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Modulating Charge Density Wave Order in a 1T-TaS2/black Phosphorus Heterostructure. Ziying Wang, Leiqiang Chu, linjun li, Ming Yang, Junyong Wang, Goki Eda, and Kian Ping Loh Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b04805 • Publication Date (Web): 01 Apr 2019 Downloaded from http://pubs.acs.org on April 1, 2019

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Modulating Charge Density Wave Order in a 1T-TaS2/Black Phosphorus Heterostructure

Ziying Wang1,2†, Leiqiang Chu,1,2†, Linjun Li 4, Ming Yang5, Junyong Wang2,3, Goki Eda2,3, Kian Ping Loh1,2* 1Department 2Centre

of Chemistry, National University of Singapore, Singapore, 117543

for Advanced 2D Materials, National University of Singapore, Singapore,

117546 3Department

4State

of Physics, National University of Singapore, Singapore, 117542

Key Laboratory of Modern Optical Instrumentation, College of Optical

Science and Engineering, Zhejiang University, Hangzhou, China 310027 5Institute

of Materials Research and Engineering, Agency for Science Technology

and Research, 2 Fusionopolis Way, Singapore 138634 Corresponding Author *Email:

[email protected] Phone: (65) 6516 2658

1

ACS Paragon Plus Environment

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Abstract: Controllability of collective electron states has been a long-sought scientific and technological goal and promises development of new devices. Herein, we investigate the tuning of charge density wave (CDW) in 1T-TaS2 via a 2D van der Waals heterostructure of 1T-TaS2/BP. Unusual gate-dependent conductance oscillations were observed in 1T-TaS2 nano-flake supported on BP in transport measurements. STM study shows that the nearly commensurate CDW (NC) phase survived to 4.5 K in this system, which is substantially lower than the NC to commensurate CDW (C) phase transition temperature of 180 K. A Coulomb blockade model was invoked to explain the conductance oscillations, where the domain walls and domains in NC phase serve as series of quantum dot arrays and tunnelling barriers, respectively. DFT calculations show that a range of interfacial interactions, including strain and charge transfer, influences the CDW stabilities. Our work sheds light on tuning CDW orders via 2D heterostructure stacking and provides new insights on the CDW phase transition and sliding mechanism.

Keywords: Coulomb oscillations, charge density wave, strongly correlated systems, two-dimensional materials, Van der Waals heterostructure, 1T-tantalum disulphide (1T-TaS2)

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Charge density wave (CDW) is one of the most intriguing subjects in condensed matter physics1-7. CDW research has prompted fundamental understanding of superconductivity8-10 and spurred the

development of new devices such as

memristive transistors5-6, pulse-duration memory devices11, and CDW based logic gates12. Transition metal dichalcogenides (TMDs) are among the most well-known CDW materials. Among them, 1T-TaS2 has been a good candidate to study CDW due to its rich phase diagram13-15. The phase diagram of 1T-TaS2 consists of normal metal (undistorted state), incommensurate charge density wave (IC), nearly commensurate charge density wave (NC), commensurate charge density wave (C), and a superconductivity (SC) phase under pressure or doping4,

16.

Figure 1a

illustrates the phase evolution of metal, IC, NC and C phase of 1T-TaS2. Both IC and C phase are long-range ordered, but the angles between CDW superlattice and original atomic lattice are 0° and 13.9° in IC and C phase, respectively. IC phase is metallic but C phase behaves as a Mott insulator13,

17.

The NC phase is an

intermediate phase, which consists of hexagonal commensurate domains divided by domain walls; at the domain boundary, the phase of the CDW changes abruptly and amplitude of CDW decreases17-19. The domain walls are called discommensurations. The atomic structures within the domains and domain walls are similar to those in C phase and high-temperature metallic IC phase, respectively17, 20-21. The ability to control different CDW states offers a means to understand the CDW formation mechanisms and promises new devices. Controlling CDW order has 3


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been widely investigated via a variety of methods, such as intercalation/chemical doping, applying pressure, laser excitation, electrical pulsing, substrate coupling and controlled synthesis4-5,

16, 22-31.

Chemical doping and applying pressure had

been reported to suppress CDW and induce superconductivity4,

20, 32.

By laser

excitation and electrical pulsing, it is possible to create the hidden metastable CDW state which is not accessible under thermal equilibrium conditions28, 33-34. Phase switching of 1T-TaS2 by current pulsing has been demonstrated by Yoshida et al.5, 35.

A recent paper reported that CDW is not traceable in monolayer 1H-TaS2

synthesised on Au substrate, due to strain and doping effect from the Au substrate 23, 25.

Also, exfoliated 1T-TaS2 nano-flakes supported on substrates of various

surface roughness show different CDW phase transition temperatures22. In recent years, the surge of 2D material research and the fascinating properties exhibited by 2D van der Waals (vdW) heterostructures36-40 have stimulated interests in studying conventional CDW conductors in the 2D limit. When CDW conductors are thinned down to the atomic limit, they exhibit new and fascinating properties distinct from their 3D counterparts3, 20, 22, 30, 41-42. However, modulating CDWs via fabricating a vdW hetero-stack is rarely studied, leaving the question of how interface effects inherent in such vdW heterostructures could be exploited to tune CDW properties open. In this study, we investigate how interface effects exerted by black phosphorous (BP) on 1T-TaS2 affect CDW by conducting transport measurements together with 4


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scanning tunnelling electron microscopy (STM). We observed gate-dependent conductance oscillations in few layer 1T-TaS2 supported on BP. STM studies found the domain-like CDW structures remained on 1T-TaS2 until 4.5 K, a coulomb blockade (CB) model was invoked to explain the conductance peaks. DFT calculations revealed that interface effects such as orbital hybridization, strain and doping played important roles in CDW stabilities.

