Localized plasmons in point contacts

Using a hydrodynamic model of the electron fluid in a point contact geometry we show that localized plasmons are likely to exist near the constriction. We attempt to relate these plasmons with the recent experimental observation of deviations of the quantum point contact conductance from ideal integer quantization. As a function of temperature this deviation exhibits an activated behavior, exp(−Ta/T ), with a density dependent activation temperature Ta of the order of 2 K. We suggest that Ta can be identified with the energy needed to excite localized plasmons, and we discuss the conductance deviations in terms of a simple theoretical model involving quasiparticle lifetime broadening due to coupling to the localized plasmons. Introduction The quantized conduction through a narrow point contact is one of the key effects in mesoscopic physics, the quantum point contact remains an important testing ground for the description of mesoscopic phenomena. Recently, significant deviations from the Landauer-Büttiker theory have been observed in quantum point contacts in the temperature dependence of the conductance quantization [1, 2] and as a so called “0.7” structure or quasi plateau, appearing around 0.7 times the conductance quantum 2e/h [3]. Invoking a Luttinger liquid approach [4] the deviations have been discussed in terms of interaction effects [5, 6, 7]. However, firm conclusions have been difficult to obtain partly due to the narrow temperature range (0.1 K 4 K) in which the effect can be studied in conventional split gate quantum point contacts, where relatively close lying one-dimensional subbands are formed. An important progress was provided with the appearance of strongly confined GaAs quantum point contacts using a combination of shallow etching and a top gate [8]. In these new samples the conduction quantization can be followed up to around 30 K. In a subsequent work [9] these samples were used to study the temperature dependence deviations from perfect conductance quantization. At low temperature (∼ 0.05 K) almost ideal quantized conductance is observed for the first conduction plateau, but deviations develop as the temperature is increased. The enlarged temperature range allowed for the observation of activated temperature dependence of these deviations: δG(T ) ∝ exp(−Ta/T ). Furthermore, by changing the top gate it was found that Ta increases with increasing density. An explanation could not be found using the standard single particle picture, and in the brief theory section of Ref. [9] we therefore suggested to include collective effects through plasmons. In short, we identified Ta as the energy needed to excite localized plasmons, and we discussed the conductance in terms of a simple theoretical model involving the additional effect of electrons scattering off the localized plasmons. In the present theoretical work we elaborate on that idea. In a point contact the charge is of course depleted. In order to study the collective excitations of such a system, we can approach it from two limits: 1) starting from a homogeneous electron liquid which is 0, or 2) starting with two spatially separated liquids. Below we follow the first approach, and we argue from a hydrodynamic model that localized plasmons may exist in realistic situations. Plasmons of a homogeneous electron liquid in a cylinder Following Fetter [10] we use a hydrodynamic model of a weakly damped, compressible charged electron fluid placed in a rigid, neutralizing positive background set to +en0. The electron density is written as n0 + n, where n is a small perturbation, and the electronic velocity field is denoted v. Finally, we include the electrostatic potential Φ and neglect radiation effects. The basic equations for the system are the linearized versions of the continuity equation and of Euler’s and Poisson’s equations[10]: