Multiple charge density wave states at the surface of $\mathrm{TbT}{\mathrm{e}}_{3}$

Multiple charge density wave states at the surface of $TbT e_{3}$

Ling Fu, Aaron M. Kraft, Bishnu Sharma, Manoj Singh, Philip Walmsley, Ian R. Fisher, and Michael C. Boyer

Phys. Rev. B 94, 205101 – Published 1 November 2016

Abstract

We studied $TbT e_{3}$ using scanning tunneling microscopy (STM) in the temperature range of 298–355 K. Our measurements detect a unidirectional charge density wave (CDW) state in the surface Te layer with a wave vector consistent with that of the bulk $q_{CDW} = 0.30 \pm 0.01 c^{*}$ . However, unlike previous STM measurements, and differing from measurements probing the bulk, we detect two perpendicular orientations for the unidirectional CDW with no directional preference for the in-plane crystal axes ( $a$ or $c$ axis) and no noticeable difference in wave vector magnitude. In addition, we find regions in which the bidirectional CDW states coexist. We propose that observation of two unidirectional CDW states indicates a decoupling of the surface Te layer from the rare-earth block layer below, and that strain variations in the Te surface layer drive the local CDW direction to the specific unidirectional or, in rare occurrences, bidirectional CDW orders observed. This indicates that similar driving mechanisms for CDW formation in the bulk, where anisotropic lattice strain energy is important, are at play at the surface. Furthermore, the wave vectors for the bidirectional order we observe differ from those theoretically predicted for checkerboard order competing with stripe order in a Fermi-surface nesting scenario, suggesting that factors beyond Fermi-surface nesting drive CDW order in $TbT e_{3}$ . Finally, our temperature-dependent measurements provide evidence for localized CDW formation above the bulk transition temperature $T_{CDW}$ .

Received 25 July 2016
Revised 30 September 2016

DOI:https://doi.org/10.1103/PhysRevB.94.205101

Physics Subject Headings (PhySH)

Charge density waves Electron-phonon coupling Peierls transition Strain

Scanning tunneling microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ling Fu¹, Aaron M. Kraft¹, Bishnu Sharma¹, Manoj Singh¹, Philip Walmsley^2,3, Ian R. Fisher^2,3, and Michael C. Boyer^1,*

¹Department of Physics, Clark University, Worcester, Massachusetts 01610, USA
²Geballe Laboratory for Advanced Materials and Department of Applied Physics, Stanford University, Stanford, California 94305-4045, USA
³Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA

^*Author to whom correspondence should be addressed: mboyer@clarku.edu

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Vol. 94, Iss. 20 — 15 November 2016