Figure 1. Schematic and characterisation of the BN/1T-TaS2/BP/BN device. (a) Illustrations of metal, IC, NC, and C phase structures. The grey dots represent Ta atoms. Grey and blue stars represent CDW superlattice in IC and C phase, 5


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respectively. (b) Side view illustration of the vdW device of BN/1T-TaS2/BP/BN. The electrodes only contact the 1T-TaS2 flake, without connecting to BP. (c) Optical images of the BN/1T-TaS2/BP hetero-stack before (left panel) and after (right panel) deposition of electrodes. scale bar: 10 µm. The metal contacts are patterned in Hall bar configuration. (d) Conductance oscillations as a function of Vg with a small Vsd = 2 mV and T = 1.5 K. Inset shows the conductance peaks between -20 and -60 Vg. (e) 2D color map of differential conductance as a function of Vsd and Vg, plotted in logarithmic scale. The Coulomb diamonds are well resolved. Results and Discussions Conductance oscillations observed in BN/1T-TaS2/BP heterostructure Figure 1c shows optical images of the BN/1T-TaS2 (5-8 nm)/BP (20 nm) heterostack before (left) and after (right) electrical contact. The electrodes are fabricated on 1T-TaS2 and in vicinity of BP. Figure 1d shows a typical example of the conductance oscillations observed in the BN/1T-TaS2/BP device, measured at 1.5 K and zero magnetic field, with a small source drain bias (Vsd) of 2 mV. All the conductance peaks are reproducible when temperature and voltage are ramped up and down. Figure 1e shows 2D color map of the differential conductance (with background subtracted) collected at different Vsd as a function of back gate voltage (Vg), at 1.5 K. Interestingly, a few Coulomb diamonds are resolved, which seems to suggest the formation of quantum dot or wire structure in the device43-47. A 6


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Coulomb diamond is defined as a diamond shape area in the Vsd–Vg plot, where the edge of the diamond is lifted for CB48. In contrast, devices of pure 1T-TaS2 or BP show no obvious conductance oscillations (see Figure S8 and Figure S9 in SI). Based on the Coulomb diamond structure in 2D contour, one may wonder whether the conductance peaks originate from CB. The conductance oscillations displayed in 1T-TaS2/BP devices meet the two basic requirements of the CB model43-47. First, ℎ

the tunnel resistance should be much larger than the resistance quantum 𝑒2 = 25.8 kΩ. The resistances measured in our samples are approximately 40 kΩ and 80 kΩ in Device 1 and 2, respectively. Secondly, the charging energy should be much larger than thermal energy. Charging energy results from the repulsion interactions between electrons and can be determined as the red arrow denoted in Fig. 1e49. The charging energy here is up to 2.4 meV, much larger than the thermal energy of 0.13 meV at 1.5 K. Formation of disordered quantum dots arrays in 1T-TaS2 To reveal the atomic origin of the conductance peaks, STM study is carried out to characterize the surface structure of TaS2 supported on BP. Sample preparation details are described in SI “STM sample preparation and experimental details” section. Figure 2a and e show surface construction at 4.5 K of bilayer 1T-TaS2 supported on silicon substrate and few-layer BP crystal, respectively. Figure 2b and 2f are black and white images of 2a and 2e for better contrast. A typical C phase 7


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shows on 1T-TaS2 supported on silicon substrate, with a periodicity of 1.3 nm (√13 × √13) and rotation angle at 13.9°, as determined from Fourier transformed image (FFT) (Fig. 2c)50. Fig. 2d is the STS data of C phase, showing a band gap around 0.34 eV, consistent with previously published work34, 51. However, on the surface of bilayer 1T-TaS2 supported on BP, as is shown in Fig. 2e, the long range ordered C phase is replaced by domain-like CDW structure50, using same sample preparation and scanning conditions applied in TaS2/Silicon sample. The dashed lines demarcate commensurate domains and domains walls17, 52-56. The periodicity and rotation angle determined from FFT image (Fig. 2g) are around 1.3 nm and 13.9°, respectively. Besides, STS data of the domain-like CDW structure (Fig. 2h) shows no band gap. The morphology and STS of superstructure are comparable with those of the NC phase17, 57-58, indicating that the NC phase survives to 4.5 K in 1T-TaS2 supported on BP. The suppressed NC to C phase transition by transport measurements will be discussed later. In comparison to reported STM study of NC phase structure17, 57-58, the domain walls in our system do not form a network but are isolated by the CDW domains. We name this “NC” phase observed at 4.5 K as NC’, which resembles a “supercooled NC phase” discovered at 4.5 K in few-layer 1T-TaS2 through fast cooling33. The reduced area of domain walls in NC’ phase in our work and the reported “supercooled NC phase” may have the same origins and can be explained as follows. In pure 1T-TaS2, as the system cools down, the commensurate domains of NC phase grow larger and domain walls melt, and finally the domains merge 8


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into a long range ordered commensurate phase—C phase55-56. However, when sample is subjected to fast cooling or doping, NC to C transitions are partially completed only13, 33, 59, leaving relatively larger domains and narrower walls than those in a normal NC phase.

Figure 2. STM topography of 1T-TaS2 supported on Silicon (a) and on BP (e) obtained at 4.5 K. Triangular √13 ×√13 C superlattice are resolved with partially resolved S atom in (a) and domain structures in (e). Scanning area: 15 x 15 nm2. (b) and (f) are black and white images of (a) and (e), respectively. (c) and (g) are FFT images of (a) and (e), respectively. The black and red circles correspond to primary atomic lattice and superlattice, respectively. (d) and (h) are STS data of areas in (a) and (e). According to previous studies, commensurate domains and walls play very different roles in the conductance of NC phase4, 13, 17, 20, 60-62. The conductance of 9


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NC phase is dominated by discommensurations4,

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20, 61.

The domain walls are

expected to be conducting whereas electrons are localized in the domains. Thus, it can be considered that the interior of each domain and wall have similar transport properties as the C and IC phase, respectively4, 20, 61. Herein, we propose that the isolated domain walls in NC’ state serve as quantum dots and the commensurate domains serve as tunnelling barriers. The chemical potential of the domain walls can be electrostatically tuned, allowing the tunnelling of electrons through domains when the energy levels are aligned, and blocking them otherwise. This process resembles CB. The non-periodicity of peaks could be due to the disordered quantum arrays63, as is known that periodicity of Coulomb peaks are difficult to identify in random quantum dot arrays64-66. A similar work from Joung et.al reported nonperiodic conductance oscillations in fabricated reduced graphene oxide (RGO)66. The conductance peaks were assigned as CB peaks and originated from the random quantum dot arrays of RGO. Coulomb oscillations are not commonly seen in quantum dot arrays as the density of states (DOS) in metallic or magnetic quantum dot arrays are too high, which quenches the gate effect. However, as the DOS in RGO is much lower, the DOS can be tuned electrostatically by gate voltage, leading to coulomb oscillations. Similarly, since TaS2/BP at 1.5 K is a semiconductor (R=40KΩ), CB-like behaviour may manifest in the quantum dot arrays formed in NC’ phase. Conductance oscillations compared with disordered quantum dot array prediction. 10


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Figure 3a shows the evolution of conductance oscillations from 1.5 K to 20 K. The conductance peaks gradually disappear as temperature increases and finally become indistinguishable at 20 K. Figure 3b displays the same data in panel (a) with linear background deducted. As can be seen, when temperature ramps up, the peak width increases, while peak height maintains almost constant. Meanwhile, no peak shift is observed, as guided by the black dotted lines. Figure 3c shows that the conductance oscillations are independent of the perpendicular magnetic field. No peak splitting, periodicity modulation, or amplitude attenuation occurs up to 5 T. The insensitivity to magnetic field suggests that the conductance peaks originate from some localized states, rather than universal conductance fluctuations or other quantum interference phenomena (similar as light in a Fabry–Perot interferometer) 67-69.

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Figure 3. Conductance oscillations analysed with disordered quantum dot array prediction. (a) Temperature dependent conductance-gate voltage curves. The curves are offset on the y-axis for a clear comparison of the peaks. The conductance peaks gradually disappear with temperature increasing and finally merge into 12


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background at 20 K. (b) The same data as in (a) with linear background subtracted. (c) Conductance-gate voltage curves at a series of magnetic fields from 0 T to 5 T at 1.5 K. The conductance oscillations are insensitive to magnetic field variations. (d) Lorentzian (red solid line) and cosh(x) (blue solid line) fits to a typical normalized Coulomb peak —inset: same figure plotted in the logarithmic scale. (e) I–V characterization of BN/1T-TaS2/BP devices from 1.5 K to 8 K. Nonlinearity is clearly seen at 1.5 K and is weakened as temperature increases. (f) I as a function of (V −Vt )/Vt curve. The symbols are data points and the solid line is the power fitting of data. Figure 3d shows a typical normalized conductance peak measured at 1.5 K analysed with CB model. The peak is fitted with a cosh (blue) and Lorentzian (red) function, respectively70. The inset shows the same peak displayed in logarithmic scale. The tails of the peak decrease slowly and, thus, are fitted more accurately with the cosh function, indicating that the Coulomb oscillations are in the weak coupling regime70. More details of peak fitting are described in SI 3 “Coulomb peak line shape analysis”. Figure 3e shows I–V curves as a function of temperature in a 1T-TaS2/BP device. A four-probe measurement is applied to exclude influence from contact resistance or Schottky barrier effect. As can be seen, the I–V curves above 4 K is linear, indicating good contact between crystal and metal contacts. However, at 1.5 K, the I–V curve is symmetrical and nonlinear. Theory predicts that in a quasi-1D and 2D 13


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quantum dot arrays, the nonlinear IV curves should follow 𝐼 ∝ (

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𝑉 ― 𝑉𝑡 𝛼 𝑉𝑡

) with the

scaling exponent α assuming values of 1 and 1.6, respectively66, 71. Such a scaling behaviour has also been applied in poly-dispersed quantum dot arrays72-75. Figure 3f shows I as a function of (𝑉 ― 𝑉𝑡)/𝑉𝑡. Vt is the threshold voltage, determined at 6.0 mV as the black dashed lines show. α value is extracted at 1.3 from fitting, which is slightly smaller than the predicted value of 1.6. Induced anisotropy in 1T-TaS2 by BP Since BP is anisotropic, it is interesting to know whether the anisotropy would transfer to 1T-TaS2. One recent work from Liu. et al demonstrated anisotropic moiré superlattice and Raman modes of graphene when superimposed on BP76. We conduct Raman and transport measurement to further characterize the influence of BP on TaS2. Angle dependent Raman intensity of low frequency modes, high frequency modes from TaS2, and 𝐴1𝑔 mode (361 cm-1) from BP are showed in left, middle and right panels in Fig. 4a. As can be seen, 𝐴1𝑔 mode of BP exhibits a periodicity of π/2 with one global maximum at 30° across π/2, which agrees with published work77. Interestingly, the Raman responses of TaS2 on BP display the same periodicity (π/2) and phase as those of the BP 𝐴1𝑔mode, which implies that the Raman modes of TaS2 become anisotropic when placed on BP. Angle-dependent polarised Raman measurements show that in both vertical (𝑥𝑥) and parallel (𝑥𝑦) configuration, the 14


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Raman responses of TaS2 show anisotropy that are correlated with that of 𝐴1𝑔 (and 𝐴2𝑔) mode of BP (Figure S6). As 𝐴1𝑔 and 𝐴2𝑔 modes of BP arise from vibrations along the c-axis and armchair direction, respectively78, correlations of the phonon modes of TaS2 with 𝐴1𝑔 and 𝐴2𝑔 mode suggest that the vibration modes of TaS2 are affected by BP in the armchair direction to a larger extent than the zigzag direction. The induced anisotropic Raman intensity for TaS2 could arise from strain effect22-23, 79 or the interlayer coupling effects 76, 80-81. We designed another type of device to probe the anisotropic transport properties of 1T-TaS2/BP heterostructure. The device characterization and fabrication details are described in the supporting information. To rule out electrical contributions from BP, we extract the parallel resistance of 1T-TaS2 (the parallel resistance model and extraction methods are described in SI “Parallel resistance extraction”. For all the transport data of heterostructure presented in this work, the armchair direction of BP is set as 0°, as determined by angle-resolved Raman spectroscopy77. Isotropic NC-to-C phase transition in pure 1T-TaS2 has been verified as Figure S11 shows. In contrast, the NC-to-C phase transitions in the BP/1T-TaS2 heterostructure are suppressed and conductivity of 1T-TaS2 become anisotropic, as is shown in Fig. 4b. It is known that around the transition temperature the resistance of C state should be one order larger than that in NC

13, 20.

