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<p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;">Hi everyone,<o:p></o:p></span></p><p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 20px; line-height: 1.6;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 20px; line-height: 1.6;">I have some questions about calculating the transition matrix elements of the momentum operator between the valence and conduction bands in quantum espresso.</span></p><p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> </span></p><p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> I know that in the file of p_avg.dat, there are three matrixs of m × n entries |<i>M</i><sub>cv</sub>|<sup>2</sup> (m-the number of valence band, n-the number of conduction band) along <i>kx, ky, kz</i>directions for every chosen k point.<o:p></o:p></span></p><p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;">So for the materials with cubic crystal structure (isotropic), is the transition matrix elements from first valence band to first conduction band is obtained directly by the equation |<i>M</i><sub>11</sub>|<sup>2</sup>= [(|<i>M</i><sub>11-</sub><i>x</i>|<sup>2</sup>)<sup>2</sup>+ (|<i>M</i><sub>11-</sub><i>y</i>|<sup>2</sup>)<sup>2 </sup>+(|<i>M</i><sub>11-</sub><i>z</i>|<sup>2</sup>)<sup> 2</sup> ]<sup>1/2 </sup>?<o:p></o:p></span></p><p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> </span></p><p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> For materials with anisotropic rhombohedral crystal structure for example, the transition matrix elements is composed of two parts along the ordinary (perpendicular to the c axis) and extraordinary direction (parallel to the c axis), how can I get the different transition matrix elements along two different directions?<o:p></o:p></span></p><p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> For the ordinary direction, |<i>M</i><sub>cv</sub>|<sup>2</sup>= [(|<i>M</i><sub>cv-</sub><i>x</i>|<sup>2</sup>)<sup>2</sup>+ (|<i>M</i><sub>cv-</sub><i>y</i>|<sup>2</sup>)<sup>2 </sup>]<sup>1/2 </sup> ?<o:p></o:p></span></p><p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> For the extraordinary direction, |<i>M</i><sub>cv</sub>|<sup>2</sup>=|<i>M</i><sub>cv-</sub><i>z</i>|<sup>2 </sup>?<o:p></o:p></span></p><p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> </span></p><p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> I have no idea about how to acquire the momentum matrix in a symmetric point like Gamma point. Could you give me some hints if you have some experience in it. </span></p><p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> Thank you very much!<o:p></o:p></span></p><p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> </span></p><p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> Best regards,</span></p><p class="MsoNormal" style="margin: 0px; color: rgb(49, 53, 59); font-family: 微软雅黑, Verdana, 'Microsoft Yahei', SimSun, sans-serif; line-height: 22.4px;"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> Jingjing</span></p><span>
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<div style="color: rgb(49, 53, 59); line-height: 22.4px;">--</div><div style="color: rgb(49, 53, 59); line-height: 22.4px;">M.Sc. Jingjing Yu<div><span style="background-color: rgb(255, 255, 255);"><span style="font-family: Arial, Helvetica, sans-serif; font-variant-ligatures: normal; orphans: 2; widows: 2;">Universität Leipzig</span><br style="font-family: Arial, Helvetica, sans-serif; font-variant-ligatures: normal; orphans: 2; widows: 2;"><span style="font-family: Arial, Helvetica, sans-serif; font-variant-ligatures: normal; orphans: 2; widows: 2;">Felix-Bloch-Institut für Festkörperphysik</span><br style="font-family: Arial, Helvetica, sans-serif; font-variant-ligatures: normal; orphans: 2; widows: 2;"><span style="font-family: Arial, Helvetica, sans-serif; font-variant-ligatures: normal; orphans: 2; widows: 2;">Halbleiterphysik</span><br style="font-family: Arial, Helvetica, sans-serif; font-variant-ligatures: normal; orphans: 2; widows: 2;"><span style="font-family: Arial, Helvetica, sans-serif; font-variant-ligatures: normal; orphans: 2; widows: 2;">Linnéstraße 5</span><br style="font-family: Arial, Helvetica, sans-serif; font-variant-ligatures: normal; orphans: 2; widows: 2;"><span style="font-family: Arial, Helvetica, sans-serif; font-variant-ligatures: normal; orphans: 2; widows: 2;">04103 Leipzig, Germany</span></span></div></div>
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