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Images

Figure 1
(a) At left, the crystal structure for $TbT e_{3}$ with a black rectangle outlining the unit cell. The dotted line indicates the $a - c$ cleave plane between the double Te layers. At right, the square lattice of the Te layer which is exposed by cleaving as well as the locations of the closest Tb ions in the rare-earth block layer directly below. The unit cell is again shown in the structures at right for reference. The crystal structures were constructed using Vesta software [51]. (b) Topographic image taken over a 90 Å square region at $I = 65 pA, V_{Sample} = - 350 mV$ . The Te square lattice of the exposed surface can be clearly seen as well as superimposed “stripes” associated with a unidirectional CDW state along the $a_{1}$ crystal axis. We use $a_{1}$ and $a_{2}$ to denote the in-plane crystal axes for our measurements since we observe unidirectional CDW order along both axes. This prevents us from unambiguously identifying the $a$ and $c$ crystal axes. (c) FFT of a typical topographic image. Orange circles identify the wave vectors associated with Te square lattice. Blue circles identify the wave vectors associated with the subsurface rare-earth block layer (Tb ions). The yellow ovals enclose peaks in the FFT which are associated with the unidirectional CDW as well as those arising from mixing between the CDW wave vector and block atomic wave vectors. (d) Line cut through the FFT, beginning at the origin (center), in the direction of the CDW (through yellow oval), and ending just past $q_{atom}$ (blue circle) associated with the block layer.
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Figure 2
(a) Line cuts through FFTs in the direction of the CDW [as in Fig. 1 but now extending past $2 q_{atom}$ ]. The harmonic of the block signal $2 q_{atom}$ is present in the top and middle plots, but absent in the bottom plot. Peak 4 is present in all three cases, indicating that peak is not the result of wave vector mixing involving the block harmonic, as the harmonic is absent in the bottom plot, but peak 4 is still present. Slightly different tip conditions lead to variations in the relative intensities of the peaks in the FFT. Each of the FFTs, from which the line cuts are extracted, were taken on 400 Å square topographic images acquired with the same settings: $I = 50 pA$ and $V_{sample} = + 150 mV$ with the same number of pixels and at temperatures at least 10 K below the bulk $T_{CDW}$ . (b)–(d) 25 Å square topographies which have been Fourier filtered to include only contributions from the Te net and rare-earth block signals. Small differences in tip conditions lead to (b) a Te-dominated topography, (c) a rare-earth block-dominated topography, and (d) a topography which has the appearance of surface dimerization.
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Figure 3
(a) and (b) 154 Å square topographies taken over the exact same location with $I = 30 pA$ and $V_{Sample} = + 100 mV$ [for (a)] and $V_{Sample} = - 100 mV$ [for (b)]. (c) and (d) Images in (a) and (b) Fourier filtered to include the Te, block, and CDW/wave-vector-mixing signals as well as low wave vector signals. The three dark regions visible in (a) and (b) are enhanced through the filtering and circled with white ovals. The white ovals extend over identical regions in the two images. (e) and (f) Using Fourier filtering, only the $\sim 2 / 7 a_{1}$ CDW for $+ 100 mV$ [in (e)] and $- 100 mV$ [in (f)] is shown. There is no phase shift evident in the CDW as imaged at positive or negative biases. (g) and (h) The CDW signals in (e) and (f) are enhanced by 15 times and added to the filtered image in (c) and (d), respectively, allowing for identification of the CDW maxima and minima relative to the three ovals for $+ 100 mV$ [in (g)] and $- 100 mV$ [in (h)]. Using the ovals as a guide, these images clearly indicate that the CDW at positive and negative biases are in phase.
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Figure 4
(a) 90 Å square topography taken at 355 K with $V_{sample} = + 200 mV$ and $I = 40 pA$ . The image was Fourier filtered to include the surface Te lattice, block layer, and CDW/wave vector mixing signals. (b) Line cut through the FFT [of the raw topographic image for (a)] beginning at the origin, in the direction of the CDW, ending at the $q_{atom}$ associated with the block layer. The standard 4 CDW/wave-vector-mixing peaks are observed. (c) A $240 \times 200 Å$ topography acquired at 339 K showing variations in the unidirectional CDW state across the region with $V_{sample} = - 200 mV$ and $I = 70 pA$ . (d) The image in (c) Fourier filtered to include Te net, block layer, and CDW/wave-vector-mixing signals to visibly emphasize local variations in the CDW state. (e) A comparison of the line cuts through the FFTs separately for the left and right halves of image (c). The $\sim 2 / 7 {a_{1}}^{*}$ CDW peak is $\sim 3$ larger in the right half as compared to that of the left, illustrating strong variation in the $a_{1} - axis$ CDW in this region.
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Figure 5
(a) FFT of a $\sim 500 Å$ square topography taken at 309 K with $V_{sample} = + 150 mV$ and $I = 50 pA$ . Standard lattice peaks are circled in orange (Te net) and blue (block layer). In addition to these peaks, we observe peaks associated with two perpendicular CDWs within this field of view. Due to noise at low wave vectors, these CDW peaks are most clearly seen in the square pattern surrounding the block peak (seen within dotted yellow circle). (b) The region within the dotted yellow circled area of the FFT in (a) is enlarged to evince the block layer and CDW peaks. The peaks associated with the CDWs along the $a_{1}$ and $a_{2}$ axes are enclosed by small yellow and red circles, respectively. (c) A 150 Å square region cropped from the larger topographic image where the two CDWs spatially coexist with one another. The image was Fourier filtered to reduce noise which obscured some of the topographic features. (d) and (e) A comparison of CDW-associated peak intensities associated with the $a_{1} - axis$ [in (d)] and $a_{2} - axis$ [in (e)] CDWs across three neighboring 150 Å square regions (designated left, middle, right). The plots show an overlay of line cuts in either (d) the ${a_{1}}^{*}$ direction or (e) ${a_{2}}^{*}$ direction taken through FFTs [such as that shown in (b)] for each of the regions. For each line cut, the rare-earth block layer peak is centered at zero and the CDW-associated peaks are seen near $\pm 0.3$ . There is a progression from an $a_{2} - axis$ -dominated CDW at left to an $a_{1} - axis$ -dominated CDW at right. (f) This progression is easily seen visually as the $a_{1} - axis$ CDW peaks (in yellow) around the block signal in the FFT become more intense from left to right while the $a_{2} - axis$ CDW peaks (in red) become less intense. The three FFTs are zoomed similar to what was done in (b) with the block layer signal centered, and share a common color scale.
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Figure 6
(a) Relative bulk positions of Te ions (red) in the Te layer and nearest Tb ions (blue) from the rare-earth block layer directly below, projected onto the $a - c$ plane. The axes are labeled as $a_{1}$ and $a_{2}$ since we are unable to distinguish the $a$ and $c$ axes in our measurements. (b)–(d) 25 Å square images cropped, respectively, from the bottom, middle, and top thirds of a Fourier filtered 120 Å square image. The Fourier filtered image only includes contributions from the Te and block-layer (Tb) structural signals. The block-layer signal was enhanced by a factor of 10 such that the Te and block-layer signals are comparable. The differing images suggest differing relative locations for the Tb and Te ions in the three regions. (e)–(g) The specific lattice positions of the Te and Tb ions superimposed on the bottom, middle, and top images. For clarity, the Te and Tb ion positions for the bottom, middle, and top images are shown separately in (h), (i), and (j), respectively. The shifts in the relative ion positions suggest a decoupling of the Te layer from the rare-earth layer below.
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Physical Review B

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Multiple charge density wave states at the surface of $TbT e_{3}$

Ling Fu, Aaron M. Kraft, Bishnu Sharma, Manoj Singh, Philip Walmsley, Ian R. Fisher, and Michael C. Boyer

Phys. Rev. B 94, 205101 – Published 1 November 2016

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Multiple charge density wave states at the surface of TbTe3

Ling Fu, Aaron M. Kraft, Bishnu Sharma, Manoj Singh, Philip Walmsley, Ian R. Fisher, and Michael C. Boyer

Phys. Rev. B 94, 205101 – Published 1 November 2016

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Multiple charge density wave states at the surface of $TbT e_{3}$