Subgap Collective Tunneling and Its Staircase Structure in Charge Density Waves

Tunneling spectra of chain materials ${\mathrm{NbSe}}_3$ and ${\mathrm{TaS}}_3$ were studied in nanoscale mesa devices. Current-voltage $I\mathrm{\text{−}}V$ characteristics related to all charge density waves (CDWs) reveal universal spectra within the normally forbidden region of low $V$, below the electronic CDW gap $2\Delta$. The tunneling always demonstrates a threshold $V_t\approx 0.2\Delta$, followed, for both CDWs in ${\mathrm{NbSe}}_3$, by a staircase fine structure. $T$ dependencies of $V_t(T)$ and $\Delta (T)$ scale together for each CDW, while the low $T$ values $V_t(0)$ correlate with the CDWs’ transition temperatures $T_p$. Fine structures of CDWs perfectly coincide when scaled along $V/\Delta$. The results evidence the sequential entering of CDW vortices (dislocations) in the junction area with the tunneling current concentrated in their cores. The subgap tunneling proceeds via the phase channel: coherent phase slips at neighboring chains.

Figure 1

Scheme of the tunneling device of type A. Crystallographic axes of ${\mathrm{NbSe}}_3$ $a^{*},b,c$ ($b$ is the chain direction) correspond to coordinates $z,x,y$. Elliptic cylinders show the cores of dislocation lines; the curved arrow shows the current path.

Figure 2

Tunneling spectra $dI/dV$ as a function of the voltage $V$ normalized to the CDW gap $2\Delta$ at different $T$: (a) CDW1 in ${\mathrm{NbSe}}_3$, (b) CDW2 in ${\mathrm{NbSe}}_3$, (c) $o\mathrm{\text{−}}{\mathrm{TaS}}_3$.

Figure 3

Fine structure of the tunneling spectra in ${\mathrm{NbSe}}_3$ within the magnified threshold region. (a) $dI/dV$ and its derivative $d^{2}I/d{V}^2$ as a function of the voltage $V$ normalized to the CDW gap, at $T=130\mathrm{K}$. (b) Comparison of $d^{2}I/d{V}^2$ for the two voltage polarities for both CDWs, at $T=130$ and 50 K and the positive polarity at $T=120\mathrm{K}$ (lines are guides for the eye). The peaks are interpreted as a sequential entering of dislocation lines into the junction area.