Commensurability-Dependent Transport of a Wigner Crystal in a Nanoconstriction

We present the first transport measurements of a classical Wigner crystal through a constriction formed by a split-gate electrode. The Wigner crystal is formed on the surface of superfluid helium confined in a microchannel. At low temperatures, the current is periodically suppressed with increasing split-gate voltage, resulting in peaklike transport features. We also present the results of molecular dynamics simulations that reproduce this phenomenon. We demonstrate that, at the split-gate voltages for which the current is suppressed, the electron lattice is arranged such that the stability of particle positions against thermal fluctuations is enhanced. In these configurations, the suppression of transport due to interelectron Coulomb forces becomes important.

Figure 1

(a) Scanning electron micrograph image of the constriction between the two SSE reservoirs. (b) Resistance of the electron system ($R$) against $T$ for $V_r=V_{\mathrm{gt}}=1.2$, 1.0 and 0.6 V. Arrows indicate the melting temperature of the Wigner solid calculated assuming a saturated electron density, taking into account the experimentally observed offset in $V_{\mathrm{gu}}$.

Figure 2

(a) $I/I_{\max }$ against $V_{\mathrm{gt}}$ for temperatures between 0.7 and 1.2 K in 50 mK steps. Here $V_r=1.2\mathrm{V}$ and $V_{\mathrm{in}}=2{\mathrm{mV}}_{\mathrm{pp}}$. With increasing $T$, each data set is shifted $-50\mathrm{mV}$ horizontally and 0.08 vertically for clarity. Arrows mark the steplike increases in current at 1.2 K. (b) Data for $T=1.2$ and 0.7 K with no vertical shift. The 1.2 K data are shifted by $-60\mathrm{mV}$ horizontally. The numbered arrows indicate points at which the current is suppressed.

Figure 3

(a) $I/I_{\max }$ against $V_{\mathrm{gt}}$ for $V_r$ values between 1.15 and 0.75 V, $T=0.7\mathrm{K}$ and $V_{\mathrm{in}}=2{\mathrm{mV}}_{\mathrm{pp}}$. With increasing $V_r$, each data set is shifted 0.1 vertically. No horizontal shift is added to the data. (b) $I$ against $V_{\mathrm{gt}}$ for $V_{\mathrm{in}}=2{\mathrm{mV}}_{\mathrm{pp}}$ and $5{\mathrm{mV}}_{\mathrm{pp}}$, $T=0.5\mathrm{K}$ and $V_r=1.2\mathrm{V}$.

Figure 4

Results of molecular dynamics simulations. (a) Conductance $G_s$ against $V_{\mathrm{gt}}^s$ for different $\Gamma$ values. Data for $\Gamma =98$ and 66 are shifted by 1 and $2\times (\mathrm{M}\Omega {)}^{-1}$, respectively. (b) Superposed images for $\Gamma =131$ and different $V_{\mathrm{gt}}^s$ values. $V_{\mathrm{gt}}^s$ values are shown on each plot. The unit of length is $l_0$.