Far-infrared excitations below the Kohn mode: Internal motion in a quantum dot

Abstract

We have investigated the far-infrared response of quantum dots in modulation doped GaAs heterostructures. We observe novel modes at frequencies below the center-of-mass Kohn mode. Comparison with Hartree-RPA calculations show that these modes arise from the flattened potential in our field-effect confined quantum dots. They reflect pronounced relative motion of the charge density with respect to the center-of-mass.PACS numbers: 71.45. Gm,78.55.Cr, According to the generalized Kohn's theorem the farinfrared (FIR) response of a quantum dot with parabolic external potential in a magnetic field B consists, independent of the number of electrons in the quantum dot, of only two modes with dispersion:[1]Here Ω 0 describes the external potential, ω c = eB/m * is the cyclotron frequency, m * the effective mass. One mode, ω + , increases with increasing magnetic field and approaches the cyclotron frequency ω c , the other mode, ω − , decreases in frequency with decreasing magnetic field. Both modes represent rigid center-of-mass motion of all electrons in the dot. This behavior is actually very often observed in experiments on quantum dots which are prepared from semiconductor heterostructures. [2,3] The reason being the electrostatic environment causing the external potential to have a nearly perfect parabolic shape. In other experiments, in particular on etched quantum dots with a larger number of electrons and a more hard-wall type of external potential, one observes additional sets of modes at higher frequencies (see for example Ref.4). Such a mode spectrum can be calculated using a mean field approach and random phase approximation (RPA).[5] They can be visualized in terms of 'confined' plasmon modes, for example in the model of Fetter [6] (See also below for details). We have performed experiments on field-effectconfined quantum dots in AlGaAs/GaAs-heterostructures. We find in FIR experiments additional modes below the high-frequency Kohn mode, ω + , which are, however, definitely higher than ω c . The cyclotron resonance itself is not observed for these isolated dots. We compare our experiments with self-consistent Hartree calculations. From this comparison we find that the new modes arise from the flattened external potential in our field-effect-induced quantum-dot array. Our calculation shows that this new mode represents a dipole active charge-density oscillation involving strong relative motion of the electrons with respect to the center-of-mass.Quantum-dot arrays were prepared from modulationdoped Al 0.33 Ga 0.67 Al-GaAs heterostructures with a heterostructure interface-to-surface distance of 55 nm. A Si-δ doped layer was grown 300 nm underneath the AlGaAsGaAs interface and served as a backgate to charge the quantum dots. The sample design is sketched in the inset of Fig. 1. The electron density and mobility at 1.8 K were N S = 3.8 · 10 11 cm −2 and µ = 300 000 cm 2 /Vs, respectively. A photoresist-dot array was prepared by holographic lithography onto the sample surface with a period of a = 330 nm, the diamet...

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Unified approach to cyclotron and plasmon resonances in a periodic 2DEG hosting the Hofstadter butterfly

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