Observation of Shapiro Steps in the Charge Density Wave State Induced by Strain on a Piezoelectric Substrate

Abstract

Recent development in nanotechnology has enabled us to investigate the dynamic properties of van der Waals materials on a piezoelectric substrate. Here we report on the dynamics of charge density wave (CDW) in NbSe$_{3}$ nanowires induced by surface acoustic waves (SAWs). Clear peaks in the differential resistance were observed at the resonant frequency of the SAW device. These peaks known as Shapiro steps are typically observed by applying an rf current to NbSe$_{3}$ nanowires. We found that the Shapiro steps induced by SAWs show several distinct features from the ones induced by an rf current. Our detailed study revealed that a strain induced by SAWs plays a significant role in the Shapiro steps. The result clearly demonstrates the importance of the strain in CDW materials and paves the way for strain-induced device applications.

Figures (4)

• Figure 1: (a), (b) Optical microscope images of (a) an exfoliated NbSe$_{3}$ nanowire and (b) the whole SAW device. The NbSe$_{3}$ nanowire is allocated in between two interdigital transducers (IDTs), i.e., IDT1 and IDT2. (c) Temperature dependence of resistance $R$ of the NbSe$_{3}$ nanowire with a thickness $t = 56nm$ (device A), normalized by $R$ at $T = 280K$. Two bumps due to the charge density wave (CDW) transitions are clearly observed. (d) Scattering parameter from IDT1 to IDT2 ($|S_{21}|$) on a logarithmic scale as a function of the frequency $f$ measured at $T = 45K$. This is the result after the time domain gating process is applied to remove electromagnetic crosstalk signals. The transmitted signal intensity has a peak at $f_{0} = 296MHz$.
• Figure 2: Differential resistance $dV/dI$ as a function of direct current $I_{\mathrm{dc}}$ measured at $T = 45K$ with different frequencies. $P_{\mathrm{in}}$ is the power applied to IDT1 and fixed at 10mW in this measurement. (b) Scattering parameter $|S_{21}|$ as a function of the frequency $f$ measured at $T=45K$. The stars in the figure indicate the measured frequencies in (a).
• Figure 3: (a) $dV/dI$ as a function of $I_{\mathrm{dc}}$ measured at $T=45K$ with different $P_{\mathrm{SAW}}$. (b) $dV/dI$ as a function of $I_{\mathrm{CDW}} \equiv I_{\mathrm{dc}} - I_{\mathrm{ohmic}}$ at $T = 45K$ with different $P_{\mathrm{SAW}}$. (c) $I_{\mathrm{CDW}}$ as a function of dc voltage $V_{\mathrm{dc}}$, obtained by integrating the $dV/dI$ curve, at typical $P_{\mathrm{SAW}}$ values. (d) $dV/dI$ as a function of $I_{\mathrm{dc}}$ measured at $T = 45K$ with different ac powers $P_{\mathrm{ac}}$. (e) $dV/dI$ as a function of $I_{\mathrm{CDW}}$ at $T = 45K$ with different $P_{\mathrm{ac}}$. (f) $I_{\mathrm{CDW}}$ as a function of dc voltage $V_{\mathrm{dc}}$ at typical $P_{\mathrm{ac}}$ values. The steps for $n=1$ and $n=2$ are indicated in (c) and (f). The threshold voltage $V_{\mathrm{th}}$ to drive CDW is also defined in (c) and (f).
• Figure 4: (a), (b) $dV/dI$ as a function of $I_{\mathrm{dc}}$ measured with (a) the SAW device (device B) and (b) the ac device at $T = 45K$. We present some representative power values where the step width of the $n = 1$ step takes a maximum and minimum. (c), (d) The step widths divided by $2V_{\mathrm{th}}(P=0)$ as a function of (c) $P_{\mathrm{SAW}}$ and (d) $P_{\mathrm{ac}}$ for the $n=1$ step. For both devices, the thicknesses $t$ of NbSe$_3$ thin films are about 30nm. $W_{0}$ is the step width maximum and $\delta W$ is the step width at each minimum point. The indices of the minimum points are also defined in the figures. (e)--(h) The same datasets obtained at $T = 130K$. (i), (j) $\delta W/W_{0}$ as a function of the index number obtained at (i) $T = 45K$ and (j) $T = 130K$.