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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 $boldsymbol{Gamma}$ point. The full structure of the single-hole eigenstates is taken into account, including the Bloch part, and the scattering processes caused by the Coulomb interaction are shown to be both intraband and interband; the interband terms are 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. Our findings can be directly used for realistic exact-diagonalization calculations related to systems of interacting holes in Silicon nanostructures, such as quantum dots.
We consider confinement of Dirac fermions in $AB$-stacked bilayer graphene by inhomogeneous on-site interactions, (pseudo-)magnetic field or inter-layer interaction. Working within the framework of four-band approximation, we focus on the systems whe
The presence of two spin-split valleys in monolayer (1L) transition metal dichalcogenide (TMD) semiconductors supports versatile exciton species classified by their spin and valley quantum numbers. While the spin-0 intravalley exciton, known as the b
Piezoresistance is the change in the electrical resistance, or more specifically the resistivity, of a solid induced by an applied mechanical stress. The origin of this effect in bulk, crystalline materials like Silicon, is principally a change in th
Electrons confined in silicon quantum dots exhibit orbital, spin, and valley degrees of freedom. The valley degree of freedom originates from the bulk bandstructure of silicon, which has six degenerate electronic minima. The degeneracy can be lifted
We present transport measurements on a tunable three-layer graphene single electron transistor (SET). The device consists of an etched three-layer graphene flake with two narrow constrictions separating the island from source and drain contacts. Thre