Observation of a topological defect lattice in the charge density wave of 1T-TaS₂

Charge density waves (CDWs), where modulations in the density of conduction electrons are accompanied by periodic distortions of the lattice, are among the earliest known manifestations of correlated electron behavior.^1–4 They manifest in low dimensional anisotropic materials^5–8 as an anomalous response in electrical transport and unusual electron diffraction patterns. The 1T polymorph of TaS₂ (1T–TaS₂) studied here, one of the first discovered in the CDW family of materials, is also one of the most fascinating.^7,9–13 It consists of stacked S–Ta–S layers [Fig. 1(a)], with each layer comprised of a triangular lattice of Ta atoms sandwiched between S atoms.^7,9,10 Below ∼540 K, 1T-TaS₂ undergoes a series of first-order transitions into CDW phases with an increase in lattice commensurability: Below 350 K, an incommensurate CDW (IC-CDW) phase transits into a nearly commensurate CDW (NC-CDW) phase,¹⁴ which is then followed by a commensurate CDW (C-CDW) below 180 K [Fig. 1(b)]. Further cooling below 2 K, the material becomes superconducting upon application of pressure and doping.¹⁵ The C-CDW is a triangular lattice of 13 Ta atom clusters arranged in a star of David (SD) formation [Figs. 1(a) and 1(b)]. In each SD, 12 Ta atoms in covalently bonded pairs shift toward the center, leaving the electron on the central Ta atom localized and unpaired¹⁶ in a polaron-like structure.¹⁷ The magnetic ordering of the C-CDW ground state, currently under debate, is dictated by the relative strengths of intra- and inter-layer Coulomb interactions. It could either lead to a Mott insulator^{7,10,12,16,18,19} with spin-1/2 polarons localized within the 2D plane or a band insulator²⁰ of spinless bipolarons, which form between adjacent layers.^9,13,21–24 Furthermore, the triangular arrangement of the unpaired S = 1/2 spins suggests the intriguing possibility for realizing a quantum spin liquid in this material.^17,25,26 Similar to the C-CDW, the NC-CDW phase also consists of a SD lattice, but here, the lattice is broken up by a network of domain walls. The vertices where domain walls intersect [Fig. 1(c)] form a lattice of topological defects dubbed “CDW vortices,” which resembles the Abrikosov vortex lattice in type II superconductors.^27–31 In addition to the importance of 1T-TaS₂ as a testbed for a range of correlated electron physics, the fact that one of its CDW transitions is close to room temperature^23,32–36 makes it a material of choice for electronics applications, such as high speed memory devices,³⁷ logic gates,³⁸ and oscillators.³⁴ 

In this work, we image the CDW modulation at the surface of exfoliated 1T-TaS₂ flakes using scanning tunneling microscopy/spectroscopy (STM/STS)³⁹ at room temperature and at 78 K by employing a graphene passivation layer.⁴⁰ Because 1T-TaS₂ is a reactive material that quickly deteriorates in ambient conditions, probing its surface is extremely challenging. Earlier STM measurements used hexadecane oil to protect the surface at all times including during scanning.⁴¹ We have found that covering the 1T-TaS₂ sample with a graphene layer provides excellent protection from ambient oxidation during sample fabrication and transfer into the measurement system and during extended measurement.⁴⁰ Using the graphene encapsulated 1T-TaS₂ sample (henceforth G/TaS₂) to image the NC-CDW phase at room temperature, we found that the topological defects (CDW vortices) in the SD array exhibit correlations with power law decay consistent with a Bragg glass phase.^42–47 The Bragg glass, first proposed to describe an Abrikosov vortex phase in the presence of weak pining, is nearly as ordered as a crystal but with power law decay of its correlations caused by interactions with lattice defects. This raises the question whether recently reported transport behavior^48–50 can be explained by transitions in the ordering of the CDW vortex lattice, similar to observations in the Abrikosov vortex lattices.^51,52 We next cooled the G/TaS₂ samples across the transitions into the NC-CDW and the C-CDW phases while monitoring the temperature dependent resistance of both bare 1T-TaS₂ and G/TaS₂ samples. We found that whereas the resistance of the bare 1T-TaS₂ sample exhibits sharp jumps as expected at these first-order transitions, the G/TaS₂ resistance varies continuously, suggesting substantial interactions and charge transfer between the two materials. This was further verified by STM/STS, which revealed a modulation of the charge density in the graphene layer that mirrored the C-CDW in 1T-TaS₂, providing evidence of an unusual CDW proximity effect.