In view of that fact that the resistance

increase in BP/1T-TaS2 heterostructure from room temperature to low temperature is less than 5 times (Fig. 4c), we infer that the NC phase remains in the system until 15


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low temperature. The suppressed NC to C phase transition is consistent with STM results showed in Figure 2. In addition, from Fig. 4b, the amplitude of the resistance jump is anisotropic. It is largest along the 90°—zigzag direction of BP and smallest along the 0°—armchair direction of BP, suggesting CDW transitions are more suppressed along the armchair than zigzag direction of BP, which agrees well with the Raman studies discussed before. Figure 4c shows the resistance–temperature curves of pure TaS2 (red line) and BP/TaS2 (black line) devices. The discontinuity in the red line results from different measurement methods. For pure 1T-TaS2, the resistance shows a steep increase of two orders from 50 K to 1.5 K, which is explained by Mott localization in C phase13. When C phase forms in 1T-TaS2, the electron clouds form superlattices that are “frozen” in the atom sites, leading to a Mott insulator state. In contrast, for 1T-TaS2 on BP, resistance increases only by a factor of ~1.6 times from 50 K to 1.5 K. At 1.5 K the conductivity of TaS2 is 1.5 × 10 ―2 Ω ∙ cm, above the minimum metallic conductivity (3 × 10 ―3 Ω ∙ cm)13, supporting Mott localization is absent in 1TTaS2. This is consistent with the absence of C phase at low temperature. According to previous work, Mott localization could be destroyed by doping and intercalations13, 32, 59. Fazekas et.al reported that low level of intercalation lowered the resistivity of TaS2 by one order of magnitude because excess electrons/holes created by intercalation destroyed Mott localization13. The same effect may be operational here when charge transfer from the BP substrate leads to collapse of the Mott insulator state. 16


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Figure 2. Raman and Temperature-dependent charge transport characterization of BN/BP/1T-TaS2 /BN device: (a) 2D color map of the Raman-scattering intensities of BN/BP/1T-TaS2/BN heterostructure. Raman modes between 60 and 330 cm-1 are from 1T-TaS2 and Raman shift at 361 cm-1 is 𝐴1𝑔 mode of BP. (b) Resistance as a function of temperature of BN/BP/1T-TaS2/BN along a range of directions. (c) Comparison of resistance from 280 K to 1.5 K of 1T-TaS2 supported on BP (black curve) and BN (red curve) substrate, respectively. Resistivity is plotted in logarithmic scale.

DFT calculations of 1T-TaS2 /BP 17


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To reveal the origins of the suppressed C phase of 1T-TaS2 on BP as well as its anisotropic characteristics, first-principles calculations were carried out to examine the effects of orbital hybridization, doping, and strain on the C phase. The TaS2/BP 2D heterostructure was modelled by placing a (1×3√3) undistorted 1T-TaS2 monolayer on (1×4) BP bilayers (Fig. 9a). The in-plane lattice parameter of 1TTaS2 unit cell is 3.365 Å, and the lattice constants of bi-layer BP are 3.308 Å (zigzag) and 4.536 Å (armchair). In this model, 1.8% compressive and tensile strains are present on 1T-TaS2 along the zigzag and armchair directions of BP, respectively. The interlayer binding energy is calculated to be -20.7 meV/Å2, which is within the vdW interaction range. Figure 5b shows the calculated band structure of the 1TTaS2/BP heterostructure, where it is seen that the orbital hybridisation between BP and TaS2 along the armchair direction (Γ-Y) of BP is stronger than that along the zigzag direction (Γ-X). The projected density of states (PDOS) of px (upper) and py (lower) orbitals of S and P atoms (Fig. 5c) clearly shows that the coupling between the S py orbital and P py orbital is much more pronounced near Fermi energy, compared with that between the S px orbital and P px orbital. It has been suggested that the orbital hybridization between Ta t2g and S p orbital is one of the crucial driving forces for the formation of the ‘David star’ C superstructure82. However, when orbital hybridization of TaS2 and BP takes place, the orbital hybridization between Ta t2g and S p orbital may be affected, and, consequently, the C phase is destabilized. Therefore, interfacial orbital hybridization between BP and TaS2 could contribute to a suppressed and anisotropic C phase. 18


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Another possibility affecting the stability of the CDW is interface strain. According to the model used in our DFT calculations, 1T-TaS2 experience a tensile strain along zigzag direction and compressive strain along the armchair direction. Figure 5e shows the relative stability between C and Non CDW phase of 1T-TaS2, ∆E (∆E = E𝐶 ― E𝑁𝑜𝑛 𝐶𝐷𝑊) as a function of the applied strain. C phase stability increases as ∆E decreases. As can be seen, C phase stability is suppressed by compressive strain. Therefore, C phase is destabilized along the armchair direction. Enhancement of CDW stability by tensile strain has been calculated by others42, 83. Gan et al. found that, for both monolayer and bilayer 1T-TaS2, tensile and compressive strains can enhance and suppress the CDW stability, respectively. Similarly, Wei et al. reported that, in 1T-TiSe2, the compressive strain can destabilize CDWs, and tensile strain can stabilize CDWs83. The doping effect on CDW stability was also investigated. Figure. 9d shows the band diagrams of BP/1T-TaS2 heterostructure and pure TaS2. The Fermi level of the BP/TaS2 heterostructure is higher than that in TaS2, indicating that electrons are transferred from BP to TaS2 when they form the heterostructure. This may have the effect of destabilizing the CDW. For example, no CDW states were observed in 1H-TaS2 monolayer grown on the Au (111), where there is a strong n-doping of the 1H-TaS2 monolayer by the Au substrate (23). Subsequent calculations23 with harmonic approximation also suggest that n-doping suppresses CDW in 1H-TaS2.

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To summarize, our DFT calculations show that a combination of factors such as orbital hybridization and doping can suppress and induce an anisotropic C phase in 1T- TaS2-on-BP substrate. Other possible factors could be interface defects, spinorbital coupling between BP and TaS284, or the modulated c-axis orbital textures in TaS233, 85. For example, the interface defects, serving as CDW pinning centres, can increase the energy barrier between the C and NC phases and slow down the nucleation process during NC to C transition86-87. Consequently, the CDWs remain pinned around the impurities until low temperature and cannot form a long range ordered C phase54, 88.

Figure 3. DFT calculation of monolayer 1T-TaS2 on bilayer BP. (a) Model used for DFT calculations consists of a monolayer 1T-TaS2 (undistorted) on bilayer BP. The (1×3√3) 1T-TaS2 monolayer matches well with the (1×4) BP bilayers. (b) Projected band structure of the undistorted 1T-TaS2/BP heterostructure, in 20


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which the red dots and blue lattice denote the contribution of BP layers and TaS2 monolayer, respectively. (c) PDOS of px (upper panel) and py (lower panel) orbital of the S and P atom, respectively. (d) Energy-level diagram of the 1TTaS2/BP heterostructure and original 1T-TaS2. (e) Energy difference between CDW and non-CDW phases as a function of compressive strain.

Conclusion In summary, we have studied how interfacing TaS2 to BP allows the CDW order on the former to be modulated, both electrically as well as spatially. The observed conductance oscillations in few-layer 1T-TaS2 -on-BP was ascribed to CB, which originate from quantum dot arrays of domain walls in NC’ phase. STM study confirmed the presence of NC’ phase at 4.5 K. Raman and transport measurements revealed that both Raman modes and conductivity of 1T-TaS2 are anisotropic due to substrate effects from BP. DFT calculations show that a combination of effects such as orbital hybridization, strain and doping contribute to these observations. Our work suggests that interface effects in a vdW heterostructure provide a new pathway to tune CDW order in 2D materials.

ASSOCIATED CONTENT Supporting Information. Sample preparation and experimental details, data analysis methods including peak analysis and parallel resistance extraction, 21


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nonlinear IV curves, polarized Raman study, Raman and transport characterization of pure 1T-TaS2 and BP devices. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *Email:

[email protected]

*Phone:

(65) 6516 2658

Author Contributions Z. W., L. L. and K. P. L. conceived the project. Z. W., L. C. and L.L. prepared the devices and performed transport. M. Y. performed the DFT calculations. J. W. and Z.W. performed Raman measurements. All authors contributed to the data analysis and read the manuscript. Z.W. and L. C. contributed equally to this work. ACKNOWLEDGMENT K.P.L. acknowledges support from National Research Foundation, Prime Minister’s office, Mid-sized Centre fund. Z. W. thanks Dr. Jens Martin, Dr. Chen chuan for their valuable suggestions and data discussion.

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TOC graph:

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References (1) Grüner, G., The dynamics of charge-density waves. Reviews of Modern Physics 1988, 60 (4), 1129-1181. (2) Wilson, J. A.; Yoffe, A. D., The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties. Advances in Physics 1969, 18 (73), 193-335. (3) Hossain, M.; Zhao, Z.; Wen, W.; Wang, X.; Wu, J.; Xie, L., Recent Advances in Two-Dimensional Materials with Charge Density Waves: Synthesis, Characterization and Applications. Crystals 2017, 7 (10), 298. (4) Sipos, B.; Kusmartseva, A. F.; Akrap, A.; Berger, H.; Forro, L.; Tutis, E., From Mott state to superconductivity in 1T-TaS2. Nat Mater 2008, 7 (12), 960-965. (5) Yoshida, M.; Gokuden, T.; Suzuki, R.; Nakano, M.; Iwasa, Y., Current switching of electronic structures in two-dimensional 1 T− Ta S 2 crystals. Physical Review B 2017, 95 (12), 121405. (6) Yoshida, M.; Suzuki, R.; Zhang, Y.; Nakano, M.; Iwasa, Y., Memristive phase switching in two-dimensional 1T-TaS2 crystals. Science advances 2015, 1 (9), e1500606. (7) Ritschel, T.; Trinckauf, J.; Koepernik, K.; Büchner, B.; Zimmermann, M. v.; Berger, H.; Joe, Y. I.; Abbamonte, P.; Geck, J., Orbital textures and charge density waves in transition metal dichalcogenides. Nature Physics 2015, 11, 328. (8) Gabovich, A.; Voitenko, A.; Ausloos, M., Charge-and spin-density waves in existing superconductors: competition between Cooper pairing and Peierls or excitonic instabilities. Physics Reports 2002, 367 (6), 583-709. (9) Li, L. J.; O’Farrell, E. C. T.; Loh, K. P.; Eda, G.; Özyilmaz, B.; Castro Neto, A. H., Controlling many-body states by the electric-field effect in a twodimensional material. Nature 2016, 529 (7585), 185-189. (10) Neto, A. C., Charge density wave, superconductivity, and anomalous metallic behavior in 2D transition metal dichalcogenides. Phys. Rev. Lett. 2001, 86 (19), 4382. (11) Coppersmith, S. N.; Littlewood, P. B., Pulse-duration memory effect and deformable charge-density waves. Physical Review B 1987, 36 (1), 311317. (12) Khitun, A. G.; Geremew, A. K.; Balandin, A. A., Transistor-Less Logic Circuits Implemented with Two-Dimensional Charge Density Wave Devices. IEEE Electron Device Letters 2018. (13) Fazekas, P.; Tosatti, E., Electrical, structural and magnetic properties of pure and doped 1T-TaS2. Philosophical Magazine Part B 1979, 39 (3), 229244. (14) Fazekas, P.; Tosatti, E., Charge carrier localization in pure and doped 1T-TaS2. Physica B+ C 1980, 99 (1-4), 183-187. (15) Yoshida, M.; Zhang, Y.; Ye, J.; Suzuki, R.; Imai, Y.; Kimura, S.; Fujiwara, A.; Iwasa, Y., Controlling charge-density-wave states in nano-thick crystals of 1T-TaS2. Scientific reports 2014, 4, 7302. 24


