Acoustic phonons and strain in core/shell nanowires

Abstract

We study theoretically the low-energy phonons and the static strain in cylindrical core/shell nanowires (NWs). Assuming pseudomorphic growth, isotropic media, and a force-free wire surface, we derive algebraic expressions for the dispersion relations, the displacement fields, and the stress and strain components from linear elasticity theory. Our results apply to NWs with arbitrary radii and arbitrary elastic constants for both core and shell. The expressions for the static strain are consistent with experiments, simulations, and previous analytical investigations; those for phonons are consistent with known results for homogeneous NWs. Among other things, we show that the dispersion relations of the torsional, longitudinal, and flexural modes change differently with the relative shell thickness, and we identify new terms in the corresponding strain tensors that are absent for uncapped NWs. We illustrate our results via the example of Ge/Si core/shell NWs and demonstrate that shell-induced strain has large effects on the hole spectrum of these systems.

Direct Rashba spin-orbit interaction in Si and Ge nanowires with different growth directions

“…Using the parameters γ 1 = 13.35 and γ s = 5.114 for Ge [109], one obtains the aforementioned values for C and U and therefore CU = 1.1 2 /m. Considering ∆ = 20 meV for instance, which is a realistic subband splitting for typical Ge/Si core/shell NWs [51,67,107], one finds α DR = 8.4 nm 2 e. This value is much greater than the calculated Rashba coefficient α el = 0.05 nm 2 e for electrons in GaAs and even exceeds α el = 1.2 nm 2 e and α el = 5.2 nm 2 e for electrons in InAs and InSb, respectively [66]. Furthermore, in stark contrast to GaAs, InAs, or InSb, Dresselhaus SOI is absent in Ge and Si because of bulk inversion symmetry.…”

“…For all these details of the model and additional information, such as magnetic-field-induced effects, we refer to Refs. [67,68,73,107] and the SI of Ref. [68].…”

Spin–Orbit Interaction and Induced Superconductivity in a One-Dimensional Hole Gas

“…Similarly to the Luttinger-Kohn Hamiltonian the spherical approximation can be used and strain may assumed to be constant in the Ge core. 12 Thus, d = √ 3b, ⊥ = xx = yy , and xy = xz = yz = 0 . The Bir-Pikus Hamiltonian then simplifies to the spherical symmetric form 12…”

“…7,8 Signatures of Majorana bound states (MBSs) have been found in multiple NW experiments. 9,10 An important intermediate result is the measurement of a hard superconducting gap, 11,12 which ensures the semiconductor is well proximitized as is needed for obtaining MBSs.…”

Quantum memories and error correction

“…One promising proposal for the full realization of the planar code, which would eventually allow its use as both a memory and a quantum computer, involves the use of quantum dots [86]. The physical quantum memory in this case would correspond to the spin qubit of the dot.…”