Efficient O(N 2 ) approach to solve the Bethe-Salpeter equation for excitonic bound states
Efficient O(N 2 ) approach to solve the Bethe-Salpeter equation for excitonic bound states
复制标题
DOI：
10.1103/physrevb.78.085103
复制
发表时间：
2008-05
影响因子：
3.7
通讯作者：
F. Fuchs;C. Rödl;A. Schleife;F. Bechstedt
中科院分区：
文献类型：
--
作者：
F. Fuchs;C. Rödl;A. Schleife;F. Bechstedt
光学光谱中的激子效应和电子-空穴对激发用Bethe-Salpeter方程（BSE）的解来描述，该方程解释了受激电子-空穴对的库仑相互作用。虽然对于扩展频率范围内激子光谱的计算有有效的方法，但是单个激子态的确定和分析仍然需要电子-空穴哈密顿量$\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}$的对角化。我们提出了一种具有二次标度复杂性的激子态计算的数值有效方法，与常用的三次标度直接对角化方案相比，它显著降低了计算成本。通过对$\mathbf{k}$空间中的Wannier-Mott两波段模型和半导体MgO和InN的BSE进行数值求解，证明了该方法的准确性和性能。对于$\mathbf{k}$-点采样的收敛性，确定了一个一般趋势，可用于推断最低界态结合能的收敛结果。
Excitonic effects in optical spectra and electron-hole pair excitations are described by solutions of the Bethe-Salpeter equation (BSE) that accounts for the Coulomb interaction of excited electron-hole pairs. Although for the computation of excitonic optical spectra in an extended frequency range efficient methods are available, the determination and analysis of individual exciton states still requires the diagonalization of the electron-hole Hamiltonian $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}$. We present a numerically efficient approach for the calculation of exciton states with quadratically scaling complexity, which significantly diminishes the computational costs compared to the commonly used cubically scaling direct-diagonalization schemes. The accuracy and performance of this approach is demonstrated by solving the BSE numerically for the Wannier-Mott two-band model in $\mathbf{k}$ space and the semiconductors MgO and InN. For the convergence with respect to the $\mathbf{k}$-point sampling, a general trend is identified, which can be used to extrapolate converged results for the binding energies of the lowest bound states.