Inter- and intra-band Coulomb interactions between holes in silicon nanostructures

Abstract

We present a full derivation of the interaction Hamiltonian for holes in silicon within the six-band envelope-function scheme, which appropriately describes the valence band close to the $\mathbf{\Gamma }$ point. The full structure of the single-hole eigenstates is taken into account, including the Bloch part. The scattering processes caused by the Coulomb interaction are shown to be both intraband and interband, the latter being mostly short-ranged. In the asymptotic long-range limit, the effective potential tends to the screened Coulomb potential, and becomes purely intraband, as assumed in previous models. We apply our model to compute the excitation spectra of two interacting holes in prototypical silicon quantum dots, taking into account different dielectric environments. It is shown that, in the highly screened regime, short-range interactions (both intra- and inter-band) can be very relevant, while they lose importance when there is no screening other than the one proper of the bulk silicon crystal. In the latter case, we predict the formation of hole Wigner molecules.

23 pages, 10 figures

References in corpus (11)

• An addressable quantum dot qubit with fault-tolerant control fidelity
• Single-electron control in a foundry-fabricated two-dimensional qubit array
• Hole spin qubits in Si FinFETs with fully tunable spin-orbit coupling and sweet spots for charge noise
• Orbital and valley state spectra of a few-electron silicon quantum dot
• Simple model for electrical hole spin manipulation in semiconductor quantum dots: Impact of dot material and orientation
• Coherent control and spectroscopy of a semiconductor quantum dot Wigner molecule
• Singlet-triplet relaxation in multivalley silicon single quantum dots
• The spectrum of interacting metallic carbon nanotubes: Exchange effects and universality
• The low energy spectrum of finite size metallic SWNTs
• Theory of Spin Relaxation in Two-Electron Lateral Coupled Si/SiGe Quantum Dots
• Interacting holes in Si and Ge double quantum dots: from a multiband approach to an effective-spin picture