Discrete Plasmons in Finite Semiconductor Multilayers

Abstract

We observe discrete plasmons in layered 2D electron gases with a large, but finte, number of periods, The twofold degeneracy of plasmon modes with wave numbers in the first Brillouin zone of the infinite system is lifted by the loss of complete periodicity in the finite system. These characteristic discrete plasmon doublets are measured in inelastic-light-scattering spectra of multilayer GaAs/(AlGa)As heterostructures. PACS numbers: 71.45.Gm, 72.15.Nj, 73.40.Lq The charge-density excitations of layered twodimensional electron systems are the subject of current theories that consider plasma modes in semifinite 1,2 and finite 3 systems. Remarkable new effects are predicted for semiconductor superlattices. Giuliani and Quinn 1 proposed a new class of surface plasmons. They are free of Landau damping because quantization of electron motion along the superiattice axis prevents their decay into electron-hole pairs. Wu, Hawrylak, and Quinn 2 have calculated the anisotropy of chargedensity excitations on the lateral surface of a semiconductor superiattice. Jain and Allen 3 have investigated the discrete plasmon spectrum of layered films. Inelastic light scattering, widely used to probe collective excitations in semiconductor superiattice, 4 " 9 has been suggested 1,310 as the experimental method to study the new charge-density excitations. This Letter reports the observation and interpretation of discrete plasmons in inelastic-light-scattering spectra of GaAs/(AlGa)As heterostructures. 11 The discrete modes are observed in multilayers with relatively large number of periods (N == 15), which demonstrates that these effects are essential to plasma oscillations in semiconductor superlattices. In the spectra we measure characteristic plasmon doublets. They are explained by the lifting of the degeneracy of pairs of modes with wave numbers q@ and lirld -q^ in the first Brillouin zone of the superiattice with period d. In the infinite superiattice these modes are degenerate because each 2D electron gas is at a plane of mirror symmetry. The lifting of the degeneracy in finite multilayers is due to the loss of these symmetries.A superiattice of 2D electron gases each with an areal density n embedded in a material with dielectric constant e$ has a plasma frequency 12 " 16 <»p(q,<lp) =o)l(q)S(g,q^),where q is the component of wave vector in the plane parallel to the layers. With N -* oo,is the perpendicular wave number and d is the super-lattice period. (o 0 (q) is the 2D plasma frequency, 17where m* is the electron effective mass and v F is the Fermi velocity. S(q,qp) = sinhqd / (coshqd -cosq^d)is a structure factor for the superiattice.For finite N the discrete plasmon modes are obtained by the coupling among oscillations with frequencies (D p (q t qp). 3,u When the layers are embedded in an infinite dielectric the €-e-e geometry of Ref. 3 is applicable and there are no surface modes. The equations for the plasmon frequencies are derived from Eq. (7) of Ref. 3 by setting a x = a 3 . We obtain two separate sets of modes that...

Plasmons in a Superlattice with a Doped Surface Layer

“…Using the same approach, Jain and Allen [8] have also obtained the determinant equation giving the discrete plasmons for the case with a finite number of layers. These discrete modes have also been observed by Pinczuk et al [9] experimentally.…”

Correlation effects and collective excitations in bosonic bilayers: Role of quantum statistics, superfluidity, and the dimerization transition

“…A variety of experimental techniques existing in solid state physics can help to perform such analyses: inelastic electronscattering spectroscopy, [8][9][10] frequency-domain far-infrared or microwave spectroscopy 11 and inelastic light-scattering spectroscopy. [12][13][14] From the experimental side the use of layered and quasi-2D coupled BECs has a number of key advantages. It has been proposed recently, [15][16][17][18][19] that the use of thin layers is an effective way to control the three-body losses and to significantly reduce the parameter space of the dynamical instability, the main problem encountered in experiments with dipolar gases.…”

Carrier relaxation due to electron-electron interaction in coupled double quantum well structures

“…The solid curves correspond to the in-phase optical, ω + (q), and the out-of-phase acoustic, ω − (q), plasmon modes in the bilayer structure [11]. These ω ± (q) modes have been observed [12] in multilayer semiconductor systems via inelastic light scattering spectroscopic experiments. They represent in-phase and out-of-phase interlayer density fluctuation modes: the out-of-phase acoustic mode, ω − (q → 0) ∼ O(q) represent densities in the two layers fluctuating out of phase with a linear wave vector dispersion and the in-phase optical mode, ω + (q → 0) ∼ √ N e q, represent densities in the two layers fluctuating in phase with the usual 2D plasma dispersion.…”

“…Using Eqs. (11)(12)(13)(14)(15) it is straightforward to calculate the imaginary part of the on-shell self-energy. For the sake of completeness, we show below the detailed expressions for Im M ij in the GW approximation for the two-subband model:…”