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<p class="MsoNormal"><span style="font-family: 'Times New Roman', serif; font-size: 20px;">Hi
everyone,<o:p></o:p></span></p>
<p class="MsoNormal"><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"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> </span></p>
<p class="MsoNormal"><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"><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"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> </span></p>
<p class="MsoNormal"><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"><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"><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"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> </span></p>
<p class="MsoNormal"><span style="font-family: 'Times New Roman', serif; font-size: 20px;">Any reply
is appreciated! Thank you very much!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> </span></p>
<p class="MsoNormal"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> Best regards,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> Jingjing<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: 'Times New Roman', serif; font-size: 20px;"> </span></p>
<p class="MsoNormal"><span style="font-family:"Times New Roman",serif"> </span></p>
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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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