We propose the concept of a device based on a square-shaped sample of a two-dimensional second-order topological helical superconductor which hosts two zero-dimensional Majorana quasiparticles at the corners. The two zero-energy modes rely on particle-hole symmetry (PHS) and their spatial position can be shifted by rotating an in-plane magnetic field and tuning proximity-induced spin-singlet pairing. We consider an adiabatic cycle performed on the degenerate ground-state manifold and show that it realizes the braiding of the two modes whereby they accumulate a nontrivial statistical phase π within one cycle. Alongside the PHS-ensured operator algebra, the fractional statistics confirms the Majorana nature of the zero-energy excitations. A schematic design for a possible experimental implementation of such a device is presented, which could be a step towards realizing non-Abelian braiding.

Abstract. The lattice mismatch strain field of core/multishell structures with spherical symmetry is modeled by a linear continuum elasticity approach. The effect of the strain on the energy structure and linear optical absorption in large core/shell/shell spherical semiconductor quantum dots is analyzed. Localization of the photoexcited carriers induced by coating is found to play an important role in explaining the optical stability of large CdSe/CdS/ZnS and ZnTe/ZnSe/ZnS quantum dots. IntroductionAs 'The Next Big Thing' in photovoltaics [1], the colloidal multishell semiconductor quantum dots (QDs) have led to the development of high-efficiency solar cells. To overcome the crystal irregularities induced by the lattice mismatch in the synthesis of these colloidal nanocrystals, the use of a strain-adapting intermediate shell in core/shell (CS) QDs has been proposed. Thus, 'giant' core/shell/shell (CSS) QDs of 18-19 monolayers shell thickness of are synthesized [2,3]. There are several theoretical studies of multi-component nanocrystals, in which the role of the strain is considered by first-principle calculations, by using, for example, the density-functional tight-binding method [4] or local density approximation [5] or densityfunctional theory [6]. Unfortunately, limitations of these ab-initio calculations (e.g., bandgap underestimation) make difficult comparison of their results with the experiment. More important, the main problem of the first-principle calculations, the computational cost, can make the method inadequate for larger structures, such as the large CSS QDs. On the other hand, the widely used for analyzing the linear elasticity of epitaxial strained heterointerfaces, the valence force field method (see, e.g., Ref. [7]) is dependent on a priori information regarding the interface structure and surface passivation. The continuum elasticity approach in the limits of homogeneous and isotropic materials has been shown to be in good agreement with the valence force field models * E-mail: cheche@gate.sinica.edu.twTel.: +40 724 536 908 2 for semiconductor QDs of spherical shape and cubic symmetry (see, e.g., Ref. [8]). In this context, we propose a continuum elasticity model for the lattice mismatch strain field in such nanocrystals. Keeping justified simplicity, based on our strain field model, we consider a twoband model within the effective mass approximation to theoretically investigate the energy structure and light absorption of a CSS QD with thick shells. In our model, we consider ideal multilayer structures. We assume the defects and impurities with low concentration are located at the interfaces, as reported by experiment, (see, e.g., Ref.[9]), and consequently, do not significantly influence the lattice mismatch strain field. Theoretical model Strain field and the band lineup in the presence of strainFirst, we describe our method for calculus of the lattice mismatch strain field. For spherical core/shell nanocrystals the displacement ( u ) has radial symmetry, that is the field is irrotation...

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