Evidence for Reentrant Melting in a Quasi-One-Dimensional Wigner Crystal

We demonstrate, for the first time, that a quasi-one-dimensional Wigner crystal formed on superfluid ${}^4\mathrm{He}$ with only a few electrons in the confined direction shows reentrant melting. By transport measurements, we find oscillations in current as a function of linear density measured at a fixed driving voltage at high temperatures, and detailed analyses of transport data reveal that the oscillations originate from the periodic reduction of the melting temperature as a function of linear density. Comparison with the structural phase diagram suggests that the reduction of the melting temperature occurs at the boundaries between the different structures as the structure evolves from a single, double, followed by a triple chain.

Figure 1

(a) Device for the transport measurement of electrons confined in the $1.6\mu \mathrm{m}$ channel. (b) Scanning electron microscope images of the device. (c) Vertical cross section of the center channel. The confining potential is produced by $V_{\mathrm{guard}}$ and $V_G$. More negative $V_{\mathrm{guard}}$ makes confinement stronger. (d) Distributions of electrons (left axis) and confining potentials (right axis) in the center channel calculated for $V_{\mathrm{guard}}^0=-0.26\mathrm{V}$. Numbers indicate $V_{\mathrm{guard}}$.

Figure 2

(a) Calculated linear density at $n_R=1.5\times {10}^{13}{\mathrm{m}}^{-2}$. The dots indicate the results of the numerical calculations, and the solid curve represents the smooth interpolation. Vertical lines indicate the phase boundaries of the ground state structures. (b) Current as a function of $V_{\mathrm{guard}}$ measured at $V_{\mathrm{ac}}=4.0\mathrm{mV}$. The dashed vertical lines indicate $V_{\mathrm{guard}}^p$. (c) Slope of the BC plateau as a function of $V_{\mathrm{guard}}$. (d) $V_{\mathrm{ac}}$ at decoupling as a function of $V_{\mathrm{guard}}$. (e) Melting temperature deduced from the slope of the BC plateau (see the text). Data in (b)–(e) are taken at $f=30\mathrm{kHz}$ and $n_R=1.5\times {10}^{13}{\mathrm{m}}^{-2}$. Note that the horizontal axis in (a) is compressed by 18%.

Figure 3

Excitation dependences of current measured for a fixed linear density (at a fixed $V_{\mathrm{guard}}^p$). The solid lines represent the slope of the BC plateau, and the arrows indicate the decoupling. The vertical line represents $V_{\mathrm{ac}}$ used for the measurements in Fig. 2b. Data are taken under the same conditions as in Fig. 2.

Figure 4

Schematic phase diagram in the Q1D geometry [3]. The melting temperature, which is defined by the modified Lindemann criterion [4], exhibits reentrant behavior as a function of linear density.