VOLUME 74, NUMBER 5 PH YS ICAL REVIEW LETTERS 30 JANUARY 1995 Dynamical Transition in the signer Solid on a Liquid Helium Surface Keiya Shirahama and Kimitoshi Kono Institute for Solid State Physics, University of Tokyo, Roppongi 7-22-I, Minato ku,-Tokyo I06, Japan (Received 29 July 1994) We have observed a dynamical transition in the Wigner solid on liquid 4He. The ac Corbino conductivity cr, jumps abruptly at certain input voltage and shows hysteretic behavior. The threshold input voltage Vt& has dependences on the magnetic field 8 perpendicular to the surface, frequency co, electron density n„and electric field E~ as V, h ~ B '~ 'n,"E~. We attribute the conductivity jump to the collective sliding of the electrons out of the periodic deformation of the He surface. PACS numbers: 73. 20.Dx, 67.40.Hf, 73. 50. Fq Electrons trapped on the liquid He surface constitute a unique two-dimensional system [1]. Since the He surface is smooth and has no impurities, it realizes extremely high mobility, even over 10 cm /V sec [2], and behaves as an ideal nondegenerate electron system. The most prominent phenomenon is a transition to the Wigner solid (WS) phase, in which the. , electrons form a triangular lattice. The WS on liquid He is accompanied with the periodic surface deformation whose wave vectors equal the reciprocal lattice vectors of the crystal. Since the deformation comes from the static part of the coupled plasmon-ripplon (CPR) modes [3], we refer hereafter to the WS state accompanied with the surface deformation as the CPR state. The first identification of the WS was made by observing the CPR resonance [4]. In this Letter, we report the observation of a dynamical transition in the WS on the liquid 4He surface. The transition appears as an abrupt jump of the electron conductivity with changing the external ac field. We attribute the transition to a collective sliding of the electrons out of the periodic surface deformation; the transition from the CPR state to the sliding state of the WS. We have conducted an accurate measurement of the diagonal component of the ac conductivity tensor, o-, . We employ a capacitive coupling method, which was first developed by Sommer and Tanner [5]. A concentric-ring copper electrode pair, which is known as the Corbino disk, is set 1 mm beneath the He surface. The inner and outer diameters are 20 and 30 mm, respectively, and the gap between them is about 0. 1 mm. The electrons are generated at 1. 4 K by thermionic emission of a tungsten filament, which is located 2 mm above the liquid. The electrodes are biased at a positive voltage Vd„and the electron density n, is determined by the shielding condition of the electric field above the liquid, n, = eVd, /4~ed, where e is the dielectric constant of liquid 4He, and d the depth of the liquid. The data reported here are taken at the electron density n, = 1. 08 &C 108 cm unless otherwise specified. A circular brass guard electrode surrounds the electrons, which is kept at — 1. 5 V to confine the electrons radially. The electrode assembly is enclosed in a copper cell, which is mounted on a dilution refrigerator. To measure o. , an ac voltage V;„of 100 kHz is superimposed to the inner electrode. The current is detected from the outer electrode, which is capacitively coupled to the electrons, as a voltage induced on both ends of a capacitor C,„„which is connected between the outer electrode and the ground. We apply a static magnetic field B perpendicular to the surface. The in- phase and quadrature components of the output voltage V, „, are monitored by a vector lock-in amplifier. We obtain o. „by fitting V, „, with a formula given by [6, 7] V, „t 22 C ', '( , ) f(P. . . ), () where X [N, (Pr, )J, (Pr;) — J, (Pr, )N, (Pr;)], and p = Q itocr, , — '(C + C'). Here r, and r; are the outer and inner radii of the Corbino disk, respectively. C denotes the sheet capacitance between the electrons and the Corbino electrodes, whereas C' is the one between the electrons and the upper cell wall. J] and N] are the Bessel and Neumann functions of first order, respectively. The inset (a) of Fig. 1 shows the temperature depen- dence of o. , at 8 = 261 G for 2.0 mVv v (peak-to-peak) input voltage. We identify the Wigner transition as an abrupt increase of o- at 220 mK. This melting tem- perature is consistent with the generally accepted value of the critical plasma parameter, I, = 127. Note that the increase of o under the Corbino geometry corresponds to the decrease of the mobility p, . In Fig. 1, we show the typical behavior of o- ' of the WS, as a function of the input voltage V;„. At about 5 mVpp o ' shows a maximum, then decreases. This strongly non-Ohmic behavior is observed only in the WS. Increasing V;„ further, o- ' tends to a constant and jumps abruptly. The fluctuation increases above the jump. In the downward sweep, o ' does not follow the same path as the upward one, and the jump occurs at lower V;„ than the upward sweep case. Below the o. jump, the upward and downward sweeps follow the same trace. Both the upward and downward threshold voltages 0031-9007/95/74(5)/781(4)$06. 00 1995 The American Physical Society 781