Understanding the Mott insulating state in 1T-TaS2 and 1T-TaSe2

In this article, we review the recent progress of the scanning tunneling microscopy studies of 1T-TaS2 and 1T-TaSe2 for bulk single crystals and molecular beam epitaxy monolayer films. We focus on how to understand the Mott insulating state in the whole set of materials, even when the stacking order takes effect. Based on this understanding, we discuss tuning the Mott insulator to a metallic state with different techniques, with Mott physics information revealed from the tuning process. The Kondo physics and quantum spin liquid state of 1T-TaS2 and 1T-TaSe2 are further discussed. This good platform of strong correlation must bring more intriguing phenomenon and physics in the future.


Introduction
Mott insulating state is a unique electron-correlationinduced property of different quantum materials [1][2][3]. A half-filled electronic band generally corresponds to a metallic state. When the ratio of Coulomb repulsion U over the bandwidth W exceeds some critical value, the density of states (DOS) around Fermi level will be split into the upper Hubbard band (UHB) and the lower Hubbard band (LHB), resulting in a Mott insulating gap [1,2]. Proximity to the Mott insulator can lead to different exotic states, such as the superconducting state in cuprates [4], alkali fulleride films [5], and magic-angle graphenes [6,7]. The transition metal dichalcogenide (TMD) 1T-TaS 2 and 1T-TaSe 2 are candidates of Mott insulators [8,9]. The understanding of Mott physics in these materials remains elusive and has been debated for a long time [10][11][12][13][14][15][16][17].
The bulk 1T-TaS 2 is the most studied subject in these related materials [18][19][20][21][22][23][24][25]. 1T-TaS 2 is a long-known charge density wave (CDW) material. In its low-temperature commensurate CDW (CCDW) phase, 1T-TaS 2 is reconstructed to a √ 13 × √ 13 superlattice (Fig. 1a). Each CDW element is called a star of David (SD), in which 12 Ta † Ying Fei and Zongxiu Wu contributed equally to this work. *Correspondence: yiyin@zju.edu.cn Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China atoms slightly shrink to the central Ta (Fig. 1a). With surrounding Ta atoms electronically bonded together, the central Ta of each SD is left with a single unpaired 5d electron. Each SD contributes one electron to the superlattice, resulting in a half-filled electronic band. The transport resistivity of bulk 1T-TaS 2 displays a typical insulating behavior (Fig. 1c). The Mott insulating state can then explain the half-filled insulator (Fig. 1b). The relatively large lattice constant of the superlattice makes the multifolded band narrow enough with a small bandwidth W. Like the magic-angle graphene [6,7], the narrow band pushs the system with a general Coulomb repulsion U into the strong-correlation limit. However, the Mott physics picture of this half-filled band is only considered in the single-layer 1T-TaS 2 . The long debate about the Mott insulating state of bulk 1T-TaS 2 is related to multilayer structure and interlayer interaction [10][11][12][13][14][15][16][17]. The density functional theory (DFT) often calculates a metallic state along the c axis, and sometimes obtain an insulating state with a bilayer dimerization from the stacking order effect [10][11][12][13][14]. Different experiments seem to have some clues of dimerization and claim that the normal insulating state is not a Mott but a band insulator [15][16][17].
This review article introduces the recent progress of scanning tunneling microscopy/spectroscopy studies of 1T-TaS 2 and 1T-TaSe 2 , for bulk single crystals and monolayer MBE films. The present paper is organized as follows. Section 2 presents the basic structural and electronic properties of 1T-TaS 2 and 1T-TaSe 2 . Section 3 focuses on the stacking order effect in bulk 1T-TaS 2 and 1T-TaSe 2 , giving a primary picture of the Mott insulating state in bulk samples. In Section 4, we elaborate on the tuning of the Mott state in 1T-TaS 2 with different techniques, including the elemental substitution, the intercalation, the strain tuning, etc. Section 5 introduces the Kondo effect and QSL phenomenon detected in monolayer films. A final summary is presented in Section 6.

Material and electronic properties of 1T-TaS /1T-TaSe 2
The single crystal of bulk 1T-TaS 2 is usually grown by the chemical vapor transport (CVT) method, using the transport agent of iodine. The multilayer structure of 1T-TaS 2 ( Fig. 1a) makes it ideal for the ultra-high vacuum (UHV) cleaving process to expose a flat and clean surface in the STM measurement. Each quasi 2-dimensional layer of 1T-TaS 2 comprises the Ta atomic layer sandwiched between the top and bottom S atomic layers (Fig. 1a). Both Ta and S atomic layers are triangular lattices. In the 1T phase, the upper and lower S atoms are misaligned, and S atoms surround each Ta atom octahedrally.
