Far infrared response of InAs–GaSb type-II quantum dots

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Abstract

We have investigated theoretically the ground state and electromagnetic response of InAs–GaSb type-II quantum dots in the presence of a vertical magnetic field. The ground state is calculated within the Hartree approximation using a 2-band k·p effective mass Hamiltonian to represent the coupling between the two spin-split sets of dot levels derived from the lowest InAs electron subband and the highest GaSb heavy hole subband. The FIR response is calculated within the RPA. We show that the interlayer Coulomb interaction between the electrons and the holes combined with the k·p mixing breaks the generalized Kohn's theorem leading to a complex FIR spectrum.

Introduction

The far infrared FIR response of quantum dot systems has been studied extensively for the past decade [1], [2]; it is characterized by a simple mode structure associated with the parabolic confinement of charge and the underlying translational invariance of the electron system [3], [4]. Lateral coupling between quantum dots has also been observed [2], [5], which leads to additional weak features in the FIR response.

In this paper, we study a different type of quantum dot system based on an InAs–GaSb layered structure. InAs–GaSb quantum well systems are characterized by unusual band structure associated with the type-II band alignment. By varying the InAs and GaSb layer thicknesses, the electron and hole subbands can be intermixed. A charge redistribution then takes place between the layers creating an interacting electron–hole gas [6], [7], [8], where the electrons (holes) are confined primarily in the InAs (GaSb) layer. We investigate theoretically here the effect of lateral confinement, which gives rise to quantum dots, on the corresponding ground state and FIR response of InAs–GaSb quantum dots.

For this investigation, we take the InAs and GaSb layers to be sandwiched between two AlSb barrier layers. We assume the barrier potential at the AlSb–InAs and GaSb–AlSb interfaces to be infinite, but we include the finite potential offset of 0.962 eV (0.568 eV) between the InAs and Gasb conduction (valence) band. We envision a scenario in which the dots are formed by etching of the AlSb–InAs–GaSb–AlSb composite quantum well so as to produce lateral parabolic confining potentials that localize electrons and holes about the same dot center.

Section snippets

Ground state

We will be focusing on the 150 meV energy range between the bottom of the conduction band in InAs and the top of the valence band in the GaSb, which characterizes the type-II band alignment. Our calculations will refer to a system with a 140 Å InAs layer and a 45 Å GaSb layer. The strong confinement due to: (i) the narrow GaSb layer, and (ii) the light conduction band effective mass in InAs, allows us to restrict our consideration to the lowest InAs electron subband, and the topmost GaSb heavy

FIR response

We consider an EM wave propagating in the z-direction and polarized in the x–y plane: Vext(ρ)eiωt. The FIR response is obtained by solving the RPA formula for the induced density [9], [10]δn(r,ω)=∫dr′χ(r,r′,ω)×Vext(ρ′)+e2ε∫dr″δn(r″)|r′−r″|,where the susceptibility isχ(r,r′,ω)=∑γ,γ′f(εγ)−f(εγ′)ℏω+εγ−εγ′+iΓ×Ψγ∗(r)Ψγ′(r)Ψγ′∗(r′)Ψγ(r′).

The axial symmetry is exploited by expanding Vext, χ and δn in angular momentum components, l. This leads to a 2D integral equation for δnl(ρ,z,ω) for each l. The

Results

We take the lateral confinement such that ω0e=10 meV, which gives ω0h=(me/mh)1/2ω0e≃6 meV. Other parameters used in the calculation are: Temperature, T=1 K, broadening, Γ=0.4 meV, static dielectric constant, ε=13.75 (average of InAs and GaSb).

We consider first the case of a distinct electron–hole system in which the electrons in the InAs layer do not interact with the holes in the GaSb layer. Thus, the each carrier species is confined by its respective 2D parabolic bare potential. The FIR

Acknowledgements

DAB and UR gratefully acknowledge the support of NATO (CRG) and the Deutsche forschungs-gemeinshaft (SFB 348).

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