Interplay of Defects and the Charge Density Wave State in Hf-Doped ZrTe$_{3}$

TL;DR

The paper investigates how atomic-scale defects influence the charge density wave (CDW) state in ZrTe$_3$ when doped with Hf, combining temperature-dependent STM with first-principles calculations. Using STM across a broad temperature range and DFT/STM simulations, the authors identify Te surface vacancies (EDD) and subsurface Zr vacancies (EBD) as the dominant extended defects, with Hf dopants showing no surface signatures. Cross-correlation between defect maps and the CDW signal reveals that CDW maxima pin to defect sites, with the zero-displacement cross-correlation increasing with temperature for both defect types, indicating stronger pinning at higher temperatures; the CDW wavevector is $q_{CDW} \approx 0.07 a^{*}$. DFT reproduces STM features and assigns Zr vacancies a higher formation energy ($E_f \approx 100\, mathrm{Ry}$) than Te vacancies ($E_f \approx 29\, mathrm{Ry}$), supporting the defect identifications. Defect densities are measured at ~0.3–0.4%, well below the 5% Hf doping, implying defect-driven CDW pinning rather than dopant effects, with implications for tuning CDW and superconductivity in MX$_3$ materials.

Abstract

We carry out temperature-dependent scanning tunneling microscopy (STM) studies of the charge density wave (CDW) compound ZrTe$_3$ which is intentionally doped with Hf. Previous bulk studies tie Hf doping to an enhancement of the CDW transition temperature (T$_{CDW}$). In our work, by combining STM measurements with density functional theory (DFT) calculations, we observe and identify multiple defects in Zr$_{0.95}$Hf$_{0.05}$Te$_3$. Surprisingly, instead of finding clear structural or electronic signatures associated with Hf dopants, we determine the origin of the observed defects are consistent with Te and Zr vacancies. Further, our temperature dependent STM measurements allow us to examine CDW pinning to both types of observed defects below and above T$_{CDW}$.

Figures (12)

• Figure 1: Crystal structure and topography of ZrTe$_3$: (a) Crystal structure showing the layered nature of ZrTe$_3$, highlighting the cleavage plane. (b) Crystal structure in the a-c plane, depicting the trigonal chains oriented along the b-axis. Figures a) and b) were created using Vesta.Momma2011 (c) 50 nm x 45 nm STM topography taken at 9 K, showing atomic resolution, defects, and the unidirectional CDW along the a-axis (I = 100 pA, V$_{Sample}$ = -420 mV). (d) Zoom of region away from defects, with an overlaid structural model of the a-c plane showing the surface Te ions imaged directly by STM as well as the neighboring Zr ions below.
• Figure 2: FFT of topographic image from Figure \ref{['fig:Fig1']}c. Peaks associated with atomic lattice periodicities are circled in dotted white and yellow. The orange box is a zoom of the center of the FFT showing q$_{CDW}$ (circled in solid white).
• Figure 3: (a) 92 nm x 64 nm topography taken at 92 K (I = 100 pA, V$_{Sample}$ = -70 mV) illustrating numerous defects throughout. Two main types of defects are seen in images at all temperatures in this study: EDDs (b) and EBDs (c). (d) An additional type of observed defect: Region with two dark, localized defects which are not EDDs. Gaussian smoothing (5 px) is needed to more-easily identify these types of defects within the image.
• Figure 4: a) Topography (10.0 nm x 4.2 nm) around an EDD acquired at 92.6 K (I = 50 pA, V$_{Sample}$ = -50 mV). b) Line cuts taken through (2) and away (1 and 3) from the defect. The linecut through the defect affected region shows a single peak instead of a double peak, indicating a missing Te ion.
• Figure 5: Extended dark defect STM image and simulation. a) STM-acquired image (4.06 nm x 1.17 nm) zoomed in on an EDD (I = 50 pA, V$_{Sample}$ = -50 mV). b) Calculated relaxed structure with single Te vacancy overlaid on the STM-acquired image from a). The ions shown in green/red are Te ions color coded to help associate features in the linecuts of d/e with ions in the topographies. c) Simulated -50 mV topography. d) Three a-axis linecuts through STM image with the center linecut through the defect region. For clarity of presentation, linecut 2 is presented on a slightly different y-scale. e) Corresponding three a-axis linecuts through the simulated image showing general agreement with those through the STM image.