mirror of
https://github.com/triqs/dft_tools
synced 2024-12-22 20:34:38 +01:00
style: pep8 autoformat
This commit is contained in:
Alexander Hampel
parent
468cf6efc7
commit
ee10eaea50
@ -34,6 +34,7 @@ __all__ = ['transport_distribution', 'conductivity_and_seebeck', 'write_output_t
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# ----------------- helper functions -----------------------
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def read_transport_input_from_hdf(sum_k):
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r"""
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Reads the data for transport calculations from the hdf5 archive.
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@ -48,43 +49,34 @@ def read_transport_input_from_hdf(sum_k):
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sum_k : sum_k object
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triqs SumkDFT object
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"""
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assert sum_k.dft_code in ('wien2k','elk'), "read_transport_input_from_hdf() is only implemented for wien2k and elk inputs"
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thingstoread = ['band_window_optics', 'velocities_k']
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sum_k.read_input_from_hdf(
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subgrp=sum_k.transp_data, things_to_read=thingstoread)
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if(sum_k.dft_code=="wien2k"):
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assert sum_k.dft_code in (
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'wien2k', 'elk', 'w90'), "read_transport_input_from_hdf() is only implemented for wien2k and elk inputs"
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if sum_k.dft_code in ('wien2k', 'elk'):
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thingstoread = ['band_window_optics', 'velocities_k']
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else:
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thingstoread = ['band_window_optics']
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sum_k.read_input_from_hdf(subgrp=sum_k.transp_data, things_to_read=thingstoread)
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if (sum_k.dft_code == "wien2k"):
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thingstoread = ['band_window', 'lattice_angles', 'lattice_constants',
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'lattice_type', 'n_symmetries', 'rot_symmetries']
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elif(sum_k.dft_code=="elk"):
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thingstoread = ['band_window', 'n_symmetries',
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'rot_symmetries','cell_vol']
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elif (sum_k.dft_code == "elk"):
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thingstoread = ['band_window', 'n_symmetries', 'rot_symmetries',
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'cell_vol']
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elif (sum_k.dft_code == 'w90'):
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thingstoread = ['band_window', 'n_symmetries', 'rot_symmetries']
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sum_k.read_input_from_hdf(subgrp=sum_k.misc_data, things_to_read=thingstoread)
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if(sum_k.dft_code=="wien2k"):
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sum_k.cell_vol = cellvolume(sum_k.lattice_type, sum_k.lattice_constants, sum_k.lattice_angles)[1]
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if (sum_k.dft_code == "wien2k"):
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sum_k.cell_vol = cellvolume(
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sum_k.lattice_type, sum_k.lattice_constants, sum_k.lattice_angles)[1]
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return sum_k
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def read_transport_input_from_hdf_wannier90(sum_k):
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r"""
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Reads the data for transport calculations from the hdf5 archive.
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Parameters
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----------
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sum_k : sum_k object
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triqs SumkDFT object
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Returns
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-------
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sum_k : sum_k object
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triqs SumkDFT object
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"""
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thingstoread = ['band_window_optics']
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sum_k.read_input_from_hdf(
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subgrp=sum_k.transp_data, things_to_read=thingstoread)
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thingstoread = ['band_window', 'n_symmetries', 'rot_symmetries']
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sum_k.read_input_from_hdf(subgrp=sum_k.misc_data, things_to_read=thingstoread)
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return sum_k
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def write_output_to_hdf(sum_k, things_to_save, subgrp='user_data'):
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r"""
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@ -103,13 +95,15 @@ def write_output_to_hdf(sum_k, things_to_save, subgrp='user_data'):
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if not (mpi.is_master_node()):
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return # do nothing on nodes
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with HDFArchive(sum_k.hdf_file, 'a') as ar:
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if not subgrp in ar: ar.create_group(subgrp)
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if not subgrp in ar:
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ar.create_group(subgrp)
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for it, val in things_to_save.items():
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if it in [ "gf_struct_sumk", "gf_struct_solver",
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"solver_to_sumk", "sumk_to_solver", "solver_to_sumk_block"]:
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if it in ["gf_struct_sumk", "gf_struct_solver",
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"solver_to_sumk", "sumk_to_solver", "solver_to_sumk_block"]:
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warn("It is not recommended to save '{}' individually. Save 'block_structure' instead.".format(it))
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ar[subgrp][it] = val
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def cellvolume(lattice_type, lattice_constants, latticeangle):
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r"""
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Determines the conventional und primitive unit cell volumes.
