Thoretical Study on First-principles Calculation of Lattice Dynamics and Pressure-Induced Superconductivity

采用第一性原理全势LAPW（FLAPW）方法和半经验紧束缚方法，对固体碘和溴高压FCC相的电子能带结构、电子-晶格相互作用、晶格动力学和超导电性进行了详细的研究.主要结果如下：1.所得到的能带结构具有三个空穴费米面，因此FCC固体碘和溴是典型的空穴金属。2.用紧束缚方法从微观上计算了电子-晶格耦合，确定了转移能及其导数，再现了FLAPW方法得到的第一性原理能带结构。随着压强的增加，费米面平均的电子-晶格耦合平方<xi ^2>显著增加。3. X（0 ...更多信息 用冻结声子方法计算了布里渊区（BZ）中的（0，0，2 pi/a）点。4.考虑电子-晶格相互作用，只考虑最近邻的短程力，用冻结声子方法计算了整个BZ的声子谱，确定了这些短程力在X点处再现Ω_L和Ω_T。声子频率的平均值<omega>和声子频率平方的平均值均随压力的增加而显著增加。5. N（E_F）&lt;xi^2&gt;随压力的增加而显著增加，但随着压力的增加，声子频率平方的平均值和声子频率平方的平均值&lt;omega^2&gt;的增加比N（E_F）&lt;xi^2&gt;的增加快。因此，无量纲的电子-声子耦合λ = N（E_F）&lt;xi^2&gt; /M &lt;omega^2&gt;成为压力的递减函数。结果表明，超导转变温度T_c也随压力的增加而降低，T_c值在1 K量级，与实验结果一致。但是，计算的T_c与压力的关系与碘中的观测结果不同。这种差异可能意味着有必要以第一原理的方式来处理电子-晶格相互作用。少

Electronic band strucutures, electron-lattice interaction, lattice dynamics and superconductivity in high pressure FCC phase of solid iodine and bromine are studied in detail on the basis of the first-principles full-potential LAPW (FLAPW) method and the semi-empirical tight-binding method. The main results are summarized as follows.1.The obtained band structures have three hole Fermi surfaces, and hence the FCC solid iodine and bromine are typical hole metals. The density of states at the Fermi energy N (E_F) decreases with increasing pressure.2.Electron-lattice coupling has been evaluated microscopically by the tight binding method in which transfer energies and their derivatives are determined so as to reproduce the first-principles band structures obatined by the FLAPW method. The Fermi surface average of squared electron-lattice coupling <xi^2> increases considerably as the pressure increases.3.The frequencies of the longitudinal (L) and the transverse (T) phonon modes at the X (0 … More ,0,2pi/a) point in the Brillouin zone (BZ) have been calculated by the frozen-phonon method. The obtained frequencies show hardening with increasing pressure.4.The phonon spectrum of the whole BZ have been calculated by taking accout of the electron-lattice interaction and by considering only the nearest neighboring short range forces which were determined to reproduce omega_L and omega_T at the X point obtained by the frozen-phonon method. The average of phonon frequency <omega> and that of squared phonon frequency <omega^2> increases significantly as the pressure increases.5.The value of N (E_F) <xi^2> increases considerably with increasing pressure, but <omega^2> increases more rapidly than N (E_F) <xi^2> as pressure increases. Therefore the dimensionless electron-phonon coupling lambda = N (E_F) <xi^2> /M <omega^2> becomes a decreasing function of pressure. As the results the superconducting transition temperature T_c also decreases with increasing pressure.The magnitude of T_c is in order of 1 K,which agrees with the experimental results. But, the calculated pressure-dependence of T_c is diffrent from that of observations in iodine. This discrepancy may suggest a necessity of treating the electron-lattice interaction in more first-principles manner. Less