In the CDW phase, every 13 Ta atoms form a reconstructed SD cluster, with 12 surrounding Ta atoms slightly shrinking to the central Ta atom. In Fig. 1a, we classify the 13 Ta atoms as one central atom (position A), six neighboring atoms (position B), and six next neighboring atoms (position C/C'). In the CCDW phase, the superlattice of SDs exhibits a long-range √ 13 × √ 13 order. The atomic reconstruction of each SD and the SD superlattice corresponds to the electronic reconstruction of the CDW phase [21]. To present the primary crystal and electronic structure, we show a typical STM topography of bulk 1T-TaS 2 in Fig. 2a, in which each bright spot represents one SD.
The triangular superlattice of SDs shows the √ 13 × √ 13 reconstruction. The top surface S atoms can be atomically resolved only when the tip is sharp enough, as shown in the inset of Fig. 2a.
The transport measurement of bulk 1T-TaS 2 displays the insulating state in the CCDW phase at low temperatures (Fig. 1c). The half-filled insulating state of bulk 1T-TaS 2 has long been associated with a correlation effect or a Mott insulating state [1]. In Fig. 2b, a typical STM dI/dV spectrum measured at one SD center shows an insulating state with zero DOS around the Fermi level (zero bias). The two coherence peaks roughly at -220 mV and 200 mV are the UHB and LHB peaks, resulting in the Mott insulating gap around 420 mV. Other peaks beyond UHB and LHB are CDW-related bands or referred to as CDW peaks.
With the CDW order of SD clusters, the dI/dV spectrum is not spatially homogeneous. Figure 2c shows a linecut map across six SDs. The vertical axis is the bias voltage ranging from -580 to 580 mV. The LHB and UHB  [58,59] peaks have the strongest intensity at SD centers, showing a periodic modulation along the SD lattice. The CDW peaks above and below the Hubbard bands show the same periodicity, while the maximum peaks shift by half the period. The periodic modulation of the spectrum corresponds to different orbital textures for dI/dV maps at UHB/LHB or CDW bias voltages [43]. With Hubbard bands originating from the central Ta orbital and the CDW bands from surrounding Ta orbitals, UHB/LHB and CDW peaks show maximum values at SD centers and SD rims, respectively. The dI/dV maps at UHB/LHB voltages exhibit a texture with bright spots located at SD centers, while the dI/dV maps at CDW peaks exhibit a honeycomblike texture with bright patterns concentrated at SD rims.
1T-TaSe 2 shares the same crystal structure as 1T-TaS 2 . The single crystal 1T-TaSe 2 can be similarly grown with the CVT method. However, the transport measurement shows a metallic behavior at low temperatures (inset of Fig. 2e). Previous STM and ARPES experiments have detected an insulating state on the surface of 1T-TaSe 2 [28][29][30]. Understanding the surface insulting and bulk metallic states in 1T-TaSe 2 has always been a problem. In our STM work of bulk 1T-TaSe 2 [58], we find both the insulating state and the metallic state on the cleaved surface of 1T-TaSe 2 at different surface regions. In Fig. 2d, the STM topography shows the same triangular SD superlattice for the insulating and metallic state. The two dI/dV spectra measured at the SD center are displayed in Fig. 2e. The insulating spectrum is similar to that of bulk 1T-TaS 2 . The LHB and UHB peaks are located at -300 and 230 mV, respectively. The gap size is around 100 mV higher than that in bulk 1T-TaS 2 . The metallic spectrum shows a nonzero DOS around the Fermi level, with a weak dip feature around the zero bias. As shown in the linecut maps (Fig. 2f), the dI/dV spectrum also shows a periodic modulation like that of bulk 1T-TaS 2 , in which the UHB/LHB peaks or zero-bias dip are evident at SD centers. In contrast, the CDW peak features are prominent between neighboring SDs [58]. Then the dI/dV maps exhibit orbital textures similar to the bulk 1T-TaS 2 .
In bulk 1T-TaS 2 /1T-TaSe 2 , the Ta atoms in different layers are aligned along the c-axis. In the low-temperature CCDW phase, how the SDs in different layers align with each other (stacking order) is hard to be determined. The Mott insulating state is considered for the single-layer superlattice of SDs. Whether and how the interlayer interaction and stacking order affect the bulk electronic properties has been debated for a long time. Before discussing this problem in the next section, we introduce the monolayer MBE films of 1T-TaS 2 /1T-TaSe 2 [31,32,35,36]. An intuitive motivation is that the monolayer film grown on some substrates will help avoid problems caused by the multilayer structure and interlayer interaction.