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@ -147,6 +141,7 @@ def cellvolume(lattice_type, lattice_constants, latticeangle):
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return vol_c, vol_p
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def fermi_dis(w, beta, der=0):
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r"""
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Fermi distribution.
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@ -174,7 +169,8 @@ def fermi_dis(w, beta, der=0):
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elif der == 1:
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return - beta * fermi ** 2 * numpy.exp(exponent)
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else:
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raise('higher order of derivative than 1 not implemented')
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raise ('higher order of derivative than 1 not implemented')
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def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='./', calc_velocity=False, calc_inverse_mass=False, oc_select='both', oc_basis='h'):
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r"""
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@ -221,12 +217,16 @@ def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='
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read_transport_input_from_hdf_wannier90(sum_k)
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# first check for right formatting of sum_k.nk_optics
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assert len(nk_optics) in [1,3], '"nk_optics" must be given as three integers or one float'
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if len(nk_optics) == 1: assert numpy.array(list(nk_optics)).dtype in (int, float), '"nk_optics" single value must be float or integer'
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if len(nk_optics) == 3: assert numpy.array(list(nk_optics)).dtype == int, '"nk_optics" mesh must be integers'
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assert len(nk_optics) in [1, 3], '"nk_optics" must be given as three integers or one float'
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if len(nk_optics) == 1:
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assert numpy.array(list(nk_optics)).dtype in (
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int, float), '"nk_optics" single value must be float or integer'
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if len(nk_optics) == 3:
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assert numpy.array(list(nk_optics)).dtype == int, '"nk_optics" mesh must be integers'
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if len(nk_optics) == 1:
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interpolate_factor = nk_optics[0]
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nk_x, nk_y, nk_z = list(map(lambda i: int(numpy.ceil(interpolate_factor * len(set(sum_k.kpts[:,i])))), range(3)))
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nk_x, nk_y, nk_z = list(
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map(lambda i: int(numpy.ceil(interpolate_factor * len(set(sum_k.kpts[:, i])))), range(3)))
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else:
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nk_x, nk_y, nk_z = nk_optics
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@ -241,10 +241,13 @@ def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='
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n_kpts = nk_x * nk_y * nk_z
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kpts = numpy.zeros((n_kpts, 3))
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hopping = numpy.zeros((n_kpts, 1, n_orb, n_orb), dtype=complex)
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proj_mat = numpy.zeros(numpy.shape(hopping[:,0,0,0]) + numpy.shape(sum_k.proj_mat[0,:]), dtype=complex)
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proj_mat = numpy.zeros(numpy.shape(
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hopping[:, 0, 0, 0]) + numpy.shape(sum_k.proj_mat[0, :]), dtype=complex)
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cell_volume = kpts = None
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if calc_velocity: velocities_k = None
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if calc_inverse_mass: inverse_mass = None
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if calc_velocity:
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velocities_k = None
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if calc_inverse_mass:
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inverse_mass = None
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if mpi.is_master_node():
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# try wannierberri import
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@ -257,8 +260,8 @@ def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='
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except:
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sys.exit()
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# initialize WannierBerri system
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shift_gamma = numpy.array([0.0,0.0,0.0])
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#wberri = wb.System_w90(pathname + seedname, berry=True, fft='numpy')
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shift_gamma = numpy.array([0.0, 0.0, 0.0])
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# wberri = wb.System_w90(pathname + seedname, berry=True, fft='numpy')
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# WannierBerri uses python multiprocessing which might conflict with mpi.
