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# Accurate prediction of Hall mobilities in two-dimensional materials through gauge-covariant quadrupolar contributions #
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# S. Ponce, M. Royo, M. Gibertini, N. Marzari, and M. Stengel
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# Long-range electrostatic contribution to the electron-phonon couplings and mobilities of two-dimensional and bulk materials #
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# S. Ponce, M. Royo, M. Stengel, N. Marzari, and M. Gibertini

The folders are arranged as follow:

1) Pseudo
Contains all the pseudopotential used in this work.
 * B-PBE.upf = Relativistic PBE psp with NLCC from PseudoDojo
 * N-PBE.upf = Relativistic PBE psp with NLCC from PseudoDojo
 * B.oncvpsp.upf = Scalar LDA psp without NLCC for comparison [see Table III]
 * N.oncvpsp.upf = Scalar LDA psp without NLCC for comparison [see Table III]
 * Sn.oncvpsp.upf = Scalar LDA psp without NLCC to reproduce previous results
 * S.oncvpsp.upf = Scalar LDA psp without NLCC to reproduce previous results
 * Mo-PBE.upf = Relativistic PBE psp with NLCC from PseudoDojo
 * S-PBE.upf = Relativistic PBE psp with NLCC from PseudoDojo
 * C-PBE.upf = Relativistic PBE psp with NLCC from PseudoDojo
 * In-PBE.upf = Relativistic PBE psp with NLCC from PseudoDojo
 * Se-PBE.upf = Relativistic PBE psp with NLCC from PseudoDojo
 * P.upf = Relativistic PBE psp with NLCC from PseudoDojo

2) Software
For compatibility, we also include the QE software (v7.1) along with modified versions of the EPW code used for this work.

Inside q-e-7.1/EPW/ we have:
 * src/ = Modified 2D version of the standard EPW v5.5 version.
          The modifications includes:
            * rigid_epw.f90 - handling of the (system_2d .AND. L > 0.001) case for dipole and quadrupole for g and D
            * Move the long-range substraction from elphon_shuffle_wrap/rg_blk_epw to ephwann_shuffle/ephbloch2wane
          Note: in this version, the Berry connection and V^Hxc terms are disabled.
 * src-noA-nodV = Modified 2D version of the standard EPW v5.5 version.
          The modifications includes:
            * rigid_epw.f90 - handling of the (system_2d .AND. L > 0.001) case for dipole and quadrupole for g and D
            * ephwann_shuffle.f90 - the phonon mode rotation is performed at the very end. Everything is now done
                                    in \kappa\alpha Cartesian direction and only rotate to mode q\nu at the very end.
                                    This removes the need to compute bmat and bmatf.
            * Move the long-range substraction from elphon_shuffle_wrap/rg_blk_epw to ephwann_shuffle/ephbloch2wane
            * The Berry connection term is set to 0 ==> "noA"
            * The V^Hxc term is not computed ==> "nodV"
 * src-A-nodV = Same as above but with Berry connection term
 * src-A-dV = Same as above but with the V^Hxc (dV)
   Note: This version requires first a calculation of the V^Hxc potential with a modified version of the PH code that
         can be found in PHonon/PH-dV/ folder. The solve_e.f90 file has been modifed.
 * src-A-dV-R2 = Same as above but where we have a gauge transformation with a R=[0,2,0] vector used in the short paper for Fig. 1c/d for MoS2.
                 The gauge vector is hardcoded in ephwann_shuffle.f90 line 384 [then follow the variable].
 * src-A-dV-R2-SrO = Same as before and allow for printing 'fort10X' files (see bloch2wan.f90 around lines 1283) for Berry connection terms.
                     It prints data along a SrO high-symmetry line with direction calculation (Bloch, Wannier, total, short-range only).
                     All are before interpolation [testing purposes].
 * src-A-dV-R2-ovlp-SrO = Same as before but prints exact overlaps for reference [testing purposes].

q-e-7.1/PHonon/PH-dV: modification to print the V^Hxc potential
q-e-7.1/PHonon/PH_code_find_L: modification to find the optimal value of the range separation parameter L within the phonon code.

3) Calculations
Contains the input and output of the calculations for each of the 7 materials (SnS2, MoS2, Graphene, BN, InSe, Phosphorene, SrO). For each materials, each folder contains
  * bands: DFT bandstructure
  * relax: structural relaxation
  * quad-Abinit: quadrupole calculation with Abinit and PSP without NLCC.
  * epwXX-TYPE-CHARG-OTHER where
    XX = coarse k and q grid density
    TYPE = 'sohier' means dipole only in the approximation from the Sohier2017 Reference.
         = 'noL' means that the L range separation function was not used [testing purposes]
         = 'dip' means dipole only
         = 'mix' means quadrupoles included in the dynamical matrix but not in the electron-phonon matrix elements
         = 'mixQ' means quadrupoles included in the electron-phonon matrix elements but not in the dynamical matrix
         = 'quad' means quadrupoles included both in dynamical matrix and electron-phonon matrix elements
         = 'spectral' contains spectral decomposition information
    CHARG = 'e' means electron calculation
          = 'h' means hole calculation
    OTHER = 'soc' means that SOC was used
          = 'A' means that the Berry connection was used
          = 'LDA' means that an LDA psp was used instead of PBE [for testing purpose]
  * phonon-E = additional calculation required for a V^Hxc calculation. The calculated drho_eX files need to be copied in the "save" folder so that EPW can read it.
               This calculation must be done with the PHonon/PH-dV/ modified version of the ph.x code.
  * gkk-X: contains the direct calculation of electron-phonon matrix elements with the ph.x code for direct comparison purpose.
           The folders contains useful Python script to generate and retreve the information.