The Band Structure of Z-like Quantum Wires

The energy eigenvalues and eigenfunctions have been obtained for a GaAs/AlGaAs quantum wire structure with multiple valence subbands, subjected to an external magnetic field. The hole wavefunctions are calculated by numerical diagonalization of Luttinger Hamiltonian in an appropriately chosen basis. The electron -hole wavefunctions thus obtained are used in conjunction with effective semiconductor Bloch equations for the study of optical coherent transient effects like optical nutation. The results show squeezing of wavefunctions with increasing magnetic field while band mixing effects lead to overlapping of peaks. The corresponding optical nutation curves show an increase in nutation frequency with magnetic field while band mixing effects are revealed through multiple oscillations.

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Wavefunction analysis and optical nutation in magnetized semiconductor quantum wires exhibiting multiple valence subbands

Kapoor

Kumar

Sen

2005

Physica Status Solidi (b)

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Lateral confinement and band mixing in ultrathin semiconductor quantum wells with steplike interfaces

et al. 2004

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Maximal symmetrization and reduction of fields: Application to wave functions in solid-state nanostructures

Dalessi¹,

Dupertuis²

2010

Phys. Rev. B

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A general formalism for the maximal symmetrization and reduction of fields ͑MSRFs͒ is proposed and applied to wave functions in solid-state nanostructures. Its primary target is to provide an essential tool for the study and analysis of the electronic and optical properties of semiconductor quantum heterostructures with relatively high point-group symmetry and studied with the k · p formalism. Nevertheless the approach is valid in a much larger framework than k · p theory; it is applicable to arbitrary systems of coupled partial differential equations ͑e.g., strain equations or Maxwell equations͒. This general MSRF formalism makes extensive use of group theory at all levels of analysis. For spinless problems ͑scalar equations͒, one can use a systematic spatial domain reduction ͑SDR͒ technique which allows, for every irreducible representation, to reduce the set of equations on a minimal domain with automatic incorporation of the boundary conditions at the border, which are shown to be nontrivial in general. For a vectorial or spinorial set of functions, the SDR technique must be completed by the use of an optimal basis in vectorial or spinorial space ͑in a crystal we call it the optimal Bloch function basis͒. The full MSR formalism thus consists of three steps: ͑1͒ explicitly separate spatial ͑or Fourier space͒ and vectorial ͑spinorial͒ part of the operators and eigenstates, ͑2͒ choose, according to the symmetry and well defined prescriptions ͑e.g., specific transformation properties͒, optimal fully symmetrized basis for both spatial and vector ͑or spin͒ space, and ͑3͒ finally apply the SDR to every individual scalar ultimate component function. We show that with such a formalism the coupling between different vectorial ͑spinorial͒ components by symmetry operations becomes minimized and every ultimately reduced envelope function acquires a welldefined specific symmetry. The advantages are numerous: sharper insights on the symmetry properties of every eigenstate, minimal coupling schemes ͑analytically and computationally exploitable at the component function level͒, and minimal computing domains. The formalism can be applied also as a postprocessing operation, offering all subsequent analytical and computational advantages of symmetrization. The specific case of a quantum wire with C 3v point group symmetry is used as a concrete illustration of the application of MSRF.

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The Band Structure of Z-like Quantum Wires

Cited by 3 publications

References 12 publications

Wavefunction analysis and optical nutation in magnetized semiconductor quantum wires exhibiting multiple valence subbands

Wavefunction analysis and optical nutation in magnetized semiconductor quantum wires exhibiting multiple valence subbands

Lateral confinement and band mixing in ultrathin semiconductor quantum wells with steplike interfaces

Maximal symmetrization and reduction of fields: Application to wave functions in solid-state nanostructures

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