition accompanied by the phase transition from the NCCDW phase to the CCDW phase near this temperature, T CCDW&Mott 19,20 . In that Mott transition, a gap was not fully opened in the investigated T region, resulting in a so-called a pseudogap structure 19,20 . In our case, such behavior was observed in the region indicated by a dashed bidirectional arrow in Fig. 3b, where the zero-bias resistivity monotonically increases with decreasing T. The dI/dV sd -V sd curves corresponding to 80 ≤ T ≤ 180 K in Fig. 3a show pseudogap-hump structures at V sd ~ ± 0.3 V with a finite zero-bias conductance, representing a small but finite density of state at the Fermi energy (E F ). Importantly, at T < 60 K, the resistivity increases substantially faster with decreasing T (see Fig. 3b) and the zero-bias conductance finally decreases to nearly zero at T < 20 K (Fig. 3a), where conductance peaks corresponding to the gap edges are clearly observed at V sd ~ ± 0.2 V, as shown in Fig. 3a (see also Fig. 2c). This result indicates that the Mott gap was fully developed at T < 20 K 21 . To test the reproducibility of these results, we also fabricated two additional 1T-TaS 2 devices with a thickness similar to that of the first 1T-TaS 2 device, and the curves for each device showed a clear conductance peak at one polar V sd of − 0.20 V and 0.18 V at T = 4 K, respectively, as shown in Fig. 3c (vertical arrows). Asymmetric gap features have been frequently observed in tunneling spectroscopy results for two electrodes (tip and metal contacts) with substantially different contact resistance levels (see Fig. 2d) 18 .  Fig. 4a shows a height profile along the dotted line depicted in the upper panel of Fig. 4a, indicating that the thickness of the Bi-2212 is ~ 70 nm. Figure 4b shows dI/dV sd as a function of V sd at V g = − 40 V for various temperatures, where the curves are vertically shifted as much as 50 nS. At T = 4 K, the gap feature was observed at V sd ~ − 58 and 50 mV, which are assigned as V p− and V p+ , respectively, as indicated by two red arrows in the figure. The observed gap sizes are consistent with previous observations of the superconducting gap energy, 26,27 . The peak signature at V p+ is relatively weak compared with that at V p− , similar to the TaS 2 case. The V p− value corresponding to the conductance peak decreases with increasing T, as indicated by the dashed green line, and is smeared out near the T c at T = 80 K. Figure 4d shows |V p− | as a function of T at V g = − 40 V, where |V p− | decreases with decreasing T. For comparison, we added a dashed curve representing �(T)/e based on the expression 28 where e is the elementary charge; 0 = 58 meV, a = 2.14, and b = 4/3 for a weak-coupling 2D d-wave superconductor; and T c = 88 K. Although we lack exact information about the T c at V g = − 40 V, the data qualitatively follows Eq. (1). Thus, we conclude that the gap feature originates from the superconducting gap. We also measured dI/dV sd as a function of V sd at V g = − 30 V as T was varied (Fig. 4c). As depicted by the dashed green line, the superconducting gap energy decreases with increasing T. However, we note that the gap feature relatively weakens at V g = − 30 V compared with that at V g = − 40 V. For instance, at V g = − 30 V, V p− decreases to approximately − 46 mV at T = 4 K, accompanied by a reduction of the conductance peak height. The conductance peak  vdW gap tunneling spectroscopy for 2H-MoS 2 . The inset of Fig. 5a shows an AFM image of the MoS 2 FET (MS1) with a thickness of ~ 10 nm. The MS1 device showed a traditional n-type transfer curve for V sd = ± 0.5 V at T = 4 K (Fig. 5a), where the I-V g curves show an asymmetric behavior depending on the polarity of V sd . Figure 5b shows a dI/dV sd map as a function of V sd and V g . In Schottky FETs, the zero-conductance region observed when V sd is swept in a depletion state decreases with positively increasing V g for an n-type device because the width of the Schottky barrier decreases with positively increasing V g . Although the conductance map in Fig. 5b appears to show such behavior for V g < 30 V (region i), a robust zero-conductance region that is independent of the change in V g was observed at − 0.45 V ≤ V sd ≤ 0.45 V (see dashed yellow lines) in the V g region labeled as region ii. Figure 5c shows I and dI/dV sd as functions of V sd at V g = 40 V in region ii. Conductance shoulders, indicated by the two vertical dashed lines, are separated from each other by an energy scale of ~ 0.96 eV, which is close to the interval bandgap of ~ 1.2 eV expected for multilayer MoS 2 29 . To confirm the consistency of the vdW gap tunneling spectroscopy, we fabricated another ~10 nm-thick MoS 2 device (MS2; inset of Fig. 5d). The overall behaviors of the electrical properties of the MS 2 device, such as the n-type behavior and the robust zero-conductance region (region ii) in Fig. 5d,e, respectively, show similar trends as those of the MS1 device. The conductance shoulders in Fig. 5f with the two vertical dashed lines provide an energy scale of ~ 0.92 eV at V g = 64 V in region ii, which is also similar to that of the MS1 device.
To determine the origin of the robust zero-conductance region, we considered the possibility of tunnel barriers with a high contact resistance due to the vdW gap between the MoS 2 and In electrodes. Figure 6a www.nature.com/scientificreports/ for representative V g regions labeled as i and ii in Fig. 5b, respectively. For simplicity, we only considered the MS1 device in Fig. 5a-c. The upper and lower solid black curves correspond to the conduction-band (CB) and valence-band (VB) edges of MoS 2 , respectively. The light-blue region under the VB edge indicates the states occupied by electrons. For V g ~ − 20 V, the MoS 2 band was found to be shifted upward, whereas the band edges were fixed at the junction interfaces, where the left electrode was grounded. E F(In) was located within the bandgap (E g ) without V sd , as shown in the left panel of Fig. 6a (horizontal red line); thus, a sufficiently high V sd is needed to overcome the E g region. The middle and right panels of Fig. 6a show V sd conditions in which the E F(In) of the right electrode reaches the CB and VB edges, respectively. Nevertheless, electrons do not flow to the edges of the MoS 2 because they experience a large Schottky barrier width. V sd values greater than those corresponding to the band edges are thus needed to make a narrower Schottky barrier for the flow of electrons. With increasing V g , the bands for the MoS 2 bend downward, leading to a relatively narrow Schottky barrier. Thus, the ± V sd that allow the current to flow decrease with increasing V g , corresponding to region i in Fig. 5b. In region ii in Fig. 5b, the interval between ± V sd locations for the finite conductance edges were found to change only slightly as V g was varied. The band diagrams corresponding to region ii are plotted in Fig. 6b. In this region, the MoS 2 electronic bands were observed to be substantially bent downward for V g ~ 40 V. Here, the alignment of E F(In) with the two band edges with proper V sd values of − V c and + V v enabled the electrons to tunnel between the electrode and MoS 2 under the assumption that the Schottky barrier widths were sufficiently narrow to allow the tunnel event, as indicated by horizontal arrows in the middle and right panels in Fig. 6b. The alignment resulted in no variation of the interval between − V c and + V v values, as indicated by the two dashed parallel lines in Fig. 5b. We note that the electrostatic band bending also occurs because of the vdW tunnel junction with a finite V sd , which leads to an additional band bending in a lower direction with the positive V sd . The observed tunnel behavior with high contact resistances at In-contacted devices with 10 nm-thick (n ~ 15, where n is the number of MoS 2 layers) MoS 2 layers appears to be inconsistent with the behavior of In/MoS 2 devices with MoS 2 thicknesses ≤ 4 nm (n ≤ 6), which exhibit Ohmic behavior 13 . For this reason, we considered the location of E F(In) . Figure 5c,f show that the location of zero bias is nearly midway between the two vertical dashed lines, which implies that E F(In) for n ~ 15 MoS 2 is located near the midgap, indicating non-Ohmic contact. However, in the case of few-layer MoS 2 , E F(In) is located just below the CB edge, resulting in Ohmic contact under the tunneling (or field-emission) mechanism through the vdW gap 13 . In this sense, performing vdW gap tunneling spectroscopy for n ≤ 6 is not possible, although the bandgap drastically increases from ~ 1.4 to ~ 1.9 eV when n is changed from 6 to 1 2 . Additional experimental and theoretical studies are needed to understand the

MoS 2 In
In www.nature.com/scientificreports/ current flowing between In and various-thickness MoS 2 to know the limit of In-contacted vdW gap tunneling spectroscopy for MoS 2 .

Conclusions
We carried out In-contacted vdW gap tunneling spectroscopy for 1T-TaS 2 , Bi-2212, and 2H-MoS 2 using an FET geometry. We clearly observed the Mott gap (~ 0.4 eV), superconducting gap (~ 58 meV), and semiconducting bandgap (~ 0.9 eV) of 1T-TaS 2 , Bi-2212, and MoS 2 , respectively, by analyzing conductance curves as a function of V sd at T = 4 K. Thus, we propose that vdW gap tunneling spectroscopy provides a feasible method to reveal the electronic band structure of inert vdW layered 2D materials. For semiconductor vdW materials of MoS 2 , we found that In-contacted vdW gap tunneling spectroscopy is applicable for only bulk MoS 2 (n ~ 15), which could be related to the location of the Fermi level of In with respect to the midgap of MoS 2 . This reflects that the relative location of the Fermi level of In with respect to the midgap of vdW material may reveal the limitations of In-contacted vdW gap tunneling spectroscopy. For non-semiconductor vdW materials of 1T-TaS2 and Bi-2212 with thickness of tens of nanometers, we confirmed the In-contacted vdW gap tunneling spectroscopy is applicable while we need further study for the validity for a few layers.