Phase-resolved terahertz nanoimaging of $\mathrm{W}{\mathrm{Te}}_2$ microcrystals

The terahertz (THz) electrodynamics of few-layer $\mathrm{W}{\mathrm{Te}}_2$ is dominated by the plasmon response. However, THz surface plasmons (SPs) with long wavelengths in two-dimensional exfoliated crystals are typically confined by the lateral geometry. Direct visualization of the plasmonic standing wave patterns is challenging due to the spatial confinement and low quality factor of the SP, especially for samples that are only a few monolayers thick. Here, we resolve subtle real-space features of the plasmonic response of $\mathrm{W}{\mathrm{Te}}_2$ by augmenting more common scattering amplitude experiments with the phase contrast accomplished within the time-domain version of THz nanoimaging. Amplitude and phase images allow us to quantitatively evaluate the evolution of the plasmonic response at cryogenic temperatures in samples with variable thickness from 3 to 12 monolayers. The proposed imaging modality is universally applicable to the THz near-field nanoscopy of low-dimensional materials.

Figure 1

Sideband detection of THz near-field signal via time-delay modulation. (a) Schematic diagram of the experimental configuration in analogy to Ref. [36]. (b) Schematic time-domain THz signals of an insulating substrate and a conductive sample on the substrate. The signals are different in both amplitude and carrier-envelope phase (CEP). Due to the CEP shift, the main peaks of the sample and the substrate occur at different time points. The shaded area indicates the range of the modulation of the measurement time delay. The inset depicts the amplitude spectrum of the THz pulses.

Figure 2

THz near-field (NF) amplitude and phase for representative materials. The simulated NF amplitude and phase of a 0.3-nm-thin crystal. (a) and (b) correspond to a band insulator, (c) and (d) to Dirac material with $\mu =0$, (e) and (f) to Dirac material with $\mu =5\mathrm{meV}$, and (g) and (h) to Dirac material with $\mu =25\mathrm{meV}$. The optical constants (conductivities) utilized for simulations are listed in Table 1. The simulations are calculated at $f=1\mathrm{THz}$ and $T=0$ K. (i) and (j) Horizontal linecuts ($Y=0$) of amplitude and phase are extracted for a range of chemical potentials ($\mu =0–37.5\mathrm{meV}$). (k) and (l) NF signal map of an infinitely large metallic sheet sample with arbitrary sheet conductivity ${\sigma }^{2d}=\sigma d$ at 1 THz. The dots mark the results of Dirac materials simulated at different chemical potentials.

Figure 3

The phase-resolved THz imaging of a multiterraced $\mathrm{W}{\mathrm{Te}}_2$ microcrystal. (a) and (b) Temperature-dependent normalized amplitude ($S_2/S_1$) and phase images (${\varphi }_2-{\varphi }_1$) of $\mathrm{W}{\mathrm{Te}}_2$ as a function of temperature. The data in each image are subsequently normalized on the $\mathrm{Si}{\mathrm{O}}_2/\mathrm{Si}$ substrate. The boundaries of all terraces are demarcated with dashed lines in the images recorded at 33 K. Solid lines in the images taken at 295 K reveal the trajectory of the linecuts analyzed in (c) and (d). (c) The amplitude and (d) phase linecuts extracted from (a) and (b). The linecuts in both channels are shifted along the vertical axis for clarity. The modulations near the sample edges (marked with black arrows and highlighted with blue shading) extend into the 12L region; the width of these peaks depends strongly on the temperature. (e) and (f) Temperature-dependent unnormalized amplitude ($S_2$) and phase (${\varphi }_2$) averaged over all pixels in each terrace.

Figure 4

Real-space modeling of surface plasmon (SP) patterns in $\mathrm{W}{\mathrm{Te}}_2$. (a) The amplitude and (b) phase images. Simulations adequately reproduce key features of the $T=295$ K experimental data in Fig. 3 using permittivity values listed in Table 2. The values are based on Ref. [36]. (c) and (d) The simulated amplitude and phase are calculated at $T=33$ K. (e) and (f) The simulated amplitude and phase linecuts of 12L $\mathrm{W}{\mathrm{Te}}_2$ at the location indicated in (a)–(d), identical to those extracted from experiments. (g) and (h) We mark the estimated conductivities of 3L–12L $\mathrm{W}{\mathrm{Te}}_2$ on the near-field amplitude and phase map generated by the lightning-rod model [53]. The dashed line highlights conductivities corresponding to $Q=1$.

Figure 5

Simulating THz plasma fringe patterns. In (a) and (b), we maintain the wavelength ${\lambda }_P=10\mu \mathrm{m}$ and tune the $Q$ factor. The $Q$-factor dependences of the amplitude and phase linecuts are shown in false-color images. We highlight three curves with $Q=0.4$, 1, and 1.6. The plasmon fringe is indicated by black arrows. In (c) and (d), we maintain the $Q$ factor $Q=0.5$ and tune the wavelength ${\lambda }_P$. We highlight three curves with ${\lambda }_P=8$, 16, and 24 $\mu \mathrm{m}$. (e) and (f) The surface plasmon (SP) pattern depends critically on the phase shift $\theta$ in the process of SP reflection from the sample edge. The $\theta$ dependence of the SP pattern is plotted. In the inset, we illustrate the phase shift acquired by the reflected SP wave.