The monolayer 1T-TaS 2 and 1T-TaSe 2 film can be successfully grown with the MBE method [35,36]. Both the 6H-SiC(0001) with bilayer graphene (BLG) and highly oriented pyrolytic graphite (HOPG) have been applied as substrates in the film growth. The monolayer 1T-TaSe 2 film is more accessible to grow than the 1T-TaS 2 film. As shown in Fig. 3a, the monolayer 1T-TaSe 2 is directly grown on the BLG-SiC substrate. The e-beam evaporated Ta and Knudsen cell evaporated Se can be controlled with a reasonable flux ratio and growth temperature. The hexagonal morphology of the 1T-TaSe 2 islands can be observed in Fig. 3b. In monolayer 1T-TaSe 2 , the √ 13 × √ 13 superlattice and the dI/dV spectrum are similar to the insulating state of bulk 1T-TaSe 2 . However, a splitting of two UHB peaks happens in the monolayer sample ( Fig. 3c) and the UHB 1 peak does not show a maximum value at the SD center, which has been explained to be from the reduced screening of monolayer film [9]. In addition to the 1T phase, the 1H phase can also be grown at a relatively lower growth temperature. For the 1H phase, the top and bottom Se atoms in each layer are aligned along the c-axis. This flexibility enables the stacking of 1T and 1H monolayer, as shown in Fig. 3a Although challenging with the high vapor pressure sulfur, the growth of monolayer 1T-TaS 2 has also been realized using FeS as the sulfur source [31,32]. Thermally decomposed FeS leaves decomposed iron in the crucible with low vapor pressure. The high purity S can also be evaporated with the Knudsen cell [35]. In Fig. 3e, both 1T and 1H phase monolayers of 1T-TaS 2 can be observed in the topography. In Fig. 3f, the dI/dV spectrum is similar to the bulk 1T-TaS 2 , although the LHB is lower and the Mott gap is relatively larger. The spatial periodicity and . c, f dI/dV spectra of the monolayer 1T-TaSe 2 and 1T-TaS 2 . Taken from ref. [35,36] orbital textures of monolayer 1T-TaS 2 are identical to the bulk sample.

Stacking order effect in 1T-TaS 2 /1T-TaSe 2
The comparison between bulk and MBE samples proves that the interlayer interaction and stacking order effect deserve further investigation. There remains a longtime debate about the mechanism of the insulating state in bulk 1T-TaS 2 [10][11][12][13][14][15][16][17]59]. The critical issue is whether it is a Mott insulator from a strong correlation effect or a trivial band insulator from the bilayer dimerization. Theoretically, the DFT calculation with on-site U can produce a Mott gap in the single-layer 1T-TaS 2 and a metallic state along the c-axis, contradicting experimental results. Further DFT calculations discuss how a particular stacking order can open a gap for the metallic c-axis electronic state [12,13]. The insulating state is not from a monolayer property but interlayer interactions at specified stacking orders. Experimentally, different STM groups have seen two terminals showing insulating gaps with two gap sizes [15,16,59,60]. The large-gap spectrum is identical to the typical spectrum on the cleaved surface. The large-gap and small-gap spectra correspond to the AA-stacking and AC-stacking orders. A bilayer unit-cell doubling model combines two stacking orders, leading to a trivial dimerized bandgap. The model suggests that the large gap on the AA-stacked terminal is the dimerized bandgap, while the small gap on a misaligned AC-stacking is the singlelayer Mott insulating gap [15,16,60].
These experimental results seem to be consistent with the DFT prediction. However, they can not explain why the MBE grown monolayer 1T-TaS 2 and 1T-TaSe 2 exhibit a large-gap insulating state [31,32,35,36]. It is also hard to explain some previous experiments about Mott-insulatormetal transition in which the large insulating gap can be effectively tuned by doping, strain, or intercalation [40,41,[43][44][45][46][47][48][49][50][51]. A systematic STM study about the stacking order effect has been implemented in bulk 1T-TaS 2 and 1T-TaSe 2 [58,59]. The method focus on the flat single-step area on the cleaved samples. The statistical result of multiple measurements is expected to reveal different possible stacking orders along the c axis and the probability of each occurrence. Figure 4a is the topography of a typical single-step area in bulk 1T-TaS 2 , with the dashed frame enlarged in Fig. 4c. We can determine the relative displacement of SD superlattices from the triangular SD superlattice on both the top and underlying layers. The red dots mark the SD centers of the lower layer. When the red dots are extended to the peninsula coverage area, they coincide with the SD centers in the upper layer. This case belongs to the AAstacking order with SD centers in the upper and lower layers aligned along the c axis. Figure 4b shows the typical dI/dV spectrum measured on the SD centers of the lower and upper terraces. They both display a large-gap insulating state, with a gap size similar to that of the typical spectrum of bulk 1T-TaS 2 . This result seems to be consistent with the unit-cell doubling model in which AA-stacking dimerization leads to a large-gap band insulting state [15]. However, multiple counter examples have been found, as shown in Fig. 4d-f. Although the largegap dI/dV spectrum is obtained on top and bottom terraces, different misaligned stacking orders are determined. Figure 4g shows the schematic diagrams of AA, AC, AB, and AC' stacking orders. The large-gap spectrum is not solely related to a dimerized AA-stacking order. Figure 5 displays two other examples of single-step areas, with the topographies shown in Fig. 5a and e. Although a large-gap insulating spectrum is obtained on the bottom terrace in both cases, a different small-gap spectrum or a V-shaped metallic spectrum is obtained on the top terrace, respectively. In Fig. 5a, the red dashed line labels a domain wall of the SD superlattice. The ACstacking order is determined on both sides of the domain wall, as shown in Fig. 5c and d. In Fig. 5e, the AB-stacking order is determined as shown in the inset. Although the single-step area with a metallic top-layer spectrum is rarely found, the case with the small-gap top-layer spectrum is a frequent occurrence. That is why the small-gap spectrum has been reported in other previous literatures [15,16,51,59]. One difference between examples in Figs. 5 and 4 is that the small-gap area is often a small region close to the step edge, while the large-gap area can extend far away from the step edge.
