[salmon-user:00335] Discrepancy between SBE and RT-TDDFT Results for Diamond (Carbon)

[ziy...@scu.edu.cn]

Dear Salmon developers and users,

I'm investigating semiconductor Bloch equation (SBE) simulations using Salmon (v2.2.1) and encountering considerable discrepancies between SBE and RT-TDDFT results for diamond (carbon).

• Silicon Benchmark: I've tried the provided example, exercise_x1_bulkSi_bloch_gs_rt, which demonstrates excellent agreement between SBE and RT-TDDFT current calculations for diamond (silicon).

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• Carbon Issue: When I applied the same methodology to diamond (carbon), the SBE-calculated current amplitudes are substantially larger than those from RT-TDDFT. I've varied the nstate parameter in the SBE calculation, but the current amplitude, while decreasing, doesn't appear to converge. Here's a comparison of the current from RT-TDDFT and SBE: 

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Questions:

1. Discrepancy Origin: What could be the cause of this considerable difference between SBE and RT-TDDFT results for diamond (carbon)? Are there specific parameters or settings that need adjustment?

2. yn_vnl_correction: I noticed the yn_vnl_correction option in the source code, which seems to control the inclusion of the non-local pseudopotential contribution. However, this option is undocumented in the manual and defaults to 'no'. Under what circumstances should yn_vnl_correction=yes be used?

3. Gauge Choice: In a previous publication (PHYSICAL REVIEW A 97, 011401(R) (2018)), SBE was implemented in the Houston basis. The current Salmon implementation (v2.2.1) appears to use the velocity gauge. While the velocity gauge may offer advantages, it also introduces challenges in directly incorporating dephasing times and distinguishing intra- and inter-band currents. What are the specific benefits of transitioning to the velocity gauge in this context?

I would appreciate any guidance on resolving the discrepancy and understanding the implementation choices in Salmon.

Cheers,

Zi-Yu Chen

College of Physics, Sichuan University

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[UEMOTO(mobile)]

Dear Prof. Zi-Yu Chen,

I apologize for the delay in my reply due to email issues.

In the current implementation, the numerical results align well when performing the Si benchmark test, but such agreement is seen in limited materials. However, numerical inconsistencies have been identified for other material systems, particularly in linear-response dominant terms.

We consider this discrepancy is likely due to limitations in the numerical precision of the velocity-gauge function implemented in Salmon. We observe similar trends in materials other than diamond: the code tends to over- or underestimate the linear response components for input signals.
The parameter `yn_.nl_correction` is related to SBE calculation accuracy as it corrects for the non-local part of the pseudopotential, which is utilized to transfer the ground state results to SBE calculations. However, its impact on the minor corrections on the current is negligible and only contributes.
Regarding the physical difficulty of velocity-gauge selection, we are still in an exploratory phase and are preparing to implement a length-gauge-based alternative approach in the near future.

Sincerely,

----
Mitsuharu UEMOTO (Assist.Prof. / Ph.D.)
E-mail: uem...@eedept.kobe-u.ac.jp Phone: 078-803-6497
Department of Electrical and Electronic Engineering,
Graduate School of Engineering, Kobe University
植本光治（うえもとみつはる）
神戸大学大学院工学研究科電気電子工学専攻
〒６５７ー８５０１ 神戸市灘区六甲台町１−１

2025年3月17日(月) 19:07 <ziy...@scu.edu.cn>: