⇦Chinese Physics Letters, 2023, Vol. 40, No. 1, Article code 017101 Observation of Charge Density Wave in Layered Hexagonal Cu$_{1.89}$Te Single Crystal Wenshuai Gao (高文帅)1†, Zheng Chen (陈正)2,4†, Wensen Wei (韦文森)2, Chao Yan (闫超)3, Shasha Wang (王莎莎)2,4, Jin Tang (汤进)2, Ranran Zhang (张冉冉)2, Lixun Cheng (程礼迅)1, Pengfei Nan (南鹏飞)1, Jie Wang (王杰)2,4, Yuyan Han (韩玉岩)2, Chuanying Xi (郗传英)2, Binghui Ge (葛炳辉)1, Lin He (何林)3, Haifeng Du (杜海峰)1,2, Wei Ning (宁伟)2, Xiangde Zhu (朱相德)2*, and Mingliang Tian (田明亮)2,5* Affiliations 1Institutes of Physical Science and Information Technology, Anhui University, Hefei 230601, China 2Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, China 3Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China 4Department of physics, University of Science and Technology of China, Hefei 230026, China 5School of Physics and Optoelectronics Engineering, Anhui University, Hefei 230601, China Received 2 October 2022; accepted manuscript online 25 November 2022; published online 21 December 2022 †These authors contributed equally to this work.
*Corresponding authors. Email: xdzhu@hmfl.ac.cn; tianml@hmfl.ac.cn Citation Text: Gao W S, Chen Z, Wei W S et al. 2023 Chin. Phys. Lett. 40 017101    Abstract We report comprehensive transport, electron microscopy and Raman spectroscopy studies on transition-metal chalcogenides Cu$_{1.89}$Te single crystals. The metallic Cu$_{1.89}$Te displays successive metal-semiconductor transitions at low temperatures and almost ideal linear MR when magnetic field up to 33 T. Through the electron diffraction patterns, the stable room-temperature phase is identified as a $3 \times 3\times 2$ modulated superstructure based on the Nowotny hexagonal structure. The superlattice spots of transmission electron microscopy and scanning tunneling microscopy clearly show the structural transitions from the room-temperature commensurate I phase, named as C-I phase, to the low temperature commensurate II (C-II) phase. All the results can be understood in terms of charge density wave (CDW) instability, yielding intuitive evidences for the CDW formations in Cu$_{1.89}$Te. The additional Raman modes below room temperature further reveal that the zone-folded phonon modes may play an important role on the CDW transitions. Our research sheds light on the novel electron features of Cu$_{1.89}$Te at low temperature, and may provide potential applications for future nano-devices.
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 DOI:10.1088/0256-307X/40/1/017101 © 2023 Chinese Physics Society Article Text The transition-metal chalcogenides (TMCs) with general formula $M_{2}X$ ($M$ = Cu, Ag; $X$ = Te, Se) have attract great interest for their exotic properties, including topological features,[1] ionic conductivity, and impressive thermoelectric properties,[2] which made them promising applications on quantum computation, solar cells,[3] and thermoelectric devices.[4] For example, Ag$_{2}$Te and Ag$_{2}$Se were ionic conductor at high temperature $\alpha$ phase,[5] but their low temperature $\beta$ phases were proved to be topological insulators.[1] Recently, Cu$_{2}$Se was discovered to show colossal Seebeck coefficient and ultrahigh $ZT$ value in high temperature range accompanied with structure transition.[6] Cu$_{2}$Te, another representative cuprous chalcogenide, was also of considerable interest in views of its thermoelectric properties and superionic conductivity at high temperatures.[7,8] Due to the weak interaction between the “mobile” cations and the anions in Cu$_{2}$Te over a certain temperature range, such an ionic conductor is instable and forms many modulated phases.[9-11] A hexagonal structure with lattice cell parameter of $a_{0}=b_{0} = 4.237$ Å, $c_{0} = 7.274$ Å and space group of P6/mmm was firstly suggested by Nowotny,[12] then a series of fundamental crystal structures, including trigonal, orthorhombic, tetragonal, monoclinic structures, were also proposed.[13-15] All of them are layered structures, with the Cu cations in the middle of the layers and the Te anions (in Nowotny and monoclinic structures) or both the Cu cations and the Te anions (in trigonal and tetragonal structures) terminating the layers. In addition, all the Te anions on the surface of the Cu$_{2-x}$Te layers are hexagonally coordinated by Cu cations in the hexagonal Nowotny, the monoclinic and the trigonal structures. In the Nowotny structure the hexagonal lattice is ideal, whereas in the monoclinic and trigonal structures they are slightly stretched. Very few compounds present the abundance of structures that Cu$_{2-x}$Te performs, but these structures have closely related to lattice parameters that can be considered to be superstructures of Nowotny's hexagonal structure. Therefore, previous reports supposed that it is more correct to index Cu$_{2-x}$Te with Nowotny structure.[11,16] Recently, a great deal of research focused on the physical properties around and below room temperatures has been carried out for potential spintronic application. The monolayer Cu$_{2}$Te film can be well characterized by ($\sqrt 3 \times \sqrt 3$) superstructure with respect to different substrates,[17-19] but two lattice-matched distinct phases were also reported in Cu$_{2}$Te monolayer growth via the vapor-liquid-solid (VLS) method.[20] Chen et al. observed a $2 \times 2$ surface reconstruction on Cu$_{2-x}$Te single crystal through spectroscopy measurements, but multiple other types of reconstruction patterns were detected meanwhile.[19] Therefore, the reconstructed structure of Cu$_{2-x}$Te seems to perform strongly samples dependence perhaps due to the existence of liquid-like Cu ions. However, the structure reconstruction may play an important role on the electronic states close to the Fermi level, and then bring new physical properties.[21] Many studies tended to recognize Cu$_{2-x}$Te as a stable p-type semiconductor due to the cation vacancies,[16,19,20] but some band structure calculations argued that Cu$_{2-x}$Te was a metallic stable conductor.[22] More interestingly, it was recently shown to have characteristics of topologically nontrivial band feature and may exhibit topological insulator or topological semimetal state.[22-25] A large linear MR associated with the stable surface states was reported in the Cu$_{2-x}$Te polycrystal.[26] Furthermore, the lattice instability in low-dimensional systems is likely to result in the charge density wave (CDW) transition, for example, the CDW character in quasi-one-dimensional (1D) CuTe single crystal.[27,28] The obvious reconstructed structures in Cu$_{2-x}$Te and analogous Cu$_{x}$Te binary compounds strongly motivated us to investigate whether Cu$_{2-x}$Te follows similar CDW behavior. It is quite desirable to make further understand on the crystal structure and electronic states of Cu$_{2-x}$Te single crystal. In this work, we successfully synthesize layered Cu$_{2-x}$Te ($x = 0.11$) single crystals, and perform systematic low temperature property measurements. Upon cooling, the temperature-dependent resistance manifests two anomalies near $T_{\rm c1}=314$ K and $T_{\rm c2}=155$ K, accompanied with large hysteresis as warming. Structural identification by electron diffraction at different temperatures clearly verify two successive modulated structural phases, the commensurate phase I (C-I) in the range $T_{\rm c2} < T < T_{\rm c1}$ and the commensurate phase II (C-II) below $T_{\rm c2}$, respectively. The C-I phase hosts a $3 \times 3\times 2$ superstructure based on the Nowotny hexagonal structure, which is different from all the previous reports, implying a new stable room temperature structure. The scanning tunneling microscopy (STM) study clearly confirms the second transition below $T_{\rm c2}$. All the results can be well understood in terms of CDW instabilities in the two-dimensional (2D) layered hexagonal Cu$_{1.89}$Te. The abnormal Raman modes below $T_{\rm c1}$ indicate that the zone-folded phonon modes may contribute synergistically to the CDW transitions. Our findings uncover the structures and electron features of Cu$_{1.89}$Te at low temperatures and shed a new light on exploring novel properties. Experimental. Cu$_{2}$Te single crystals were grown via the Bismuth flux method. High purity Cu plate (99.99%), Te sponge (99.9999%) and Bi shot (99.999%) were mixed in mole ratio of $2\!:\!1\!:\!30$ and put in a 5 mL alumina crucible. Another alumina crucible filled with quartz wool was inversed and placed above the crucible mentioned. Then, the alumina crucibles were put in a quartz tube with diameter of 23 mm. The quartz tube was sealed under vacuum and heated in a box furnace at 773 K for one day, then slowly cooled to 673 K in two days. At this temperature, the tube was transferred into a centrifuge to separate the flux as soon as possible. After about 30 s, the tube was quenched in water. The synthetic centimeter-scale crystals were planar hexagonal shaped with silvery surfaces, as shown in the inset of Fig. 1(c). The powder x-ray diffraction (XRD) patterns were collected from the Rigaku-TTR3 x-ray diffractometer using the high intensity graphite monochromatized Cu $K\alpha$ radiation. Magnetotransport measurements were carried out using both a 16 T physical property measurement system (PPMS, Quantum Design Inc.) and the $\sim$ 35 T dc-resistive magnet at the China High Magnetic Field Laboratory in Hefei. The electron diffraction experiments were performed on Talos F200X transmission electron microscope (TEM, Thermo Scientific Inc.). The STM experiments were carried out using ultrahigh vacuum scanning probe microscopes (USM-1400. UNISOKU Inc.).
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Fig. 1. (a) Three-dimensional crystal structure of Nowotny hexagonal unit cell. (b) Top view of the lattice. The yellow and blue spheres show the Te and Cu atoms, respectively. (c) The x-ray diffraction pattern of Cu$_{1.89}$Te single crystal. Inset: photo of typical Cu$_{1.89}$Te single crystals. (d) The x-ray diffraction pattern of Cu$_{1.89}$Te polycrystalline powder.
Results and Discussion. Although there was no consensus on the fundamental structure of room-temperature Cu$_{2-x}$Te, recent studies have focused more on the stable Nowotny hexagonal structure.[15,18-20,22] In this layered structure, the Cu cations lie in the middle of the Te anions layers, the adjacent Te–Te layers stack along the $c$ axis and bond with weak van der Waals force, while the Cu–Te and Cu–Cu bonds are mainly strong covalent, as shown in Fig. 1(a). Figure 1(b) is the top view of Nowotny hexagonal Cu$_{2-x}$Te, it shows that all the Te anions on the surface of the layers are hexagonally coordinated by Cu cations. Figures 1(c) and 1(d) display the XRD patterns of Cu$_{2-x}$Te single crystal and polycrystalline powder at room temperature, respectively. Through the Rietveld refinement of the power XRD spectrum, as shown in Fig. 1(b), the lattice parameters are identified with $a_{0}=b_{0} = 4.186$ Å, $c_{0} = 7.232$ Å and $\alpha =\beta = 90^{\circ}$, $\gamma = 120^{\circ}$, which are consistent with the previous reports.[15,18-20,22] The estimated layer spacing revealed by atomic force microscopy (AFM) is about $7 \pm 0.5$ Å as shown in Figs. S1(b) and S1(c) in the Supplementary Materials (SM). The stoichiometric ratio of Cu$_{2-x}$Te is identified to be Cu$_{1.89}$Te ($x=0.11$) using energy dispersive spectroscopy (EDS) (the detailed stoichiometry determination is included in Fig. S2 and Table 1 in the SM). All these results help us establish a comprehensive understanding on the Nowotny structure.
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Fig. 2. (a) Temperature dependence of resistivity for three separate Cu$_{1.89}$Te samples (S1–S3). The black lines and blue lines represent cooling and heating process, respectively. The yellow line in the top panel is the first derivative of resistance upon warming. (b) The magnetoresistance of Cu$_{1.89}$Te with the field (up to 33 T) parallel to the $c$ axis at 2 K.
The temperature-dependent in-plane resistance of three separate Cu$_{1.89}$Te samples (S1–S3) are shown in Fig. 2(a), for both cooling (black lines) and warming (blue lines) cycles. The $R$–$T$ curves exhibit metallic behavior with two anomalies at $T_{\rm c1}=314$ K and $T_{\rm c2}=155$ K, respectively, accompanied with significant hysteresis. Such two unusual upturn kinks at 314 K and 155 K are quite analogous to those in many CDW materials.[29-32] Magnetoresistance (MR) measurement was performed on the Cu$_{1.89}$Te single crystal by sweeping magnetic fields from $-33$ T to $+$33 T. When the magnetic field is applied along the $c$ axis at low temperature of $T=2$ K, the Cu$_{1.89}$Te single crystal hosts an almost ideal linear MR (MR = $\{[R(B)-R(0)]/R(0)\}\times 100{\%}$) of 166% without any sign of saturation, as shown in Fig. 2(b). Many possible scenarios can contribute to the linear MR, including the quantum critical limit in topological materials[33-37] and the complicated geometry or reconstruction of the Fermi surface.[38-41] It is fair to note that the linear MR behavior in different materials is generally not well understood, and the exact mechanism is still an open problem. To trace the structure evolution of Cu$_{1.89}$Te, we performed the transmission electron microscopy (TEM) measurements at different temperatures. Figure 3(a) and 3(b) show the electron diffraction patterns at 300 K along the [001] and [010] zone axes, respectively. The configuration of main bright spots marked with red circles in Fig. 3(a) displays the hexagonal symmetry, and can be well defined using the Nowotny hexagonal structure mentioned above. It is noteworthy that the weak superlattice spots marked with yellow circles also remain a hexagonal symmetry, showing a modulated 1/3 $q$-vector. Similar lattice modulation is also found along the $c$ axis with a modulated 1/2 $q$-vector as shown in Fig. 3(b). Therefore, the structure of Cu$_{1.89}$Te at room temperature can be defined as a commensurate $3 \times 3\times 2$ superstructure derived from a Nowotny