Page 24 of 30

Page 25 of 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(16) Perello, D. J.; Chae, S. H.; Song, S.; Lee, Y. H., High-performance ntype black phosphorus transistors with type control via thickness and contactmetal engineering. Nature Communications 2015, 6, 7809. (17) Thomson, R. E.; Burk, B.; Zettl, A.; Clarke, J., Scanning tunneling microscopy of the charge-density-wave structure in 1T-TaS2. Physical Review B 1994, 49 (24), 16899-16916. (18) Nakanishi, K.; Takatera, H.; Yamada, Y.; Shiba, H., The Nearly Commensurate Phase and Effect of Harmonics on the Successive Phase Transition in 1T-TaS2. J. Phys. Soc. Jpn. 1977, 43 (5), 1509-1517. (19) Nakanishi, K.; Shiba, H., Domain-like Incommensurate ChargeDensity-Wave States and the First-Order Incommensurate-Commensurate Transitions in Layered Tantalum Dichalcogenides. I. 1T-Polytype. J. Phys. Soc. Jpn. 1977, 43 (6), 1839-1847. (20) Tsen, A. W.; Hovden, R.; Wang, D.; Kim, Y. D.; Okamoto, J.; Spoth, K. A.; Liu, Y.; Lu, W.; Sun, Y.; Hone, J. C.; Kourkoutis, L. F.; Kim, P.; Pasupathy, A. N., Structure and control of charge density waves in twodimensional 1T-TaS2. Proc Natl Acad Sci U S A 2015, 112 (49), 15054-9. (21) Spijkerman, A.; de Boer, J. L.; Meetsma, A.; Wiegers, G. A.; van Smaalen, S., X-ray crystal-structure refinement of the nearly commensurate phase of 1T-TaS2 in (3+2)-dimensional superspace. Physical Review B 1997, 56 (21), 13757-13767. (22) Zhao, R.; Wang, Y.; Deng, D.; Luo, X.; Lu, W. J.; Sun, Y.-P.; Liu, Z.K.; Chen, L.-Q.; Robinson, J., Tuning Phase Transitions in 1T-TaS2 via the Substrate. Nano Lett. 2017, 17 (6), 3471-3477. (23) Albertini, O. R.; Liu, A. Y.; Calandra, M., Effect of electron doping on lattice instabilities in single-layer 1H-TaS2. Physical Review B 2017, 95 (23), 235121. (24) Fu, W.; Chen, Y.; Lin, J.; Wang, X.; Zeng, Q.; Zhou, J.; Zheng, L.; Wang, H.; He, Y.; He, H.; Fu, Q.; Suenaga, K.; Yu, T.; Liu, Z., Controlled Synthesis of Atomically Thin 1T-TaS2 for Tunable Charge Density Wave Phase Transitions. Chem. Mater. 2016, 28 (21), 7613-7618. (25) Sanders, C. E.; Dendzik, M.; Ngankeu, A. S.; Eich, A.; Bruix, A.; Bianchi, M.; Miwa, J. A.; Hammer, B.; Khajetoorians, A. A.; Hofmann, P., Crystalline and electronic structure of single-layer TaS2. Physical Review B 2016, 94 (8), 081404. (26) Di Salvo, F.; Wilson, J.; Bagley, B.; Waszczak, J., Effects of doping on charge-density waves in layer compounds. Physical Review B 1975, 12 (6), 2220. (27) Li, L. J.; Lu, W. J.; Zhu, X. D.; Ling, L. S.; Qu, Z.; Sun, Y. P., Fedoping–induced superconductivity in the charge-density-wave system 1T-TaS 2. EPL (Europhysics Letters) 2012, 97 (6), 67005. (28) Stojchevska, L.; Vaskivskyi, I.; Mertelj, T.; Kusar, P.; Svetin, D.; Brazovskii, S.; Mihailovic, D., Ultrafast Switching to a Stable Hidden Quantum State in an Electronic Crystal. Science 2014, 344 (6180), 177-180. (29) Vaskivskyi, I.; Mihailovic, I. A.; Brazovskii, S.; Gospodaric, J.; Mertelj, T.; Svetin, D.; Sutar, P.; Mihailovic, D., Fast electronic resistance switching 25


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involving hidden charge density wave states. Nature Communications 2016, 7, 11442. (30) Zhao, R.; Grisafe, B.; Ghosh, R. K.; Holoviak, S.; Wang, B.; Wang, K.; Briggs, N.; Haque, A.; Datta, S.; Robinson, J., Two-dimensional tantalum disulfide: controlling structure and properties via synthesis. 2D Materials 2018, 5 (2), 025001. (31) Nakata, Y.; Yoshizawa, T.; Sugawara, K.; Umemoto, Y.; Takahashi, T.; Sato, T., Selective Fabrication of Mott-Insulating and Metallic Monolayer TaSe2. ACS Applied Nano Materials 2018, 1 (4), 1456-1460. (32) Yu, Y.; Yang, F.; Lu, X. F.; Yan, Y. J.; ChoYong, H.; Ma, L.; Niu, X.; Kim, S.; Son, Y.-W.; Feng, D.; Li, S.; Cheong, S.-W.; Chen, X. H.; Zhang, Y., Gate-tunable phase transitions in thin flakes of 1T-TaS2. Nat Nano 2015, 10 (3), 270-276. (33) Ma, L.; Ye, C.; Yu, Y.; Lu, X. F.; Niu, X.; Kim, S.; Feng, D.; Tománek, D.; Son, Y.-W.; Chen, X. H.; Zhang, Y., A metallic mosaic phase and the origin of Mott-insulating state in 1T-TaS2. Nature communications 2016, 7. (34) Cho, D.; Cheon, S.; Kim, K.-S.; Lee, S.-H.; Cho, Y.-H.; Cheong, S.-W.; Yeom, H. W., Nanoscale manipulation of the Mott insulating state coupled to charge order in 1T-TaS2. Nature communications 2016, 7, 10453. (35) Yoshida, M.; Suzuki, R.; Zhang, Y.; Nakano, M.; Iwasa, Y., Memristive phase switching in two-dimensional 1T-TaS2 crystals. Science Advances 2015, 1 (9). (36) Novoselov, K.; Mishchenko, A.; Carvalho, A.; Neto, A. C., 2D materials and van der Waals heterostructures. Science 2016, 353 (6298), aac9439. (37) Kang, J.; Li, J.; Li, S.-S.; Xia, J.-B.; Wang, L.-W., Electronic structural Moiré pattern effects on MoS2/MoSe2 2D heterostructures. Nano Lett. 2013, 13 (11), 5485-5490. (38) Wang, X.; Xia, F., Van der Waals heterostructures: Stacked 2D materials shed light. Nature materials 2015, 14 (3), 264. (39) Fang, H.; Battaglia, C.; Carraro, C.; Nemsak, S.; Ozdol, B.; Kang, J. S.; Bechtel, H. A.; Desai, S. B.; Kronast, F.; Unal, A. A., Strong interlayer coupling in van der Waals heterostructures built from single-layer chalcogenides. Proceedings of the National Academy of Sciences 2014, 111 (17), 6198-6202. (40) Huo, N.; Wei, Z.; Meng, X.; Kang, J.; Wu, F.; Li, S.-S.; Wei, S.-H.; Li, J., Interlayer coupling and optoelectronic properties of ultrathin twodimensional heterostructures based on graphene, MoS2 and WS2. Journal of Materials Chemistry C 2015, 3 (21), 5467-5473. (41) Damjan, S.; Igor, V.; Petra, S.; Evgeni, G.; Jan, G.; Tomaz, M.; Dragan, M., Transitions between photoinduced macroscopic quantum states in 1T-TaS 2 controlled by substrate strain. Applied Physics Express 2014, 7 (10), 103201. (42) Gan, L.-Y.; Zhang, L.-H.; Zhang, Q.; Guo, C.-S.; Schwingenschlogl, U.; Zhao, Y., Strain tuning of the charge density wave in monolayer and bilayer 1TTaS2. PCCP 2016, 18 (4), 3080-3085. (43) Fuhrer, A., Phase coherence, orbital and spin states in quantum rings. Ph.D. thesis, Swiss Federal Institute of Technology (2003). 2003. (44) Beenakker, C. W. J., Theory of Coulomb-blockade oscillations in the conductance of a quantum dot. Physical Review B 1991, 44 (4), 1646-1656. 26


