Topological effects of charge density waves in ring-shaped crystals of $\mathrm{Nb}{\mathrm{Se}}_3$

We studied the differences of the charge density wave (CDW) dynamics in closed-ring and open-ring topologies by measuring the frequency-dependent resistance in the radio-frequency range. We performed a two-probe ac resistance measurement for a ring-shaped crystal of niobium triselenide $\left(\mathrm{Nb}{\mathrm{Se}}_3\right)$ in the $300\mathrm{kHz}\text{to}1.3\mathrm{GHz}$ frequency range. We compared the frequency dependence of the resistance of closed-ring and open-ring crystals and found that the pinning potential in the former is smaller than that in the latter. The open-ring crystal was obtained by changing of the topology of the closed-ring crystal. We believe that the reduction in the pinning effect is caused by a CDW circulating current in the closed-ring topology.

Figure 1

(a) Scanning ion beam microscopy (SIM) image of a typical ring crystal with a radius of $18.2\mu \mathrm{m}$ and a thickness of $0.47\mu \mathrm{m}$. It is a closed ring. (b) SIM image of the ring crystal after focused ion beam (FIB) surgery. The FIB surgery provided two edges in the ring crystal. The forms in (a) and (b) are referred to in the text as a closed-ring topology and an open-ring topology, respectively. This is a useful method for investigating topology dependence alone, without sample dependence.

Figure 2

Electrical circuit for the frequency-dependent resistance measurement. The ring at the center of the circuit indicates a ring crystal, which is attached to two contacts.

Figure 3

Temperature dependence of resistance in a closed-ring topology and in an open-ring topology. The line thickness indicates the frequencies, and the dashed lines are linear fitting lines, $R\left(T\right)=\alpha T+R_0$, fitted to the metallic region in the $160–200-\mathrm{K}$ range. The inset shows the temperature dependence of the normalized resistance, $\tilde{R}(\omega ,T)=[R(\omega ,T)-R_0]∕\alpha -T$. The first CDW transition temperature $T_{\mathrm{C}1}$ is $\sim 145\mathrm{K}$ in both topologies. The resistance peak below $T_{\mathrm{C}1}$ is maximum at the same temperature.

Figure 4

The frequency dependence of the normalized resistance, $\tilde{R}(\omega ,T)=[R(\omega ,T)-R_0]∕\alpha -T$, at $T=100$, 110, and $120\mathrm{K}$ below the first CDW transition temperature $T_{\mathrm{C}1}=145\mathrm{K}$. The black dots are experimental data for the closed-ring topology, and the gray dots are data for the open-ring topology. The solid and dashed lines indicate the fitting curves given in the text for the closed-ring and open-ring topologies, respectively. The fitting parameter $\beta$ is set at 0.8 in both topologies and for all temperatures. The characteristic frequency ${\omega }_C∕2\pi$ is $0.85\mathrm{GHz}$ in the closed-ring topology and $1.2\mathrm{GHz}$ in the open-ring topology at all temperatures.