View source for Pump and Probe: Time resolved ARPES

In this tutorial we show how to reconstruct the TR-ARPES spectral function in presence of excitons. See Refs.<ref name="Perfetto2019"/> <ref name="Sangalli2021"/>

== ARPES from real-time propagation ==

The first part describes how to reconstruct the spectral function from after real-time propagation. If the real-time propagation has been done at the TD-HSEX level in a material with (strongly) bound excitons, and the pump pulse is tuned in resonance with an excitonic peak, the spectral function will show a fingerprint of the excitonic state, e.g. a replica of the valence band.


=== Store the history of the density matrix to disk ===
In order to reconstruct the ARPES response function, just run any real time propagation tutorial base on the `yambo_rt` executable (see for example this one: [[Real_time_Bethe-Salpeter_Equation_(density_matrix_only)]]) and add the following line to the input file
 SaveGhistory

Please be aware that this will create a very large file containing the whole history of the density matrix. You can control how often the density matrix is written to disk with the second value in this input variable
 % IOtime
  0.5 |5.0 |0.5 |  fs    # [RT] Time between to consecutive I/O (J,P,OCCs - GF - OUTPUT)
 %
Usually the density matrix is used for restart only, and saving every 5 fs or so is reasonable. To reconstruct the TR-ARPES response function however, one needs to perform a Fourier transform, and it is usually need to write data more often to disk.

Run the real time simulation
 yambo_rt -F inputs/td_run -J TD-RUN-NAME -C TD-RUN-NAME


=== Use the GKBA approach to reconstruct the spectral function ===

After the history is saved to disk, you can use `ypp_rt` to reconstruct the spectral function. Here an input file to be used to this end

 TDplots                       # [R] Real-Time Post-Processing
 RTGtwotimes                      # [R] Construct G<(t,tp)
 RTtime                         # [R] Post-Processing kind: function of time
 TimeStep= 0.01      fs      # Time step
 % TimeRange
  25.00000 | 75.0000 | fs      # Time-window where processing is done
 %
 LoadGhistory                  # [NEGF] Build the NEQ density from the G_lesser
 % EnRngeRt
  -2.00000 | 14.00000 | eV      # Energy range
 %
 ETStpsRt= 501                 # Total Energy steps

 BuildGles
 KeepCC        # This includes the contribiution from the c and c' terms of the density matrix in conduction
 
 DampFactor= 50.0    meV
 RhoDeph= 5.0    meV

 INTERP_mode= "BOLTZ"              # Interpolation mode (NN=nearest point, BOLTZ=boltztrap aproach)
 OutputAlat= 3.851738           # [a.u.] Lattice constant used for "alat" ouput format
 cooIn= "rlu"                   # Points coordinates (in) cc/rlu/iku/alat
 cooOut= "rlu"                  # Points coordinates (out) cc/rlu/iku/alat

 INTERP_Shell_Fac= 20.00000     # The bigger it is a higher number of shells is used
 #BANDS_path= "L G X"            # BANDS path points labels (G,M,K,L...)
 BANDS_steps= 50                # Number of divisions
 BANDS_built_in                 # Print the bands of the generating points of the circuit using the nearest internal point
 %BANDS_kpts                    # K points of the bands circuit
    0.5000000 |  0.5000000 |  0.5000000 | #L(111)
    0.0000000 |  0.0000000 |  0.0000000 | #G
    0.0000000 |  0.5000000 |  0.5000000 | #X
 %

You can also replace 
 BuildGles
with
 BuildGret

Some extra options, which you can add to the input file, are available. For example
 IncludeEQocc  # This includes the contribiution of the equilibrium occupations
 KeepCV        # This includes the contribiution from the c and v  terms of the density matrix
 KeepVC        # This includes the contribiution from the v and v' terms of the density matrix in valence

After your input file is ready just run 
 ypp_rt -F inputs/Gless_reconstruc -J "Gless,TD-RUN-NAME" -C TD-RUN-NAME




== ARPES as BSE post processing ==

'''Warning: this is not yet available in the GPL release'''.
You can download and use the following yambo fork if you are interested:  https://gitlab.com/sangallidavide/lumen/-/tree/phys-excitons

In this second part we show instead how to simply reconstruct the spectral function from a post-porcessing of a BSE simulations at all transferred momenta in the IBZ. The BSE eigenvectors are needed. They can be obtained either via direct diagonalization or via iterative solvers like Slepc. The excitonic population is also needed as an input. The final the spectral functio will very similar to the real time approach if the population is assumed to be peaked at the bright excitonic state resonant with the pump pulse.