Flakes of 1T-TaS₂ are exfoliated from bulk inside an argon-filled glovebox onto a SiO₂ coated Si wafer. A graphene flake is separately prepared by mechanical exfoliation from natural graphite onto a PMMA film and located under an optical microscope situated inside the glovebox. The graphene flake is then aligned and transferred onto a 1T-TaS₂ flake and heated to approximately 120 °C to soften and relax the PMMA/graphene film. Bias contact is made using standard e-beam lithography, electrode evaporation [Ti (5 nm)/Au (45 nm)] and lift off (outlined in the supplementary material). Following electrode fabrication, the sample is gently heated to 230 °C in forming gas (10% hydrogen in argon) for 5 h to remove polymer residues without inducing a structural phase change in the 1T-TaS₂ crystal.

Graphene on 1T-TaS₂ (G/TaS₂) samples is then measured using a homebuilt STM system utilizing an RHK Technology R9 controller at room temperature and in vacuum (<10⁻⁶Torr). A schematic of the measurement is given in Fig. 1(b).

Figure 2(b) is a representative STM topography image of the sample surface. Two spatially periodic patterns emerge, which show up as peaks in the 2D fast-Fourier transform (FFT) of the topography image [Fig. 2(b) inset] corresponding to the atomic lattice of graphene and the CDW modulation of 1T-TaS₂ (green and red circles, respectively). Note that the constant-height measurement scheme, where the tunneling current is monitored as the tip quickly raster scans across the surface, is chosen to reduce distortion due to thermal drift. Additionally, we assume the lattice constant of graphene to be the known value (⁠$ag=0.242 nm$⁠) to determine the CDW wavelength $λCDW=1.193 nm$⁠. The CDW wavelength measured here agrees with the measured value (1.18 nm) of the intrinsic CDW modulation in 1T-TaS₂.¹¹ 

We probe the density of states (DOS) at the surface of the G/TaS₂ structure by measuring the bias-dependent differential tunneling conductance [dI(V_b)/dV]. The average of 64 tunneling spectra taken at the G/TaS₂ surface is displayed in Fig. 2(c). There is a DOS dip at the Fermi level (zero bias marked as E_F) and a shoulder near 500 mV. Interestingly, this spectrum is nearly identical to previous reports of STM spectra taken on bare TaS₂ at this temperature^53,54 with no spectroscopic signature of the graphene passivation layer. We attribute this to the large difference in intrinsic carrier concentrations of these materials (∼10¹² cm⁻² for graphene and ∼10¹⁵ cm⁻² for 1T-TaS₂).³³ Despite the closer proximity of the graphene layer to the STM tip, the large intrinsic DOS of 1T-TaS₂ dominates the measurement and obscures the expected Dirac spectrum of graphene. Thus, we conclude that electrons in graphene do not strongly interact with the CDW phase of 1T-TaS₂ at room temperature. This further supports graphene as a superior passivation/encapsulation material for measurements using conducting surface probes.

The observation of the charge density modulation through the graphene passivation layer is highly beneficial. We can map the full CDW order parameter within the NC-CDW phase of 1T-TaS₂ over relatively large areas (compared to the CDW wavelength) without interference from the passivation layer. On larger length scales, there are nearly periodic changes in the CDW amplitude and phase, as expected from previous measurements of the NC-CDW phase [Fig. 3(a)]^28,30,31 and the Landau–Ginzburg type model developed by Nakanishi and Shiba.²⁹ However, these are subtle and difficult to see from the topography image alone. In Fig. 3(b), we plot the gradient of the STM current signal. Monitoring the measured current, rather than the piezo extension, is commonly used to highlight small differences in topography as the current is exponentially sensitive to variations of the sample height. The current gradient [Fig. 3(b)] shows more clearly the positions of the CDW domain walls, where the CDW amplitude is reduced and the CDW phase changes locally.