Page 26 of 30

Page 27 of 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

(45) Kouwenhoven, L. P.; Marcus, C. M.; McEuen, P. L.; Tarucha, S.; Westervelt, R. M.; Wingreen, N. S., Electron transport in quantum dots. In Mesoscopic electron transport, Springer: 1997; pp 105-214. (46) Scott-Thomas, J. H. F.; Field, S. B.; Kastner, M. A.; Smith, H. I.; Antoniadis, D. A., Conductance Oscillations Periodic in the Density of a OneDimensional Electron Gas. Phys. Rev. Lett. 1989, 62 (5), 583-586. (47) Staring, A. A. M.; van Houten, H.; Beenakker, C. W. J.; Foxon, C. T., Coulomb-blockade oscillations in disordered quantum wires. Physical Review B 1992, 45 (16), 9222-9236. (48) Coulomb blockade in Quantum Dots. (49) Beenakker, C., Theory of Coulomb-blockade oscillations in the conductance of a quantum dot. Physical Review B 1991, 44 (4), 1646. (50) Han, W.; Hunt, E. R.; Pankratov, O.; Frindt, R. F., Bias-dependent STM images of charge-density waves onTaS2. Physical Review B 1994, 50 (19), 14746-14749. (51) Ekvall, I.; Kim, J.-J.; Olin, H. a., Atomic and electronic structures of the two different layers in 4Hb-TaS2 at 4.2 K. Physical Review B 1997, 55 (11), 6758-6761. (52) Nakanishi, K.; Shiba, H., Theory of Three-Dimensional Orderings of Charge-Density Waves in 1T-TaX2 (X: S, Se). J. Phys. Soc. Jpn. 1984, 53 (3), 1103-1113. (53) Wu, X. L.; Lieber, C. M., Direct observation of growth and melting of the hexagonal-domain charge-density-wave phase in 1T-TaS2 by scanning tunneling microscopy. Phys. Rev. Lett. 1990, 64 (10), 1150. (54) Wilson, J., Solution of the 1T2 discommensurate state of 1T-TaS2. An example of rotated hexagonal discommensuration. J. Phys.: Condens. Matter 1990, 2 (7), 1683. (55) Ishiguro, T.; Sato, H., Electron microscopy of phase transformations in 1T-TaS2. Physical Review B 1991, 44 (5), 2046-2060. (56) Ishiguro, T.; Sato, H., High-resolution electron microscopy of discommensuration in the nearly commensurate phase on warming of 1T-TaS2. Physical Review B 1995, 52 (2), 759-765. (57) Kim, J.-J.; Olin, H., Atomic- and electronic-structure study on the layers of 4Hb-Ta2 prepared by a layer-by-layer etching technique. Physical Review B 1995, 52 (20), R14388-R14391. (58) Tanaka, M.; Mizutani, W.; Nakashizu, T.; Yamazaki, S.; Tokumoto, H.; Bando, H.; Ono, M.; Kajimura, K., Study of Charge Density Waves in 4Hb– TaS2 by STM/STS. Japanese Journal of Applied Physics 1989, 28 (3R), 473. (59) Fujisawa, Y.; Shimabukuro, T.; Kojima, H.; Kobayashi, K.; Ohta, S.; Machida, T.; Demura, S.; Sakata, H., Appearance of a Domain Structure and Its Electronic States in Iron Doped 1T-TaS2 Observed Using Scanning Tunneling Microscopy and Spectroscopy. J. Phys. Soc. Jpn. 2017, 86 (11), 113703. (60) Mutka, H.; Housseau, N.; Zuppiroli, L.; Pelissieb, J., The pinning of the charge density wave to irradiation-induced defects. Philos. Mag. B 1982, 45 (3), 361-373.