hexagonal subcell, namely C-I phase. The high-resolution TEM image (Figs. S3(a) and S3(b) in the SM) further confirmed the lattice modulation along the $c$ axis at $T=300$ K. Such a C-I phase is a new stable phase at room temperature that has never been reported before. The structural above room temperature is beyond our experimental determination. Figures 3(c) and 3(d) show the electron diffraction patterns at low temperature of 110 K along the [001] and [010] zone axes, respectively. The superlattice spots of the C-I phase remain, compared to that of $T=300$ K. However, series pristine lattices with hexagonal symmetry are generated along the [001] zone axis, marking with yellow arrows in Fig. 3(c). Such weak superlattice spots remain to be commensurate with modulated 1/6 $q$-vector in $ab$ plane and 1/2 $q$-vector along the $c$ axis [in Fig. 3(d)], which can be defined as commensurate II (C-II) phase with $6 \times 6\times 2$ superstructure. Such structure reconstructions combine with the striking unusual upturn kinks of resistance near 314 K and 155 K, yield strong signal of the formation of CDW order in 2D layered hexagonal Cu$_{1.89}$Te.
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Fig. 3. [(a), (b)] The electron diffraction patterns of Cu$_{1.89}$Te at 300 K along the [001] and [010] zone axes. [(c), (d)] The electron diffraction patterns of Cu$_{1.89}$Te at 110 K along the [001] and [010] zone axes.
The STM experiments provide more intuitive evidences for the CDW formations in Cu$_{1.89}$Te at low temperature. Figure 4(a) shows the topographic STM image of $ab$ surface taken with a sample-tip voltage of $-320$ mV and tunneling current of 230 pA at $T = 77$ K. The surface was cleaved under vacuum atmosphere and then cooling to 77 K. The CDW order can be clearly seen as the bright spots, almost every three atoms with hexagonal atomic lattice compared to the STM image of 290 K [inset of Fig. 4(a)]. The corresponding Fourier transform in Fig. 4(b) unambiguously reveals a commensurate CDW modulation of 1/2 $q$-vector with the superlattice spots marked with yellow arrow. Compared with the TEM results of Figs. 3(a) and 4(c), the STM experiments clearly reveals the C-II phase at $T=77$ K.
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Fig. 4. (a) Topographic STM image ($V_{\rm bias}= -320$ mV, $I_{\rm t}= 230$ pA) of Cu$_{1.89}$Te single crystal in area of $6 \times 6$ nm$^{2}$. The surface is cleaved under vacuum atmosphere and then cooled to 77 K. (b) The corresponding Fourier transform. Yellow arrows indicate the CDW modulation spots of the C-II phase.
In most quasi-1D systems, the CDW formations are driven by perfect Fermi surface nesting effect, the fully gapped Fermi surface will result in a semiconducting or insulating phase.[42] However, the physical mechanisms of 2D CDW states are controversial, and the $q$-dependent electron-phonon coupling induced period-lattice distortion is another widely accepted mechanism.[43-46] Raman spectroscopy has been a powerful tool for revealing information about interlayer coupling[47,48] and stacking configurations.[49] In Fig. 5(a), we show Raman spectra between 45 cm$^{-1}$ and 250 cm$^{-1}$ of the Cu$_{1.89}$Te bulk sample for a series of temperatures upon warming. They are taken with 532 nm laser light focused to a spot size of $\sim $ 2 µm. At 300 K (C-I phase), two broad swells satisfied gaussian distribution (red lines) with peaks centered at $\sim$ 53 cm$^{-1}$ and $\sim$ 115 cm$^{-1}$ are observed. However, below about 150 K where the CDW transition from the C-I to the C-II phase takes place, the Raman spectra display obvious peak splitting along with new peaks appearing. Especially the emergence of the new mode around 137 cm$^{-1}$ [black dashed rectangle in Fig. 5(a)] whose intensity starts to rise significantly upon cooling, which should be attributed to the phonon modes upon the CDW transition from the C-I to the C-II phase. Similar behavior has been observed in other TMDs.[50-53] Many additional peaks appear at low temperature 5 K (C-II phase), which could be a consequence of decreased disorder. We then plot in Fig. 5(b) the Raman frequencies for each discernible peak as a function of temperature for cooling (purple dots) and warming (green dots). Clear changes in both the number of modes and new frequencies appear near the transition temperature $T_{\rm c2}$ (marked by the red dashed line). Such modulation in the Raman spectra with temperature can be related with the onset of CDW transition below $T_{\rm c2}\approx 155$ K. Generally, along with the emergence of the CDW order, there will be two kinds of new modes, i.e., amplitude (amp) mode and zone-folded (ZF) mode, in the Raman response. The amplitude mode corresponds to a soft-phonon coupled to the electronic density at the CDW wavevector $q$ and dressed by the amplitude fluctuations of the CDW order parameter. Nevertheless, owing to its strong fluctuating characteristic and weakness in intensity, the amplitude mode cannot be always observed in CDW materials. In addition, the amplitude mode features characteristic dropping to zero frequencies rapidly upon approaching $T_{\rm CDW}$ from low temperature. The ZF mode corresponds to normal phonons folded to the zone center of the Brillouin zone due to the establishment of the CDW state. Characteristically, the ZF modes always show slight dependence on temperature below $T_{\rm CDW}$. As shown in Fig. 5(b), the additional Raman modes show only a slight change with temperature, thus they should be assigned as the ZF modes. This finding reveals that zone-folded phonon modes may play an important role on the C-I–C-II CDW transition in Cu$_{1.89}$Te.
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Fig. 5. (a) Temperature-dependent Raman scattering spectra of Cu$_{1.89}$Te. The black rectangle displays the new phonon modes below $T_{\rm c1}$. (b) Frequencies of discernible peaks as a function of temperature (purple dots).
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Fig. 6. (a) Temperature-dependent Hall resistance of Cu$_{1.89}$Te. (b) Temperature-dependent carrier concentrations (blue dots) and mobilities (red dots) extracted from the Hall resistance.
To further investigate the carrier characteristics of Cu$_{1.89}$Te, we systemically measured the Hall resistance at different temperatures. The Hall measurements were carried on the exfoliated clean and fresh $ab$-plane surface, and the magnetic field was perpendicular to the plane. The temperature-dependent Hall resistance curves are shown in Fig. 6(a). For the whole temperature range from 1.6 K to 300 K, the Hall resistance $R_{xy}$ shows nearly linear behavior with positive slopes, indicating that the hole-type carriers dominate the transport behavior of Cu$_{1.89}$Te. Figure 6(b) shows the temperature-dependent carrier concentrations and mobilities extracted from the Hall resistance. At $T=1.6$ K, the obtained carrier concentrations and mobilities are $7.98 \times 10^{20}$ cm$^{-3}$ and $2.20 \times 10^{2}$ cm$^{2}\cdot$V$^{-1}\cdot$s$^{-1}$, respectively. Due to the presence of Cu deficiency, previous theoretical and experimental propose Cu$_{2-x}$Te to be a heavy doped p-type semiconductor, which is consistent with the Hall results. In summary, the layered transition-metal chalcogenides Cu$_{1.89}$Te single crystals are synthesized and systematically studied using transport and electron microscopy experiments. The metallic Cu$_{1.89}$Te displays successive metal-semiconductor transitions defined from the resistance kinks. The electron diffraction patterns reveal that the stable room-temperature phase of Cu$_{1.89}$Te is a commensurate $3 \times 3\times 2$ modulated superstructure based on the fundamental Nowotny hexagonal structure. The TEM and STM measurements clearly show the distinct evolution of hexagonal superlattice spots, hinting the structure transitions from the C-I to the C-II phase below room temperature. All the results can be understood in terms of CDW instability, yielding evidences for the CDW formations in Cu$_{1.89}$Te at low temperature. The further Raman spectroscopy provides meaningful discussions on the possible origination of the low-temperature CDW states. The exotic electronic feature and 2D van der Waals structure help Cu$_{2-x}$Te establish advantage for potential applications in the future nano-devices. Acknowledgments. We are grateful to Professor Lei Shan for helpful discussion. This work was supported by the National Natural Science Foundation of China (Grant Nos. U19A2093, 11904002, U2032214, U2032163, and 11774353), the National Key Research and Development Program of China (Grant No. 2017YFA0403502), the Natural Science Foundation of Anhui Province (Grant No. 1908085QA15), and the Youth Innovation Promotion Association CAS (Grant No. 2017483). 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