Magnetoplasmons in nondegenerate quantum wires on suspended helium films Antonio Carlos A. Ramos, 1 O. G. Balev, 1,2 and Nelson Studart 1 1 Departamento de Física, Universidade Federal de São Carlos, 13565-905, São Carlos, São Paulo, Brazil 2 Institute of Semiconductor Physics, National Academy of Sciences, 45 Pr. Nauky, Kiev 252650, Ukraine (Received 16 October 2003; published 23 July 2004) Magnetoplasmon spectra for the nondegenerate surface electrons confined in a quasi-one-dimensional chan- nel over a liquid helium film are determined within a microscopic approach in the limit of strong magnetic fields when the electrons occupy the lowest spin-split Landau level. It is shown that the dispersion relation and the spatial structure, transverse to the channel, of the magnetoplasmons have a length scale  T =  2T / m 2   0 , where  is the confining frequency and  0 is the magnetic length. We find acoustic modes, whose velocities as a function of the gate distance exhibit a highly nonlinear behavior under certain conditions, in particular, the appearance of anticrossings. DOI: 10.1103/PhysRevB.70.035414 PACS number(s): 73.20.Mf, 73.20.At I. INTRODUCTION Electrons trapped in quantum surface states deposited over the surface of a liquid helium or other cryogenic sub- strates have been extensively studied both theoretically and experimentally for the last 30 years. 1 The quantum confine- ment along the z direction perpendicular to the surface due to a combination of the attractive liquid polarization potential and a repulsive barrier coming from the Pauli exclusion prin- ciple leads to the formation of electron subbands analogous to the electron system in semiconductor heterostructures. 2 At low temperatures, the electrons are frozen out in the lowest state of the potential well floating more or less freely over the surface. The resulting two-dimensional electron system (2DES) can be considered as nondegenerate (N2DES) be- cause the Fermi energy is much less the thermal energy at electron densities attainable experimentally. Special attention has been given in understanding many- body properties of the N2DES motivated initially by the ex- perimental investigation of the 2D plasmon dispersion and damping. 3 Afterwards the observation of edge magnetoplas- mons (EMPs) constituted another intriguing and unexpected discovery in the N2DES. 4,5 EMPs are chiral collective modes that only propagate within a narrow strip very close to the boundary of the electron sheet. The important properties of the EMPs are: (i) a gapless spectrum in contrast with the usual bulk magnetoplasmon; and (ii) their frequency dimin- ishes with increasing magnetic field. The theories of EMPs in a N2DES were developed initially (as well as for the degen- erate “compressible” 2DES) within classical hydrodynamic models. 6–13 In particular, Aleiner and Glazman 12 demon- strated for a strong magnetic field B the existence of low- energy and long-wavelength acoustical excitations in addi- tion to the fundamental EMP with frequency q  qln1/ q where q is the one-dimensional (1D) wave vector. The existence of new patterns for EMP charge distributions is a general characteristic of the nonhomogeneous 2DES subjected to a magnetic field with a finite region where the equilibrium density profile varies. These new edge excita- tions have been studied experimentally in Ref. 14 for the N2DES on the helium surface. In order to further reduce the degree of freedom of the surface electrons, a structured substrate (V-shaped, rectangu- lar stripes, bent foil, etc.) should be introduced to restrict the electron motion to a narrow channel forming a nondegener- ate quasi-one-dimensional electron system (NQ1DES). 15 The NQ1DES was also created by suspending a helium film be- tween metallic ribs which are also used as measuring elec- trodes for probing a single isolated electron wire in the channel. 16 In Ref. 16, the authors observed resonances in the measured current along the channel as a function of the mag- netic field which were attributed to low-frequency magneto- plasmon excitations of the NQ1DES. Recently microelec- tronic devices confining the electrons in microchannels have been fabricated 17 which constitute potential tools for the re- alization of quantum computing with electrons floating on liquid helium, as suggested by Platzman and Dykman. 18 Previous microscopic study on the long wavelength fun- damental magnetoplasmon excitation of the NQ1DES, later- ally confined by a parabolic potential, somehow analogous to the fundamental EMP, showed that the spectrum has the fol- lowing form: 19  2 q = 2e 2 ma q 2  2  2 +  c 2 ln 1 |q| , 1 where  2 =  / m 2 +  c 2  1/2 ,  c = |e | B / mc, and  are the cy- clotron and confinement frequencies, and a = L / n s is the mean distance between electrons in the wire of length L with n s being the 2D electron density. Equation (1) is valid for values of B satisfying the condition  c . It is worthwhile to point out that the dispersion of the Q1D magnetoplasmon, given by Eq. (1), has the same form q  q ln1/ q as the fundamental magnetoplasmon mode of “classical” narrow channels in the long wavelength limit. 7,13 Inspired by the observed Q1D magnetoplasmon spectra, 16 we investigate in this paper the collective-mode excitations of the NQ1DES over a suspended liquid-helium film, with thickness d He , deposited over a solid substrate with dielectric constant  s in the presence of a strong magnetic field in the direction perpendicular to the surface. At a distance d below the suspended-film structure, a gate electrode is inserted and PHYSICAL REVIEW B 70, 035414 (2004) 0163-1829/2004/70(3)/035414(7)/$22.50 ©2004 The American Physical Society 70 035414-1