We describe procedures to obtain the electronic structure of disordered systems using either tight binding like models or quite directly from ab inito density functional band structure calculations. The band structure is calculated using super cells much larger than those containing a single minority component atom. We average over a large number of different super cell calculations containing different randomly positioned minority component atoms in the super cell as well as a varying total number of minority component atoms, weighted by the statistical probability. We develop an efficient and simple algorithm for unfolding of these bands, based on Bloch's theorem. The unfolded band-structure obtained in this way exhibits momentum and energy broadened structures replacing the gaps observed in often used single super cell calculations. Using the super cell averaged band-structure one can introduce a self-energy, resulting from the scattering of randomly positioned alloy components. The self-energy is causal, and shows strong energy and some momentum dependence. The self-energy shows rather non-trivial behavior and is in general non-zero at the Fermi-energy, resulting in an ill or undefined Fermi surface. The real-part of the self-energy at the Fermi-energy relates to an apparent violation of Luttinger's theorem. There is no simple relation between the apparent Fermi-surface volume and the electron count. Examples introducing these effects both for model and real binary alloy systems are presented.
Co-substituted BiFeO3: electronic, ferroelectric, and thermodynamic properties from first principles
铋铁氧体BiFeO3是一种多铁性固体，由于铁电极化增强了光生载流子的分离，因此作为潜在的光催化材料越来越受到关注。为了寻找既能控制能带结构又能保持或提高铁电性能的方法，我们采用密度泛函理论研究了BiCoxFe 1 xO 3（0 < x < 0.13）固溶体的热力学、电子学和铁电性质.我们表明，钴取代的带隙可以从2.9 eV减少到2.1 eV，同时增加自发极化，这是与一个显着较大的Born有效电荷的Co相比，Fe阳离子。我们讨论了钴杂质之间的相互作用，这是强烈的吸引力，并会驱动聚集的钴，证明了蒙特卡罗模拟。因此，预测相分离成富Co相是化学上优选的，并且均匀固溶体只能以亚稳形式存在，受到缓慢阳离子扩散动力学的保护。最后，我们讨论了纯的和Co取代的BiFeO3与相关的氧化还原电位的能带排列，在其适用性的上下文中，在氧化还原。
Post density functional theoretical studies of highly polar semiconductive Pb(Ti$_{1-x}$Ni$_{x}$)O$_{3-x}$ solid solutions: The effects of cation arrangement on band gap
First-principles studies of the local structure and relaxor behavior of Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$-PbTiO$_3$-derived ferroelectric perovskite solid solutions
研究了过渡金属掺杂对0.75 Pb（Mg $_{1/3}$ Nb $_{2/3}$）O $_3$-0.25 PbTiO $_3$弛豫铁电体局域结构的影响。我们发现，这些掺杂剂引起非常不同的局部结构和其他物理性质。例如，当Mg被Cu或Zn部分取代时，Cu或Zn的位移远大于Mg的位移，甚至与Nb的位移相当。这些系统的极化也增加，特别是对于Cu掺杂的溶液，由于大的极化率的Cu和Zn。结果，预测的最大介电常数温度（$T_m$）增加。另一方面，用Mo或Tc替换Ti原子显著地降低了阳离子的位移和极化，因此，$T_m$值也显著降低。较高的$T_m$不能用基于阳离子离子半径的传统论点来解释。此外，我们发现，Cu，Mo，或Tc掺杂增加阳离子位移无序。还讨论了掺杂剂对温度色散$ΔT_m$的影响，即不同频率下$T_m$的变化。我们的研究结果奠定了基础，为进一步调查未开发的掺杂剂。
