Valley degeneracy in biaxially strained aluminum arsenide quantum wells

Abstract

This paper describes a complete analytical formalism for calculating electron subband energy and degeneracy in strained multi-valley quantum wells grown along any orientation with explicit results for AlAs quantum wells. In analogy to the spin index, the valley degree of freedom is justified as a pseudospin index due to the vanishing intervalley exchange integral. A standardized coordinate transformation matrix is defined to transform between the conventional-cubic-cell basis and the quantum well transport basis whereby effective mass tensors, valley vectors, strain matrices, anisotropic strain ratios, piezoelectric fields, and scattering vectors are all defined in their respective bases. The specific cases of (001) (411)-oriented QWs and we define and solve for a shear-to-biaxial strain ratio. The notation is generalized to address non-Miller-indexed planes so that miscut substrates can also be treated, and the treatment can be adapted to other multi-valley biaxially strained systems. To help classify anisotropic intervalley scattering, a valley scattering primitive unit cell is defined in momentum space which allows one to distinguish purely in-plane momentum scattering events from those that require an out-of-plane momentum component.

Multicomponent Skyrmion Lattices and Their Excitations

“…With increasing d, the number of possible types of anisotropies grows quickly along 00 00 00 00 with the d 2 − 1 generators of SU (d), and we concentrate on the simplest nontrivial, yet instructive, and hitherto unstudied case of SU (3) Skyrmions. These are of experimental interest for quantum wells grown in a [111] direction, in particular a nascent effort on AlAs, where one finds the appearance of three almost degenerate valleys [8]. The latter are subject to a 'nematic' anisotropy recently discussed in the context of SU (2) valley degrees of freedom [14], which we generalise to the case of an arbitrary number of valleys.…”

“…In presence of Coulomb interactions the ground state of the system is a triangular Skyrmion lattice, which breaks all the symmetries of the internal SU (d), as well as translational symmetry, generating d 2 Goldstone modes, d 2 − 1 of which correspond to breaking of the SU (d), and the remaining one being a magnetophonon mode. We have explored the phase diagram of a SU (3) QHE ferromagnet, which is expected to be relevant to semiconductor nanostructures with valley-degeneracies [8]. The lattice tilts continuously as a function of anisotropy strength and becomes square through a phase transition at a critical anisotropy value.…”

Optimization of AlAs/AlGaAs quantum well heterostructures on on-axis and misoriented GaAs (111)B

“…[2][3][4] The three-fold valley degeneracy is broken due to strain and quantum confinement effects in these biaxially strained AlAs/AlGaAs QW heterostructures, leading to either double [in (001)-oriented QWs] or single [in (110)-oriented QWs] valley degeneracy. [2][3][4]8 In addition, a transition between double and single valley degeneracy was observed in piezoelectrically strained (001) AlAs QWs and as a function of QW width, 1 facilitating dynamic control of valley occupancy and tuning of valley effective mass. 5,6 In contrast, the symmetrical (111)-oriented AlAs QWs should preserve the three-fold valley degeneracy as found from systematic strain tensor calculations in biaxially strained multivalley AlAs QW heterostructures.…”

“…5,6 In contrast, the symmetrical (111)-oriented AlAs QWs should preserve the three-fold valley degeneracy as found from systematic strain tensor calculations in biaxially strained multivalley AlAs QW heterostructures. 7,8 This perfect SU(3) symmetry is expected to add an extra valley degree of freedom as compared to (001)-oriented AlAs QWs, allowing for ultimate exploration of interaction effects such as anisotropic composite Fermion mass and possible SU(3) valley skyrmions [8][9][10] or related valley textures. 11,12 Accessing these interesting properties in (111) AlAs QWs demands growth of high-quality electrically active silicon (Si) modulation-doped AlAs/AlGaAs heterostructures on (111)-oriented substrates.…”

Piezoplasmonics: Strain-induced tunability of plasmon resonance in AlAs quantum wells

“…The diode was placed outside the cryostat. To apply tunable strain we glued the sample with CPW to one side of a piezostack actuator (PSA) [19][20][21][22][23]. The [010] crystallographic direction was aligned along the stroke direction of the actuator.…”