In Table 1, multiple measurements of bulk 1T-TaS 2 are collected and classified. With the small-gap region often a small area close the step edge, it is referred to a surface and edge phenomenon. In contrast, the large-gap area is more related to the bulk property of the material. The domain wall of SD superlattice is commonly found to be together with two large-gap spectrum on either side, compatible with the non-AA stacking orders in Fig. 4. The consecutive large-gap spectra on misaligned non-AA stacking orders rule out the unit-cell doubling model. The largegap insulating spectrum is more possibly related to the single-layer property, consistent with the MBE film result [32,35]. In the ideal bulk material, the stacking order does not disturb the main feature of the large-gap spectrum. Around the step edge, the AC or AB stacking orders can disturb the large-gap spectrum to a small-gap and metallic spectrum. Our experimental results are consistent with a recent DFT calculation which adopts a generalized basis and supports the Mott insulating state on AA-stacked layers [14].
The similar STM technique has been applied to the bulk 1T-TaSe 2 [58]. Sharing the same valence, structure, and low-temperature √ 13 × √ 13 CCDW phase, the bulk 1T-TaSe 2 should be very similar to the bulk 1T-TaS 2 . How- Three misaligned examples on the single-step area. The red (blue) dots label SD centers in the lower (upper) layer. g Schematic diagrams of the AA, AC, AB, and AC' stacking orders. Taken from ref. [59] ever, the suface insulating and bulk metallic state made 1T-TaSe 2 a more complicated system. How the stacking order affects the electronic state in 1T-TaSe 2 is an intriguing problem. Figure 6a is the topography of a multistep area on the cleaved surface of 1T-TaSe 2 , with the schematic side view in Fig. 6b. From the dI/dV spectrum on different steps in Fig. 6c, three types of spectra can be observed, exhibiting a large-gap, small-gap and metallic state, respectively. Here the so-called small-gap spectrum exhibit a finite zero-bias DOS. The large-gap insulating and metallic spectrum are similar to that obtained on the normal surface (Fig. 2e). We find that the small-gap spectrum is also a surface and edge phenomenon. In contrast, the large-insulating and metallic spectrum can extend far away from the step edge, compatible with the bulk property.
Both the large-gap and metallic spectrum have been found on the bottom terrace of the bulk 1T-TaSe 2 . For the metallic spectrum on the bottom terrace, the spectrum on the top terrace is either metallic or large-gap insulating, as shown in Fig. 6d-e and f-g, respectively. The displacement between two SD superlattices is the ACstacking and AA-stacking, respectively. For the large-gap insulating spectrum on the bottom terrace, the spectrum on the top terrace is found to be the large-gap insulating state or metallic state in Fig. 6h-j. The ACstacking, AC'-stacking, and AB-stacking are determined in Fig. 6h-j. In Table 2, the different stacking orders and corresponding electronic states are classified, together with the occurrence time of each case. The same stacking can lead to different states on the top terrace. The stacking order and the bottom layer state are two tuning factors. The large-gap insulting state is considered to be the singlelayer property. Then a perturbation on the Mott state can result in the metallic state under some particular misaligned stacking orders. Although the large-gap insulating state is dominant in bulk 1T-TaS 2 , both the large-gap insulating and metallic states are frequently found in bulk 1T-TaSe 2 , possibly due to similar energy scales during the cooling process. This picture is consistent with the largegap insulating state in MBE monolayer 1T-TaSe 2 [31,32,36]. The metallic resistivity of bulk 1T-TaSe 2 can then be related to the connected metallic areas of electrodes in the transport measurement. From the experimental point of view, we give a relatively conclusive result about the stacking order effect in the bulk 1T-TaS 2 and 1T-TaSe 2 . Here we focus on the bulk properties of the two materials. For 1T-TaS 2 , only the large-gap insulating state can exist in a large area away from the step edge. Then the large-gap state is the intrinsic property of the ideal bulk material. The small-gap and metallic states are both related to the edge phenomenon. For 1T-TaSe 2 , both the large-gap and metallic state can exist in a large area away from the step edge. These two states are the intrinsic property of the ideal bulk material. For the intrinsic state in ideal bulk 1T-TaS 2 , the large-gap insulating spectrum appears with different stacking orders (AA, AC, AB, AC'), and the AA-stacking is relatively more dominant. The large-gap insulating spectrum is most possibly from the single-layer property, consistent with the monolayer film result. The different stacking orders in the bulk material will not perturb this large-gap spectrum. Stacking order effect in 1T-TaSe 2 . a A 100 × 100 nm 2 topography in bulk 1T-TaSe 2 , with a schematic side view shown in b. c Typical dI/dV spectra on different regions in a. d-g The stacking orders and corresponding dI/dV spectra with a lower-layer metallic spectrum. The SD centers in the upper layer are aligned with the d SD outer-corner sites (AC-stacking order), and f center sites (AA-stacking order) in the lower layer. h-j The stacking orders and corresponding dI/dV spectra with a lower-layer insulating spectrum. The corresponding stacking orders are h AC, i AC', j AB. Taken from ref. [58] In 1T-TaSe 2 , the large-gap insulating and metallic spectrum both exist as the intrinsic properties of the ideal bulk material. When the lower terrace is in a large-gap insulating state, the AC' and AB stacking orders can lead to a metallic state on the top terrace. The difference between 1T-TaSe 2 and 1T-TaS 2 is that the stacking order in 1T-TaSe 2 has a more substantial perturbation, and the AC' and AB stacking orders induce a similar metallic state in the bulk material. On top of the metallic state, either the metallic or the large-gap insulating state can be induced by the AC or AA stacking orders. The different perturbation strengths of stacking orders can be attributed to the subtle material details of the two sister compounds. Although the stacking order has been clarified in the STM measurement, how the different stacking induces the small-gap or metallic state should be further explored from the theoretical respect. In addition, understanding the dimerization evidence in ARPES and XRD measurements is still a remaining problem [17].

