In this paper, we study the critical behaviors in the non-Hermitian disorder Aubry-André (DAA) model, and we assume the non-Hermiticity is introduced by nonreciprocal hopping. We employ the localization length $\xi$, the inverse participation ratio ($\mathrm{IPR}$), and the energy gap $\mathrm{\Delta }E$ as the characteristic quantities to describe the critical properties of the localization transition. By performing scaling analysis, the critical exponents of the non-Hermitian Anderson model and the non-Hermitian DAA model are obtained, and these critical exponents are different from their Hermitian counterparts, indicating that the Hermitian and non-Hermitian Anderson and DAA models belong to different universality classes. The critical exponents of the non-Hermitian DAA model are remarkably different from both the pure non-Hermitian AA model and the non-Hermitian Anderson model, showing that disorder is an independent relevant direction at the non-Hermitian AA model critical point. We further propose a hybrid scaling law to describe the critical behavior in the overlapping critical region constituted by the critical regions of the non-Hermitian DAA model and the non-Hermitian Anderson localization.

Effects of the titanium dopant on the physical properties and structure of SbSe thin films were systematically investigated by experiments and first-principles calculations. The amorphous-to-polycrystalline transformation induced by heat was examined by in situ electrical resistance measurements. With the incorporation of titanium atoms, both the crystallization temperature and electrical resistance increase, revealing the improvement of the amorphous thermal stability and programing energy consumption. X-ray diffraction, transmission electron microscopy, and density functional theory calculations illustrate that a small amount of titanium dopant can inhibit the grain growth and refine the crystal size. The shift of Raman modes associated Sb upon the crystallization was observed. X-ray reflectivity and atomic force microscopy results prove the smaller volume fluctuation and the smoother surface morphology, meaning the better interfacial property and reliability of titanium-doped SbSe materials. Phase change memory cells based on titanium-doped antimony-selenium were fabricated to evaluate the electrical performance as well. All these results indicate that the suitable incorporation of the titanium element will be an effective method to optimize the physical properties and tune the structure of the SbSe phase change material.

The influence of nitrogen dopant on the structure of the phase-change material Sb has been investigated by ab initio molecular dynamics simulations. The doped N exist as SbN complex in amorphous phase and would not enter into the rhombohedra phase of crystalline Sb. During crystallization of the amorphous phase, no N ₂ molecule is formed and part of the N–Sb bonds are broken to release Sb atoms which contribute to growth of crystal nuclei by forming more Sb–Sb bonds. Remaining N–Sb bonds would segregate at the grain boundaries and retard growth of crystal nuclei.