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<p class="MsoNormal"><font face="Times New Roman, serif"><span style="font-size: 18.6667px; line-height: 19.9733px;">Dear QE community,</span></font></p><p class="MsoNormal"><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"> </span></p><p class="MsoNormal"><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"> I am a beginner in learning DFT calculation by using Quantum Espresso. I have some problems in calculating the transition matrix elements (momentum operator).</span></p><p class="MsoNormal"><font face="Times New Roman, serif"><span style="font-size: 18.6667px; line-height: 19.9733px;"><br></span></font></p><p class="MsoNormal"><font face="Times New Roman, serif"><span style="font-size: 18.6667px; line-height: 19.9733px;"> </span></font><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;">I know that there are three mainblocks of m × n entries </span><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;">|</span><i style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;">M</i><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;">cv|</span><sup style="font-family: 'Times New Roman', serif; line-height: 107%;">2</sup><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"> (m-the number of valence band, n-the number of conduction band) along x, y, z directions in Cartesian coordinate system for every selected k point.</span></p><p class="MsoNormal"><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"> </span></p><p class="MsoNormal"><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"> In my case, the number of valence bands and conduction bands are 62 and 24, respectively, and it should be 62 x 24 entries </span><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;">|</span><i style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;">M</i><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;">cv|</span><sup style="font-family: 'Times New Roman', serif; line-height: 107%;">2</sup><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"> along every direction at all the k points. In the output, it showed 62 x 24 entries at other k points, but 61 x 25 entries |Mcv|2 only at Gamma point, as shown in the attachment. </span></p><p class="MsoNormal"><font face="Times New Roman, serif"><span style="font-size: 18.6667px; line-height: 19.9733px;"><br></span></font></p><p class="MsoNormal"><font face="Times New Roman, serif"><span style="font-size: 18.6667px; line-height: 19.9733px;"> </span></font><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;">My questions are as following:</span></p><p class="MsoNormal"><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"><br></span></p><p class="MsoNormal"><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"> 1. Why does the output show 61 x 25 entries </span><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;">|</span><i style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;">M</i><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;">cv|</span><sup style="font-family: 'Times New Roman', serif; line-height: 107%;">2</sup><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"> only at the Γ point but 62 x 24 entries at other k points ?</span></p><p class="MsoNormal"><font face="Times New Roman, serif"><span style="font-size: 18.6667px; line-height: 19.9733px;"><br></span></font></p><p class="MsoNormal"><font face="Times New Roman, serif"><span style="font-size: 18.6667px; line-height: 19.9733px;"> </span></font><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;">2. How to calculate the 62 entries </span><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;">|</span><i style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;">M</i><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;">cv|</span><sup style="font-family: 'Times New Roman', serif; line-height: 107%;">2</sup><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"> in one subblock of transition matrix (from 62 valence bands to one conduction band)? More specifically, the calculation order of the 62 values is from the first occupied valence band to the last occupied valence band (the maximal valence band)?</span></p><p class="MsoNormal"><span style="font-size: 18.6667px; line-height: 19.9733px; font-family: 'Times New Roman', serif;"> The calculation order of total 24 subblocks is from the highest conduction band to the minimal conduction band? </span></p><p class="MsoNormal"><span style="font-size: 18.6667px; line-height: 19.9733px; font-family: 'Times New Roman', serif;"> The corresponding diagram is shown in the attachment.</span></p><p class="MsoNormal"><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"><br></span></p><p class="MsoNormal"><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"> 3. For every selected k point, there are three mainblocks of 62 × 24 entries </span><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 19.9733px;">|</span><i style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 19.9733px;">M</i><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 19.9733px;">cv|</span><sup style="font-family: 'Times New Roman', serif; line-height: 12.84px;">2</sup><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"> along x, y, z directions in Cartesian coordinate system. </span></p><p class="MsoNormal"><span style="font-size: 18.6667px; line-height: 19.9733px; font-family: 'Times New Roman', serif;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 18.6667px; line-height: 19.9733px;"> How can I obtain one unique transition matrix element at one k point ( Γ point for example) in the case of an isotropic crystal structure (cubic) , and two transition matrix elements (in-plane and out-of plane direction) in the case of anisotropic crystal structure (rhombohedral) ?</span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Times New Roman",serif;
mso-ansi-language:EN-US"> </span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:"Times New Roman",serif;
mso-ansi-language:EN-US"> </span><span style="font-family: 'Times New Roman', serif; font-size: 14pt; line-height: 107%;">I am looking forward to getting your reply! Thank you very much!</span></p></div><div>
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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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