From analysis of the FFT of Fig. 3(a), we find that the average spacing between domains in this region is 6.2(3) nm; however, the sizes and shapes of the domains are clearly not perfectly uniform. This variation is reflected in the spacing and relative orientations of the CDW vortex positions, which similar to the Abrikosov lattice case can be quantified by calculating the respective correlation functions.^27–31 The CDW vortex positions, determined from the STM measurement, are used to calculate the translational and orientational correlation functions for the CDW vortex lattice. The translational correlation function (⁠$GTr)$⁠, which correlates the spacing between CDW vortices, and the sixfold orientational correlation function [$G6r]$⁠, which measures the correlation in the bond angles between neighboring vortices, are plotted on log –log scales in Figs. 3(d) and 3(e), respectively. These functions are constant as a function of inter-particle spacing for an ordered crystal lattice and decay exponentially for a disordered liquid. We find that both G_T(r) and G₆(r) decay as power laws in inter-vortex spacing (for $r≤10λd$⁠), but with very different exponents. G_T(r) decays faster than G₆(r), indicating that the vortex spacing (domain wall length) is not as uniform across the lattice as the orientation between vortices (domain wall direction). Such scaling laws are consistent with those of a Bragg glass,⁵⁵ a quasi-long range ordered state of matter observed in flux line lattices in type-II superconductors.^47,52 The Bragg glass phase in superconducting vortex lattices is thought to arise from weak pinning of the vortex core to defects along the length of the vortex through the thickness of the superconductor.^42,47 In the case of the CDW vortex lattice, the CDW vortex positions are likely disordered by weak pinning of the domain walls to defects within the 2D plane of the CDW, which can be seen in the STM topography and current gradient images [Figs. 2(a) and 2(b), respectively].^56,57 Additionally, the CDW vortices are known to order in the out-of-plane direction with 3-layer periodicity [as depicted in Fig. 3(c)], indicating that interlayer interactions might play a role in stabilizing the Bragg glass phase.⁵⁸ 

A commonly asserted picture is that conduction in this complex CDW phase is mediated by conducting domain walls surrounding insulating domains.⁵⁹ However, this is inconsistent with transport measurements, which show Ohmic resistance that does not scale quadratically with the domain size, as expected from domain wall conduction in 2D.⁶⁰ While we do not expect to see a full gap at the surface of the structure (due to the conducting graphene layer), we do not observe gap-like features (such as sharp band edges or coherence peaks) anywhere on the sample surface, consistent with previous STM works²³ and early angle-resovled photoemission spectroscopy (ARPES) measurements,⁶¹ which show a strong reduction in gap size within the NC-CDW phase and a non-zero DOS at the Fermi level. This suggests that the low energy electrons are not strongly localized in this phase (even within domains) as is the case in the low temperature, commensurate CDW phase.^12,19,61

As we reduce the temperature from room temperature, 1T-TaS₂ undergoes a CDW commensuration transition around 180 K where the CDW modulation commensurate with the atomic lattice forms star-shaped clusters involving 13 Ta ions each. Due to strong Coulomb interactions, this commensuration additionally induces a metal-to-insulator transition in 1T-TaS₂.²² The emergent ground state in the low temperature phase is, thus, semi-conducting. This transition and resulting semi-conducting behavior is evident from the two-terminal resistance measurement of both bare 1T-TaS₂ and a region partially covered with graphene, given in Figs. 4(b) and 4(c).

A cartoon depiction of the transport measurement is given in Fig. 4(a). There are two important regions to the device: a region of bare 1T-TaS₂ and a region partially covered by graphene (see also supplementary material). A current is sourced through both regions, while the voltage across each region is monitored as a function of temperature. The resistance vs temperature curve for bare 1T-TaS₂ [black points in Figs. 4(b) and 4(c)] shows the expected first-order transition, and corresponding hysteresis window, between the nearly commensurate and commensurate CDW phases (between approximately 180 and 240 K). As temperature is reduced, the sample undergoes the NC-CDW to C-CDW transition at about 192 K, where the resistance suddenly jumps up by more than a factor of two and continues to rise as temperature reduces further [see Fig. 4(c)]. This regime where the system seems to be gradually entering the commensurate phase is likely due to the reordering of domains, which have been quenched into metastable configurations during the initial, sudden commensuration of the majority of the sample. After the CDW becomes fully commensurate (below approximately 150 K), the resistance continues to increase with decreasing temperature, consistent with the expected semiconducting properties of the C-CDW phase.

In the region partially covered by graphene, the current flows through both graphene and 1T-TaS₂ [Fig. 4(a)], making it difficult to separate their contributions (see the supplementary material). Instead, we simply compare the resistance vs temperature curves here and look to STM/STS for a better microscopic understanding (see below). As the G/TaS₂ region is cooled from room temperature [red data points in Figs. 4(b) and 4(c)], the resistance increases linearly with a slope that follows that of 1T-TaS₂ at this temperature.⁶² This indicates that the resistance contribution from the 1T-TaS₂ dominates in this temperature region. Upon approaching the C-CDW transition (∼192 K) in bare 1T-TaS₂ from above [see Fig. 4(c)], the resistance of the G/TaS₂ sample begins to turn slightly downward, consistent with the metallic nature of doped graphene, followed by a gradual resistance increase below ∼192 K. This crossover from graphene-like to 1T-TaS₂-like behavior in dR/dT, without any sharp change signaling the charge ordering of 1T-TaS₂, suggests that the graphene layer responds to the imminent ordering of domain walls in 1T-TaS₂ near commensuration and prevents or delays its formation.^63,64 One would expect that the sudden enhancement of electron–electron interactions and loss of carriers at the Fermi level within in the 1T-TaS₂ would cause a corresponding abrupt jump in the resistance of the G/TaS₂ sample. However, it seems that screening and/or charge transfer between graphene and 1T-TaS₂ provides feedback, which hinders commensuration of the CDW near the graphene layer. Below this temperature, in the commensurate regime, we observe metallic behavior of the G/TaS₂ system, while bare 1T-TaS₂ is semiconducting, indicating that graphene is likely providing carriers within the gap of 1T-TaS₂.

