Melting of a quasi-one-dimensional Wigner crystal: Electrons on superfluidH4ein a narrow channel

Abstract

We have investigated the melting process of electron crystals ͑or Wigner crystals͒ confined in quasi-onedimensional channels 10-60 electrons in width, formed on the surface of superfluid 4 He, paying special attention to the nonlinear behavior in resistivity unique to the crystal phase, the Bragg-Cherenkov ͑BC͒ scattering of surface waves. We observed that the BC scattering disappears at a higher temperature for fewer electrons in the confined direction, indicating that the crystal-like structure persists to a higher temperature. We show that this behavior is understood in terms of a naive model describing how the positional correlation is disordered by free dislocations in the quasi-one-dimensional geometry.The dimensionality of a system has a significant influence on the natures of phase transition and ordered states. It is generally accepted that in one-dimensional ͑1D͒ XY magnets, superfluids, and crystals, thermal fluctuations completely destroy the long-range order ͑LRO͒ at any finite temperature. In two-dimensional ͑2D͒ systems, the LRO is also destroyed but the weaker thermal effect allows the quasi-LRO to survive at low temperatures. The quasi-LRO is destroyed at a high temperature by the unbinding of pairs of topological defects, according to Kosterlitz and Thouless ͑KT͒. 1 In a quasi-1D geometry, such as in a strip or on the surface of a tube, the system shows 1D-like behavior when the coherence length is longer than the confining dimension whereas it is 2D-like in the opposite case. In such systems, fundamental questions arise as to whether the quasi-LRO develops at low temperatures and how the quasi-LRO is destroyed with increasing temperature. Experimentally, the superfluid has, surprisingly, been observed for 4 He films formed on the surface of long cylinders, 2,3 which promoted many theoretical works. [4][5][6] In the case of the melting of a crystal in the quasi-1D geometry, a number of computer simulations have been carried out for particles interacting with the Coulomb repulsion 7,8 or other types of interactions, 9,10 and most simulations suggest an interesting anisotropic melting process. However, there have been few experiments on the melting process in the quasi-1D geometry because a very clean system must be used to obtain a clear result.In this Rapid Communication, we experimentally address the melting mechanism of electron crystals in a quasi-1D geometry by employing a very clean electron system, i.e., electrons formed on the superfluid 4 He. 11,12 We carried out transport measurements of the electrons confined in micrometer-wide channels 10-60 electrons in width, paying special attention to the nonlinear transport unique to the electron crystal, the Bragg-Cherenkov ͑BC͒ scattering. [13][14][15][16] The understanding of the properties of confined electrons on a micrometer scale is also of particular importance in the context of quantum information processing. 17,18 In a 2D system, the melting of a crystal is considered to be the KT-type transition but with a slight difference. A 2D hexag...

Formation of defects in multirow Wigner crystals

“…At a critical density, ν (5) I−II = 4.712, structures with a different type of defect corresponding to a sinusoidal distortion of the rows with a phase shift of half a period between the two outer rows become become the ground state. This second regime is characterized by a defect density that barely varies with density and extends up to the transition to six rows.…”

“…At low density, it describes a metastable state. However, its energy with respect to the other minimum decreases with density until, at ν (5) I−II = 4.712, it eventually becomes the global minimum and, therefore, the ground state. Both the defect density (Fig.…”

“…The three-dimensional Wigner crystal and its two-dimensional counterpart have been extensively studied, and there exist beautiful experimental realizations of the latter using electrons trapped on the surface of liquid Helium [2][3][4][5] . More recently, Wigner crystallization in one dimension has received renewed interest [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] ; for recent reviews see Refs. 23 and 24.…”

Quantum ballistic transport by interacting two-electron states in quasi-one-dimensional channels

“…Similar structural transitions of a Wigner crystal to a zigzag crystal in an ion chain 18 and in quantum wires controlled by an external gate 19 were also explored. In addition, the spin Peierls quantum phase transition in cold Coulomb crystals of trapped ions, 20 the spontaneous spin polarization due to the electron-electron interactions under a bias-field control, 21,22 and the phase diagram of zigzag Wigner crystals with spin coupling for two-, three and four-particle ring exchange processes, 23 as well as melting of a quasi-1D Wigner crystal observed from the nonlinear resistivity 24 of electrons confined in quasi-1D channels formed on the surface of superfluid 4 He, were reported. There were extensive theoretical studies on zigzag crystals for a long quantum wire.…”

Bistable transport properties of a quasi-one-dimensional Wigner solid on liquid helium under continuous driving

“…The electron density, pressing electric field, effective channel width, strength of the lateral electrostatic confinement and the commensurability of the electron lattice within the quasi-1D confinement are all dependent on the electrode bias values [34,35]. Each of these parameters can influence the WS-DL decoupling threshold force.…”