After solving BSE as discussed above, with `yambo_rt`
 yambo_rt -F inputs/bse -J bse_allq -C bse_allq

just use the following input file (change it according to your needs) with `ypp_rt` 
 TDplots                          # [R] TD observables plot
 TDplotmode                       # [R] TD plot control
 RTARPES                          # [R] Transient ARPES
 RTtime                           # [R] Post-Processing kind: function of time
 
 % EnRngeRt
   8.00000 | 17.00000 | eV      # Energy range
 %
 ETStpsRt=  901                  # Total Energy steps
 DampFactor= 0.10000       eV    # Damping parameter
 
 Gauge= "length"                  # [RT] Gauge (length|velocity)
 #FullExpansion
 
 EXCTemp = 300.00 Kn
 #TRabsNExc= 6
 States= "1 - 100"                  # Index of the BS state(s)
 
 INTERP_mode= "BOLTZ"              # Interpolation mode (NN=nearest point, BOLTZ=boltztrap aproach)
 INTERP_Shell_Fac= 20.00000     # The bigger it is a higher number of shells is used
 BANDS_path= "L,G,X"            # BANDS path points labels (G,M,K,L...)
 BANDS_steps= 50                # Number of divisions
 %BANDS_kpts                    # K points of the bands circuit
   0.5000000 |  0.5000000 |  0.5000000 | #L(111)
   0.0000000 |  0.0000000 |  0.0000000 | #G
   0.0000000 |  0.5000000 |  0.5000000 | #X
 %

and finally run ypp_rt
 ypp_rt -F inputs/arpes_from_bse -J "ARPES,bse_allq" -C ARPES

Below the output plotted with python using different excitonic distributions
<gallery  widths=400 heights=270 caption="Reconstructed ARPES spectral function in LiF">
File:TD-PE ypp 5b e60 kx6 kx24 ALL 12.50.1 cond distr T0.png|600px|temperature T=0 K
File:TD-PE ypp 5b e60 kx6 kx24 ALL 12.50.1 cond distr T300.png|600px|temperature T=300 K
File:TD-PE ypp 5b e60 kx6 kx24 ALL 12.50.1 cond distr T3000.png|600px|temperature T=3000 K
</gallery>
While at low temperature the signal is a replica of the valence band, at higher temperature the excitonic dispersion is obtained.

A similar feature was implemented in yambopy. See Ref.<ref name="Cervantes2025"/>

== References ==

<references>
<ref name="Perfetto2019">E. Perfetto, D Sangalli, A Marini, G Stefanucci, ''Pump-driven normal-to-excitonic insulator transition: Josephson oscillations and signatures of BEC-BCS crossover in time-resolved ARPES'', [https://journals.aps.org/prmaterials/abstract/10.1103/PhysRevMaterials.3.124601 Physical Review Materials '''3''', 124601 (2019)]</ref>
<ref name="Sangalli2021">  D Sangalli, ''Excitons and carriers in transient absorption and time-resolved ARPES spectroscopy: An ab initio approach'', [https://journals.aps.org/prmaterials/abstract/10.1103/PhysRevMaterials.5.083803 Phys. Rev. Mat. '''5''', 083803 (2021)]</ref>
<ref name="Cervantes2025">V. Gosetti, J. Cervantes-Villanueva, S. Mor, D. Sangalli, A. García-Cristóbal, et al., ''Unveiling exciton formation: exploring the early stages in time, energy and momentum domain''
[https://arxiv.org/abs/2412.02507 preprint arXiv:2412.02507 (2025)]</ref>
</references>