Tuning the Mott insulating state in 1T-TaS 2
With the Mott insulating state in 1T-TaS 2 confirmed, we can revisit the tuning of this Mott state with different techniques. We first discuss the tuning with elemental substitutions [40, 41, 43-46, 49, 50]. For the binary compounds, either the cation or anion substitution can be implemented. Due to the critical role of Ta atoms in the Hubbard bands, the anion substitution often introduces a weaker perturbation than the cation substitution.
For example, the substitution of S with Se gradually suppresses the CCDW phase until x = 0.8 [40][41][42], while the substitution of Ta with Fe or Ti can quickly suppress the CCDW phase with low doping of x = 0.01 [49,50].
The pristine 1T-TaS 2 and 1T-TaSe 2 share a similar crystal structure, low-temperature CCDW superlattice, and even the Mott insulating spectrum [58,59]. The isovalent substitution of S with Se is an effective method to tune the Mott state without introducing extra electron or hole carriers. In the phase diagram of 1T-TaS 2−x Se x (Fig. 7a), the Mott and CCDW phase is suppressed with increasing x, while a superconducting dome emerges in a wide range of 0.8 < x < 1.6. The optimal doping of the superconducting state occurs at x = 1.0 with the transition temperature T c ∼ 3.5 K.
With high-quality single crystal of 1T-TaS 2−x Se x , the STM measurement can directly map the real-space evolution of electronic state [43]. When x > 0.8, the longrange CDW phase is destroyed, and domain walls emerge between domains with varied sizes. The triangular superlattice of SDs is retained within each domain (Fig. 7b). However, the point spectrum measured at the central Ta of each SD shows a strong inhomogeneity. As shown in Fig. 7c, very different spectra were detected in the same domain of 1T-TaSSe including a nearly unperturbed Mott gap, a broad V-shaped spectra reminiscent of the pseudogap (PG) in cuprates, and a sharp peak near Fermi level similar to the van Hove singularity in overdoped cuprates. The inhomogeneity is most likely from the inhomogeneous Se concentration. The calculated DOS confirms the various spectra as a function of Se concentration. The DFT calculation also proves that the main effect of Se substitution is to increase the local buckling of the Ta-Se-Ta bonding, and the Mott-insulator-metal transition happens when the CDW bands merge into the LHB.
Titanium is a cation doping element used to tune the bulk 1T-TaS 2 . The Ti doping replaces one of the 13 Ta 4+ ([Xe]4f 14 5d 1 ) ions with a nonmagnetic and isovalent Ti 4+ ([Ar]) ion, depleting the unpaired 5d electron in a SD. The doped system is relatively stable due to the similar radii of Ti and Ta atoms. A combination of STM, transport, and DFT calculations has been applied to systematically investigate the Ti-doped 1T-Ti x Ta 1−x S 2 at a wide range of doping levels from x = 0 to x = 1 [49,50]. Figure 8a shows the phase diagram of 1T-Ti x Ta 1−x S 2 derived from the transport measurements [50]. The CCDW state is gradually suppressed with the increase of Ti doping, and disappears around x = 0.01 (Fig. 8b). The system then experiences an insulator-metal transition at low temperature. An interesting hidden anomaly in this regular phase evolution is reflected in the peak of resistivity ratio ρ 2K /ρ 360K .