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(61) Fujisawa, Y.; Shimabukuro, T.; Kojima, H.; Kobayashi, K.; Demura, S.; Sakata, H., Effect of Fe-doping on CDW state in 1T-TaS2 investigated by STM/STS. Journal of Physics: Conference Series 2017, 871, 012003. (62) Zwick, F.; Berger, H.; Vobornik, I.; Margaritondo, G.; Forró, L.; Beeli, C.; Onellion, M.; Panaccione, G.; Taleb-Ibrahimi, A.; Grioni, M., Spectral Consequences of Broken Phase Coherence in 1T-TaS2. Phys. Rev. Lett. 1998, 81 (5), 1058-1061. (63) Field, S. B.; Kastner, M. A.; Meirav, U.; Scott-Thomas, J. H. F.; Antoniadis, D. A.; Smith, H. I.; Wind, S. J., Conductance oscillations periodic in the density of one-dimensional electron gases. Physical Review B 1990, 42 (6), 3523-3536. (64) Stafford, C.; Sarma, S. D., Collective Coulomb blockade in an array of quantum dots: A Mott-Hubbard approach. Phys. Rev. Lett. 1994, 72 (22), 3590. (65) Grabert, H.; Devoret, M. H., Single charge tunneling: Coulomb blockade phenomena in nanostructures. Springer Science & Business Media: 2013; Vol. 294. (66) Joung, D.; Zhai, L.; Khondaker, S. I., Coulomb blockade and hopping conduction in graphene quantum dots array. Physical Review B 2011, 83 (11), 115323. (67) Lee, P. A.; Stone, A. D., Universal conductance fluctuations in metals. Phys. Rev. Lett. 1985, 55 (15), 1622. (68) Skocpol, W.; Mankiewich, P.; Howard, R.; Jackel, L.; Tennant, D.; Stone, A. D., Universal conductance fluctuations in silicon inversion-layer nanostructures. Phys. Rev. Lett. 1986, 56 (26), 2865. (69) Taychatanapat, T.; Tan, J. Y.; Yeo, Y.; Watanabe, K.; Taniguchi, T.; Özyilmaz, B., Conductance oscillations induced by ballistic snake states in a graphene heterojunction. Nature Communications 2015, 6, 6093. (70) Song, X.-X.; Zhang, Z.-Z.; You, J.; Liu, D.; Li, H.-O.; Cao, G.; Xiao, M.; Guo, G.-P., Temperature dependence of Coulomb oscillations in a fewlayer two-dimensional WS2 quantum dot. Scientific Reports 2015, 5, 16113. (71) Middleton, A. A.; Wingreen, N. S., Collective transport in arrays of small metallic dots. Phys. Rev. Lett. 1993, 71 (19), 3198-3201. (72) Black, C. T.; Murray, C. B.; Sandstrom, R. L.; Sun, S., Spin-Dependent Tunneling in Self-Assembled Cobalt-Nanocrystal Superlattices. Science 2000, 290 (5494), 1131-1134. (73) Noda, Y.; Noro, S.-i.; Akutagawa, T.; Nakamura, T., Electron transport in a gold nanoparticle assembly structure stabilized by a physisorbed porphyrin derivative. Physical Review B 2010, 82 (20), 205420. (74) Beecher, P.; Quinn, A. J.; Shevchenko, E. V.; Weller, H.; Redmond, G., Insulator-to-Metal Transition in Nanocrystal Assemblies Driven by in Situ Mild Thermal Annealing. Nano Lett. 2004, 4 (7), 1289-1293. (75) Tan, R. P.; Carrey, J.; Desvaux, C.; Lacroix, L. M.; Renaud, P.; Chaudret, B.; Respaud, M., Magnetoresistance and collective Coulomb blockade in superlattices of ferromagnetic CoFe nanoparticles. Physical Review B 2009, 79 (17), 174428. (76) Liu, Y.; Rodrigues, J. N. B.; Luo, Y. Z.; Li, L.; Carvalho, A.; Yang, M.; Laksono, E.; Lu, J.; Bao, Y.; Xu, H.; Tan, S. J. R.; Qiu, Z.; Sow, C. H.; Feng, 28


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Y. P.; Neto, A. H. C.; Adam, S.; Lu, J.; Loh, K. P., Tailoring sample-wide pseudo-magnetic fields on a graphene–black phosphorus heterostructure. Nature Nanotechnology 2018. (77) Wu, J.; Mao, N.; Xie, L.; Xu, H.; Zhang, J., Identifying the Crystalline Orientation of Black Phosphorus Using Angle-Resolved Polarized Raman Spectroscopy. Angew. Chem. Int. Ed. 2015, 54 (8), 2366-2369. (78) Ling, X.; Liang, L.; Huang, S.; Puretzky, A. A.; Geohegan, D. B.; Sumpter, B. G.; Kong, J.; Meunier, V.; Dresselhaus, M. S., Low-Frequency Interlayer Breathing Modes in Few-Layer Black Phosphorus. Nano Lett. 2015, 15 (6), 4080-4088. (79) Sadhu, K.; Manuel, B.; Yujing, M.; Horacio Coy, D.; Matthias, B., Layer- and substrate-dependent charge density wave criticality in 1T–TiSe2. 2D Materials 2018, 5 (1), 015006. (80) Havener, R. W.; Zhuang, H.; Brown, L.; Hennig, R. G.; Park, J., Angleresolved Raman imaging of interlayer rotations and interactions in twisted bilayer graphene. Nano Lett. 2012, 12 (6), 3162-3167. (81) Cai, Y.; Ke, Q.; Zhang, G.; Feng, Y. P.; Shenoy, V. B.; Zhang, Y. W., Giant phononic anisotropy and unusual anharmonicity of phosphorene: Interlayer coupling and strain engineering. Adv. Funct. Mater. 2015, 25 (15), 2230-2236. (82) Yi, S.; Zhang, Z.; Cho, J.-H., Coupling of charge, lattice, orbital, and spin degrees of freedom in charge density waves in 1T-TaS2. Physical Review B 2018, 97 (4), 041413. (83) Wei, M. J.; Lu, W. J.; Xiao, R. C.; Lv, H. Y.; Tong, P.; Song, W. H.; Sun, Y. P., Manipulating charge density wave order in monolayer 1T-TiSe2 by strain and charge doping: A first-principles investigation. Physical Review B 2017, 96 (16), 165404. (84) Yu, X.-L.; Liu, D.-Y.; Quan, Y.-M.; Wu, J.; Lin, H.-Q.; Chang, K.; Zou, L.-J., Electronic correlation effects and orbital density wave in the layered compound 1T-TaS2. Physical Review B 2017, 96 (12), 125138. (85) Ritschel, T.; Trinckauf, J.; Koepernik, K.; Büchner, B.; Zimmermann, M. v.; Berger, H.; Joe, Y.; Abbamonte, P.; Geck, J., Orbital textures and charge density waves in transition metal dichalcogenides. Nature physics 2015, 11 (4), 328. (86) Hellmann, S.; Beye, M.; Sohrt, C.; Rohwer, T.; Sorgenfrei, F.; Redlin, H.; Kalläne, M.; Marczynski-Bühlow, M.; Hennies, F.; Bauer, M., Ultrafast Melting of a Charge-Density Wave in the Mott Insulator 1T-TaS2. Phys. Rev. Lett. 2010, 105 (18), 187401. (87) Prelovsek, P.; Rice, T., Nucleation processes in the charge density wave state of 2H-TaSe2. Journal of Physics C: Solid State Physics 1983, 16 (34), 6513. (88) Ishiguro, T.; Sato, H., High-resolution electron microscopy of discommensuration in the nearly commensurate phase on warming of 1T-TaS 2. Physical Review B 1995, 52 (2), 759.

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