Soft-Phonon and Charge-Density-Wave Formation in Nematic ${\mathrm{BaNi}}_2{\mathrm{As}}_2$

We use diffuse and inelastic x-ray scattering to study the formation of an incommensurate charge-density-wave (I-CDW) in ${\mathrm{BaNi}}_2{\mathrm{As}}_2$, a candidate system for charge-driven electronic nematicity. Intense diffuse scattering is observed around the modulation vector of the I-CDW, $Q_{\text{I-CDW}}$. It is already visible at room temperature and collapses into superstructure reflections in the long-range ordered state where a small orthorhombic distortion occurs. A clear dip in the dispersion of a low-energy transverse optical phonon mode is observed around $Q_{\text{I-CDW}}$. The phonon continuously softens upon cooling, ultimately driving the transition to the I-CDW state. The transverse character of the soft-phonon branch elucidates the complex pattern of the I-CDW satellites observed in the current and earlier studies and settles the debated unidirectional nature of the I-CDW. The phonon instability and its reciprocal space position are well captured by our ab initio calculations. These, however, indicate that neither Fermi surface nesting, nor enhanced momentum-dependent electron-phonon coupling can account for the I-CDW formation, demonstrating its unconventional nature.

Figure 1

Intensity maps of the $HK1$ reciprocal lattice plane around the ${\mathrm{\Gamma }}_{411}$ Brillouin zone center at (a) 293, (b) 154, and (c) 139 K. Intensity maps of the $4KL$ plane at (d) 293, (e) 154, and (f) 139 K. (g) Cut of the DS maps across $Q_{\text{I-CDW}}$ at 293, 175, 151, and 141 K along the $[0k0]$ direction. Lines are fit to the data using a Lorentzian model that reproduces the line shape accurately down to $T_{\text{I-CDW}}$. (h) Same as (g) but for cuts along the [00l] direction. (i) $T$ dependence of the normalized intensity of the I-CDW superstructure peak and of the inverse I-CDW correlation length in the in-plane $[0k0]$ and out-of-plane [00l] directions. (j) Thermal expansion coefficient along the $a$ axis, $\alpha =1/LdL/dT$ ($L$ stands for the length of the sample) and $B_{1g}$ symmetry-resolved $m_{12}-m_{11}$ elastoresistance coefficient from Refs. [28, 29].

Figure 2

(a) IXS spectra taken from ${\mathrm{\Gamma }}_{411}$ along the $[0k0]$ direction at 250 K (vertically shifted for clarity). Thick solid lines correspond to fit of the data (Supplemental Material [15]). Fitting details are shown for the spectra at $Q=(41.051)$. The dashed lines represent the two individual phonons (both the Stokes and anti-Stokes parts are included). The gray line represents the elastic contribution. Momentum dependence of the (b) elastic line intensity, (c) linewidth of the low-energy phonon, and (d) energy of the two phonons shown in (a) at 250 K. The color map represents the scattering intensity along $[0k0]$ in the zone centered around ${\mathrm{\Gamma }}_{411}$ calculated by DFPT. The gray dashed line is the phonon dispersion calculated using a large Gaussian smearing that simulates high temperatures and stabilizes the tetragonal phase [15].

Figure 3

(a) $T$ dependence of the IXS spectra at $Q_{\text{I-CDW}}$. (b) Normalized IXS intensity at $Q_{\text{I-CDW}}$ as a function of temperature. (c) $T$ dependence of the integrated spectral weight and of the HWHM of the quasielastic line at $Q_{\text{I-CDW}}$.

Figure 4

Calculated momentum-dependent electronic and EPC quantities at the 2D plane $k_z=0$ (see Supplemental Material for their definitions [15]): (a) Joint density of states, (b) total linewidth, i.e., phonon linewidth summed over all phonon branches, (c) ratio of total linewidth and JDOS, which represents an average EPC strength. The arrow in (a)–(c) indicates $q_{\text{I-CDW}}$. (d) Line cuts along the [100] direction for the quantities shown in (a)–(c).