The STM measurements further give the doping effect and the phase transition from the microscopic level [49]. Figure 8c shows the typical dI/dV spectrum of undoped sample, x = 0.004, and x = 0.01 sample. The insulating state remains for the x = 0.004 sample, consistent with the macroscopic transport result. While for the x = 0.01 sample, the V-shaped dI/dV spectrum is related to the metallic state. For more details, STM topography shows a continuous triangular SD superlattice in lowdoping (x < 0.01) samples, with the long-range CDW order preserved. At this low-doping level, the DOS is locally perturbed inside the Ti-doped SD, while the DOS of undoped SDs maintains insulating, with the spectra compared in Fig. 8e. The impurity spectrum of Ti-doped SD has a suppressed LHB and enhanced DOS roughly  b, c Temperature-dependent in-plane resistivity ratio ρ(T)/ρ(360K) and typical dI/dV spectra for samples with different doping levels. d A 9 × 9 nm 2 topography for the x = 0.004 sample. Red and blue circles mark a symmetric and an asymmetric Ti-doped SD, respectively. e dI/dV spectra measured at the center of an undoped SD, a symmetric, and an asymmetric Ti-doped SDs, respectively. f First-principles DFT calculation of symmetric Ti-doped SD. Red contours represent high charge densities. g-j Experimental dI/dV maps around a symmetric Ti-doped SD at different energies on the x = 0.004 sample. Taken from ref. [49,50] above 200 mV. In the topography with negative bias voltage, the three-petal-shaped SD instead of a bright spot corresponds to the Ti-doped SD (Fig. 8d). The symmetric and non-symmetric pattern of the doped SD depends on whether the Ti atom is substituted in the central Ta site. The DFT simulation reproduced the three-petal feature (Fig. 8f ), and the strongly enhanced DOS above 200 mV is related to the d orbitals of Ti atoms. In addition to the local effect of Ti doping, unusual orbital textures appears in the dI/dV maps at different bias voltages (Fig. 8g-j). The three-petal orbital texture is shown in the -390 mV dI/dV map. With the LHB suppression of doped SD, the three-petal feature becomes prominent at doped SDs in the negative-voltage-biased topography (Fig. 8d).
From transport measurement, the low-temperature insulator-to-metal transition occurs around a critical point x = 0.01, where the CCDW phase is completely suppressed [49]. Figure 9a is an STM topography of the x = 0.01 sample, in which large insulating domains and small metallic domains coexist. The appearance of domains is related to the doping-induced subtle crystal structure modification and destabilization of long-range CDW Fig. 9 Topography and electronic state for a x = 0.01 sample of 1T-Ti x Ta 1−x S 2 . a A 75 × 75 nm 2 topography shows the coexistence of different domains. b A series of dI/dV spectra measured along three adjacent SDs insides a metallic domain. Taken from ref. [49] order. The V-shaped metallic spectrum in Fig. 8c is taken within the small domains. The dI/dV spectrum linecut in Fig. 9b is taken across three undoped SDs. Except for the periodic evolution, the V-shaped metallic spectrum is relatively homogeneous within small domains. The Ti-doping introduces holes and destroys the electron correlation, resulting in the V-shaped metallic spectrum. The hole doping in cuprate superconductors transfers the spectral weight from Hubbard bands to low-energy states near the Fermi level, exhibiting a PG state. The Vshaped spectrum after Mott collapse in 1T-TaS 2 looks similar to the cuprate PG state. Unfortunately, because of the domain structure, we can not detect a smooth evolution of how the V-shaped spectrum emerges. The three-petal orbital texture also emerges at a broader bias voltage range, revealing its competition with the electron correlation.
When x reaches 0.08 (a doping level of one Ti atom per SD), the trapped electrons in undoped SDs can be directly visualized in dI/dV maps. The low-temperature upturn of resistivity is related to the disorder-induced potential fluctuation, showing a typical Anderson insulator behavior. In addition, an unexpected chiral CDW phase is observed with the chiral effect mainly contributed by the Ti orbitals [50]. As x further increases, the number of domain walls increases, and the size of domains decreases until x = 0.2. Then the SD superlattice becomes distorted and the domain walls disappear, corresponding to the disappearance of the IC-NCCDW transition in transport measurements.
Another Ta-site substitution worth mentioning is the Fe-doping [44][45][46]. Only a few percentage of the 3delement Fe 2+ ([Ar]3d 6 ) replacement [61] can induce superconductivity in 1T-Fe x Ta 1−x S 2 [44][45][46]. The superconducting state appears at low temperatures with the suppression of the CCDW as 0.01 < x < 0.04. The maximum superconducting transition temperature T c is 2.8 K at x = 0.02. As x > 0.04, the Anderson localization state appears, resulting in a large increase of resistivity at low temperature [44]. Compared to Se-doping compound, the superconducting range of Fe-doped 1T-TaS 2 is much narrower. Similar domain structure was also observed in STM measurement in Fe-doped 1T-TaS 2 [46]. The SD superlattice starts to be separated by domain walls as the doping increases, and finally is completely distorted without any domain walls. The superconducting T c of Sedoping and Fe-doping systems are below the liquid helium temperature. The STM study of their superconducting state is still lacking. More in-depth research is needed to reveal whether the superconducting state is related to the strong correlation Mott physics.
