Dear Xavier, Thank you very much for your valuable reply. I actually also found these two papers relevant after a long search in the literature, mainly because I suspected that tKwant might be much slower in this case. Your confirmation is very encouraging and now I know these two are the state of the art if we want to take advantage of the periodicity.
I understand technically that [2012] is NEGF + general response formulas and [2018] is static scattering matrix + an energy integral. The crucial energy integral formula Eq. (7) in [2018] deals with dc current but seems readily generalizable to any harmonics by doing the Fourier transform of Eq. (6). So it looks like both methods can deal with any harmonic response. Then the difference between them puzzles me. Are they mathematically equivalent, apart from possible technical differences? (Technically, I suppose [2012] needs to use the less stable and slower GF solvers in Kwant, which is different from [2018].) I also noticed that [2018] assumes a sharp ac voltage drop at the lead interface, which is not mentioned or clear in [2012]. Any comment will be appreciated. -- Sincerely Xiao-Xiao From: Xavier Waintal <xavier.wain...@cea.fr> Date: Tuesday, July 25, 2023 23:33 To: Xiaoxiao Zhang <xiaoxiao.zh...@riken.jp> Cc: kwant-discuss@python.org <kwant-discuss@python.org> Subject: Re: [Kwant] Is Tkwant capable of simulating nonlinear optical responses Hi, I see two ways to address this problem - You can use Tkwant and indeed do a FFT afterwards. It works but it is somewhat overkill and cumbersome. However, one advantage of this approach is that if you use self-consistent Tkwant, you will be able to take interactions effect at a level equivalent to RPA which is important for these types of calculaitons - You can use Kwant and one of the many formula that relates its outputs to finite frequency conductivities. See e.g. the following references to find them: * https://arxiv.org/abs/1802.05924 * https://arxiv.org/abs/1211.2768 (this will involve computing an integral over energy of some object calculable with Kwant). Hope it helps, Xavier > Le 17 juil. 2023 à 04:20, X.-X. Zhang <xiaoxiao.zh...@riken.jp> a écrit : > > Hello Kwant community, > The Kwant package deals with the (dc) linear response for tight-binding > models while TKwant is time-dependent. But it is not obvious to me from the > documentation whether TKwant is capable of simulating nonlinear responses (at > finite frequencies). Instead of naively assuming that it does not go beyond > linear Kwant, it is probably worth asking here. > > I'm particularly interested in finding nonlinear conductivities like a > second-harmonic sigma(2w; w, w) and a dc response sigma(0; w, -w) with w the > driving frequency. They are generated, e.g., by applying the ac bias driving > voltage/current through the attached leads. If Tkwant does capture all such > nonlinear effects, I presume one can simulate in the real time and transform > the current/voltage response to the frequency space and obtain these results. > > Any relevant comment will be appreciated!
