Atomic-scale mapping of pressure-induced deformations and phase defects in the charge density wave order parameter

Understanding the intricate interplay between multiple electronic phases in quantum materials such as charge density wave (CDW), superconducting, and metallic phases is a challenging issue. Systematic introduction of pressure is one approach that has been used to probe this interplay. However, the influence of pressure together with the intricate interaction between electronic and lattice degrees of freedom can trigger complex structural evolution and distribution of various electronic phases at the atomic scale, the characterization of which demands high spatial resolution. We investigate the atomic-scale response of the charge density waves and the underlying atomic lattice in $1T\text{−}\mathrm{Ta}{\mathrm{S}}_2$ after exposure to hydrostatic pressure. High-resolution transmission electron microscopy images show that the CDW order parameter reacts with an elasticlike strain response to pressure-induced stacking faults and dislocations in the lattice. This is characterized by a proliferation of phase defects including CDW dislocations, discommensurations, and domain walls. Our results evidence the importance of pressure-induced lattice deformations and defects in modulating, stabilizing, or destroying electronic phases at the atomic scale.

Figure 1

(a) Electron diffraction pattern for $1T\text{−}\mathrm{Ta}{\mathrm{S}}_2$ obtained at room temperature and zero pressure. The pattern shows Bragg diffraction spots from the atomic lattice (110, 100, 010, dotted circles) and from the second-order superlattice spots arising from the nearly commensurate CDW modulation (marked with a triangle). (b) After applying a hydrostatic pressure of 2.5 GPa. The rectangles mark the streaking observed after pressure application. (c) Comparing the positions of the second-order CDW superlattice peak positions before (0 GPa) and after applying pressure (2.5 GPa).

Figure 2

(a) HRTEM image of the layer structure along the [001] direction after pressure application. (b) FT of the HRTEM image. The inset displays the streaking in the Bragg spots. (c) HRTEM image showing the layer structure in greater details. (d) Lattice fringes from the (010) atomic planes obtained by selecting the 010 Bragg spot [depicted in (b)] with a Gaussian mask followed by inverse FT. A stacking fault (SF) is marked with an arrow. (e) Zoomed region of the HRTEM image showing the SF position. (f) (010) lattice fringes in the region with a SF and a dislocation. (g) Calculated shear strain ${\epsilon }_{xy}$ in the vicinity of the SF and dislocation. The strain scale ranges from $+$ 2 to – 2%, where regions with high strain correspond to high intensity and vice versa. The position of the dislocation core is marked with a circle.

Figure 3

(a) HRTEM image obtained perpendicular to the [001] direction with deformation defects in the layer plane. (b) Fourier transform (FT) of the HRTEM image with the Bragg spots from the underlying atomic lattice (marked with circles) as well as first- (square) and second-order (triangle) superlattice spots from the CDW/PLD modulation. (c) First-order superlattice reflections $q_1, q_2$, and $q_3$ depicted in greater details. Color maps showing the calculated strain profiles in the atomic lattice along the (d) $x$ direction, ${\epsilon }_{xx}$, and (e) $y$ direction, ${\epsilon }_{yy}$. (f) Shear strain ${\epsilon }_{xy}$. The intensity in the color maps represents strain values in the range $-3.0$ to 3.0%, where regions with high strain correspond to a high intensity and vice versa. The dotted circles indicate the presence of dislocation cores.

Figure 4

Intensity maps representing the (a)–(c) magnitude $\left|q\right|$ and (d)–(f) phase $\phi$ of the individual CDW wave vectors $q_1, q_2$, and $q_3$, respectively. The high and low intensity of the color maps, respectively, corresponding to elongated or shortened CDW wave vector with respect to the unstrained parameter. The color scale in the phase images ranges from –$\pi$ to $\pi$. The dotted circles in (b) and (e) indicate the positions of the dislocation cores and phase singularities, respectively. (g) Magnitude and (h) phase in the vicinity of a pair of CDW dislocation cores.