Intercalation is a different effective method to tune the electronic state of TMD materials [47,48,62,63]. Unlike the elemental substitution, some atoms are prone to be intercalated between different layers of TMD materials. In copper-intercalated 1T-TaS 2 , a scanning transmission electron microscopy (STEM) image helps determine the intercalated Cu atoms between adjacent layers of 1T-TaS 2 (Fig. 10a). The interlayer distance slightly expands due to the intercalation of Cu atoms. The Cu atoms are also at the middle position between neighboring layers, without any apparent offset. The transport measurement shows that the CCDW state is completely suppressed with the Cu-intercalation (Fig. 10b), while it is challenging to determine the precise amount of Cu atoms. The STM topography presents how the long-range CCDW phase is divided into multiple domains with domain walls (Fig. 10c). The electronic state mostly becomes a V-shaped spectrum within each domain, although a small number of insulating domains are still preserved (Fig. 10d). This transition is related to the transferred carriers of Cu atoms. Around the edge of the insulating domain, we can sometimes observe an evolution of the suppressed UHB and emerging in-gap state ( Fig. 10e-f ), similar to the doped-electron-induced state evolution in cuprate Ca 2 CuO 2 Cl 2 Mott insulator [64]. This electronic evolution further solidifies the Mott insulating state in 1T-TaS 2 .
The strain is another tuning parameter [65][66][67][68][69] to induce Mott gap collapse in 1T-TaS 2 [51]. The straininduced corrugation is unusual for introducing a smooth evolution from the Mott insulator to the metallic state. Figure 11a shows the topography of a strain-induced corrugated surface, on which the periodic SD superlattice exists without any domain walls. A series of dI/dV spectra along the white straight line is shown in Fig. 11b, and some typical spectra are selectively chosen and displayed in Fig. 11c. The location of each spectrum is labeled by a colored dot along the line in Fig. 11a. A smooth evolution of Mott-gap collapse can be observed when approaching the dark groove from both sides. Both UHB and LHB peaks move gradually toward the Fermi energy until an in-gap state develops to form a metallic V-shaped spectrum. A Mott-insulator-metal transition can be generally explained by a reduced ratio of U/W in the one-band Hubbard model. As shown in Fig. 11d, when approaching the groove from the left side, the Mott gap gradually decreases while the bandwidth of both UHB and LHB peaks is nearly unchanged (brown region). Here, the decrease of U is mainly responsible for the reduced U/W . When being closer to the groove (purple region), the LHB bandwidth rapidly increases, accompanied by the development of two symmetric in-gap peaks and a Vshaped dip. Although U still decreases in this region, the increase of bandwidth is the dominant factor in reducing U/W . However,the mechanism of the emergent V-shaped in-gap state is till unclear. The Se substitution increases the local buckling of the Ta-Se-Ta bonding geometry [43], which can be compared to the strain effect. In this sense, Topography and a series of dI/dV spectra in an insulating domain. Taken from ref. [48] different tuning techniques may share a similar mechanism of Mott-insulator-metal transition.
The atomic substitution and intercalation often trigger the domain structure. A different perturbation is to directly evaporate alkali K atoms on top of the cleaved 1T-TaS 2 [70]. This surface alkali doping metallizes the Mott insulating state while maintaining the long-range CCDW phase. The metallization brings in-gap excitation near the top of the LHB. Theoretical analysis and numerical calculation suggest that the near-LHB in-gap state is related to reduced on-site Coulomb energy by adsorbed alkali ions. How to combine this picture with the two different Mott gaps deserves further investigation [16].
Various electrically/optically driven methods [71][72][73][74][75][76] successfully induce the Mott-gap collapse in 1T-TaS 2 . A voltage pulse applied across the tip-sample junction causes the Mott-gap collapse in the STM experiment [52,53]. It results in a metallic mosaic state, whose relation with the stacking order has been discussed [52]. The electrically/optically driven excitation can apply to a switching device for possible applications. External pressure is a tool to influence electronic interactions without increasing the degree of internal disorder. It can tune the bulk 1T-TaS 2 from a Mott insulator to a superconductor (T c ∼ 5 K) [8]. The ionic gating induces multiple Mott-insulator-metal phase transitions in 1T-TaS 2 thin flakes, particularly with a superconducting state (T c ∼ 2 K) over a certain gating voltage range [56].