At 78 K, we image the G/TaS₂ surface by STM and STS [Figs. 4(d) and 4(e)]. As in the room temperature measurement, we observe both the CDW modulation of 1T-TaS₂ as well as the graphene atomic lattice [FFT in Fig. 4(d) inset]. Here, the CDW amplitude and phase remain constant over the measured region of the sample, indicating the absence of domain walls and CDW vortices. Tunneling spectroscopy reveals that the local DOS at the surface of the structure contains features expected of both 1T-TaS₂ and graphene. The low energy dI/dV measurement in Fig. 4(e) shows large peaks on either side of the Fermi level (marked with red and blue dashed lines) near the energies of the localized bands in 1T-TaS₂, often denoted as upper and lower Hubbard bands.^19,65 However, between the peaks, where 1T-TaS₂ is expected to exhibit a gap, we find a finite DOS with a linear slope near the Fermi level characteristic of the Dirac electrons in graphene. The linear slope at low energies indicates that the Dirac point of graphene has moved to higher (positive) energies due to charge transfer with the 1T-TaS₂ flake. Thus, the DOS at the sample surface does not go to zero at the Fermi level, as in pristine graphene, consistent with the low temperature metallic behavior observed in the transport measurement [Fig. 4(b)].

The observed convolution of the DOS of these two materials at the surface of their heterostructure could be the result of several effects. As the STM tip is closer to the graphene layer than to 1T-TaS₂, the tunneling measurement preferentially samples states, which lie within the graphene layer due to the exponential decay of the electronic wavefunction into the vacuum gap.⁶⁶ Therefore, features inherent to the DOS of 1T-TaS₂ (such as the localized peaks near the Fermi level) should be highly suppressed compared to the DOS of graphene; however, 1T-TaS₂ has an intrinsic 2D carrier concentration, which is three orders of magnitude larger than that of graphene.³³ Then, the large DOS in 1T-TaS₂ could be the reason we are able to see features of 1T-TaS₂ through the graphene layer. Furthermore, as these are quantum electronic systems in close contact, we expect that the interaction of electrons within host materials might modify their low energy properties (Fermi velocity, “gap” size, etc.) in addition to generating states described by the superposition of their electronic wavefunctions at their interface. At the junction between metals and superconductors, this gives rise to the superconducting proximity effect. However, a CDW proximity effect has not yet been observed. A detailed comparison of the low energy electronic properties of bare 1T-TaS₂ and G/TaS₂, a theoretical model, which captures electronic interactions in the heterostructure, and the CDW proximity effect at the G/TaS₂ interface will be given in a forthcoming publication.

In conclusion, we have demonstrated that passivating the reactive surface of 1T-TaS₂ with a graphene cover layer makes it possible to probe its CDW phases by STM. At room temperature, we show that the NC-CDW is broken into nearly periodic domains by a network of CDW vortices. By analyzing the spatial distribution of the CDW vortex network, we find that both the translational and orientational correlation functions exhibit a power law decay with exponents η_T = 0.77 and η₆ = 0.03, respectively, consistent with the quasi-long range order predicted for a Bragg glass phase. Cooling down to 78 K, we found that the G/TaS₂ heterostructure combines the properties of both the semi-conducting 1T-TaS₂ and semi-metallic graphene, including localized bands associated with the C-CDW state of 1T-TaS₂ and low energy carriers associated with states in the semi-metallic graphene layer. Finally, we discuss charge transfer and interactions at the interface between graphene and 1T-TaS₂, including the possibility of a proximity-induced charge density wave in graphene.

See the supplementary material for sections providing details about sample fabrication in argon atmosphere, current distribution through graphene/TaS2 transport sample, Moiré pattern between graphene and 1T-TaS2, and CDW disorder in thin 1T-TaS2.