Kondo effect and possible quantum spin liquid in 1T-TaS 2 /1T-TaSe 2
Combining the Mott insulator scenario and the triangular superlattice of SDs, 1T-TaS 2 /1T-TaSe 2 is a candidate for the QSL system [33][34][35][36]. No magnetism has been observed in superconducting quantum interference devices (SQUID) or transport measurements of related materials [77][78][79]. It is natural to ask about the magnetic ground state of the spin lattice from unpaired 5d electrons. In the MBE growth of monolayer films, the 1H phase can be grown together with the 1T phase by controlling the substrate temperature in the growing process [35,36]. This different 1H phase has helped provide additional information about the spin lattice [36]. Both 1H-TaS 2 and 1H-TaSe 2 show a 3 × 3 CDW reconstruction and a metallic DOS with a slight CDW dip in STM measurements [35,36]. After controlling the growth of a monolayer 1T-TaS 2 (or 1T-TaSe 2 ) on top of its 1H phase monolayer film, the dI/dV spectrum is surprisingly found to present a zero bias resonance peak, which can be referred to as the Kondo physics phenomenon [35,36]. Many-body physics will induce the screened spin when a local spin interacts with surrounding metallic electrons, leaving a zero bias resonance in the DOS [35,36]. Figure 12a-c shows the Kondo resonance of 1T-TaS 2 on 1H-TaS 2 . In Fig. 12b, the dI/dV spectrum as a function of temperature displays how the Kondo resonance evolves when temperature increases. The resonance width fit with a well-known formula yields a Kondo temperature of T K = 18 K. Zeeman splitting of the Kondo resonance is also confirmed by a strong magnetic field, as shown in Fig. 12c. Figure 12d-e shows the similar Kondo resonance of 1T-TaSe 2 on 1H-TaSe 2 . The dI/dV spectrum as a function of temperature in Fig. 12e leads to an estimated Kondo temperature of T K = 57 K. We note that a similar Kondo resonance has also been found in the 1T-NbSe 2 /2H-NbSe 2 heterostructure [80]. Due to the superconducting state of 2H-NbSe 2 , the Yu-Shiba-Rusinov (YSR) bound state [80] coexists with the Kondo resonance, which further verifies the local spin of the SD cluster. The Kondo resonance may also explain the narrow electronic band near the Fermi level in bulk 4Hb-TaS 2 , with the narrow band measured on the 1T-TaS 2 /1H-TaS 2 stacking [81].
The Kondo effect can only confirm the localized spin in the triangular SD superlattice at each site. It is not easy to further investigate the QSL phenomenon using general techniques. The QSL electron comprises a spinon without Fig. 12 Kondo resonance of a-c TaS 2 and d-e TaSe 2 heterostructures. a, b Typical dI/dV spectra and the spectra of the Kondo resonance measured at different temperatures on 1T/1H-TaS 2 vertical heterostructures. c Magnetic field dependence of the Kondo resonance in tunneling spectra of 1T/1H-TaS 2 . d, e Typical dI/dV spectra and the spectra of the Kondo resonance measured at different temperatures on the 1T/1H-TaSe 2 vertical heterostructures.Taken from ref. [35,36] charge and a chargon without spin [36]. The QSL then induces emergent gapless spinon excitation that carries spin but no charge [36]. The chargeless nature of spinon excitation disables the detection with general electronic techniques like STM. Recently STM spectroscopy, on the other hand, reveals long-wavelength super-modulations with momentum consistent with predictions of itinerant spinons [36]. The dI/dV maps in Fig. 13a-c and their corresponding Fourier transforms (FTs) in Fig. 13d-f show that an incommensurate super-modulation (ICS) occurs near the Hubbard band energy. Figure 13h presents the FTs intensity as a function of the wavevector q = q(b 1 + b 2 ) along the − K direction and the sample bias voltage. The wavevector of ICS is independent of bias voltage in Fig. 13h, and the amplitude of ICS is peaked around LHB and UHB energies in Fig. 13i. The ICS also vanishes above 77 K. All information indicates that it reflects a spinon Fermi surface instability transition. The ICS is theoretically explained as the higher harmonics of the primary P i vectors from the spinon Fermi surface instability in monolayer 1T-TaSe 2 , as shown in Fig. 13j-l. The ICS occurs on both BLG-SiC and HOPG substrates, while an additional 2 × 2 super-modulation sometimes exists in the 1T-TaSe 2 /HOPG (Fig. 13m). Other experimental evidence of QSL includes the Co-adatom-induced side resonance peaks, explained by the gauge-field fluctuations and spin-chargon binding.

Summary
In the present article, we have reviewed the recent progress of STM measurements on 1T-TaS 2 and 1T-TaSe 2 . By comparing bulk and monolayer film properties, we verify the Mott insulating state in the set of materials by excluding disturbing and distracting information. The tuning of the Mott insulating state further provides more Mott and QSL properties. Due to the h Plot of FT amplitude as a function of both wavevector q = q(b 1 + b 2 ) along the − K direction and sample bias voltage. i Energy dependence of the incommensurate super-modulation strength (blue dots) and the reference dI/dV spectrum (black curve). j-m Super-modulation periodicities predicted from the spinon Fermi surface compared with experiment. Taken from ref. [36] space limitation, plentiful phenomena of this exotic system are not all discussed, such as the metallic domain wall properties [60,63,82,83], the phononic coupling of doublonlike excitation [84], etc. The metallic domain wall has been connected to the superconducting state in another TMD material Cu-TiSe 2 [63]. The complicated domain wall in 1T-TaS 2 and 1T-TaSe 2 deserves further study. Although some elusive problems still exist, the 1T-TaS 2 and 1T-TaSe 2 are flexible platforms for studying the strong-correlation physics and deserve further in-depth study.