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# if there's a segfault, uncomment the following line
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wberri = wb.System_w90(pathname + seedname, berry=True, fft='numpy', npar=16)
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@ -267,20 +270,21 @@ def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='
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# read in hoppings and proj_mat
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if oc_basis == 'h':
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hopping[:,0,range(hopping.shape[2]),range(hopping.shape[3])] = dataK.E_K
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hopping[:, 0, range(hopping.shape[2]), range(hopping.shape[3])] = dataK.E_K
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elif oc_basis == 'w':
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hopping[:,0,:,:] = dataK.HH_K
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hopping[:, 0, :, :] = dataK.HH_K
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fake_proj_mat = numpy.zeros(numpy.shape(dataK.UU_K), dtype=complex)
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fake_proj_mat[:,range(numpy.shape(fake_proj_mat)[1]),range(numpy.shape(fake_proj_mat)[2])] = 1. + 1j*0.0
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fake_proj_mat[:, range(numpy.shape(fake_proj_mat)[1]), range(
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numpy.shape(fake_proj_mat)[2])] = 1. + 1j*0.0
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for isp in range(n_inequiv_spin_blocks):
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iorb = 0
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for icrsh in range(sum_k.n_corr_shells):
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dim = sum_k.corr_shells[icrsh]['dim']
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if oc_basis == 'h':
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proj_mat[:,isp,icrsh,0:dim,:] = dataK.UU_K[:,iorb:iorb+dim,:]
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proj_mat[:, isp, icrsh, 0:dim, :] = dataK.UU_K[:, iorb:iorb+dim, :]
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elif oc_basis == 'w':
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proj_mat[:,isp,icrsh,0:dim,:] = fake_proj_mat[:,iorb:iorb+dim,:]
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proj_mat[:, isp, icrsh, 0:dim, :] = fake_proj_mat[:, iorb:iorb+dim, :]
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iorb += dim
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if calc_velocity:
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@ -296,16 +300,17 @@ def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='
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# first term
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Hhbar_alpha = dataK.Xbar('Ham', 1)
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# second term
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c_Hh_Ahbar_alpha = _commutator(hopping[:,0,:,:], dataK.Xbar('AA'))
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c_Hh_Ahbar_alpha = _commutator(hopping[:, 0, :, :], dataK.Xbar('AA'))
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velocities_k = (Hhbar_alpha + 1j * c_Hh_Ahbar_alpha) / HARTREETOEV / BOHRTOANG
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# split into diag and offdiag elements, corresponding to intra- and interband contributions
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v_diag = numpy.zeros(numpy.shape(velocities_k), dtype=complex)
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v_diag[:,range(numpy.shape(velocities_k)[1]),
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range(numpy.shape(velocities_k)[2]),:] = velocities_k[:,range(numpy.shape(velocities_k)[1]),
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range(numpy.shape(velocities_k)[2]),:]
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v_diag[:, range(numpy.shape(velocities_k)[1]),
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range(numpy.shape(velocities_k)[2]), :] = velocities_k[:, range(numpy.shape(velocities_k)[1]),
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range(numpy.shape(velocities_k)[2]), :]
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v_offdiag = velocities_k.copy()
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v_offdiag[:,range(numpy.shape(velocities_k)[1]),range(numpy.shape(velocities_k)[2]),:] = 0. + 1j*0.0
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v_offdiag[:, range(numpy.shape(velocities_k)[1]), range(
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numpy.shape(velocities_k)[2]), :] = 0. + 1j*0.0
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if oc_select == 'intra':
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velocities_k = v_diag
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@ -326,12 +331,13 @@ def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='
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Hw_alpha = dataK.fft_R_to_k(Hw_alpha_R, hermitean=False)[dataK.select_K]
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# second term
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Aw_alpha = dataK.fft_R_to_k(dataK.AA_R, hermitean=True)
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c_Hw_Aw_alpha = _commutator(hopping[:,0,:,:], Aw_alpha)
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c_Hw_Aw_alpha = _commutator(hopping[:, 0, :, :], Aw_alpha)
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velocities_k = (Hw_alpha + 1j * c_Hw_Aw_alpha) / HARTREETOEV / BOHRTOANG
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if calc_inverse_mass:
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V_dot_D = numpy.einsum('kmnab, knoab -> kmoab', dataK.Xbar('Ham', 1)[:,:,:,:,None], dataK.D_H[:,:,:,None,:])
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V_dot_D_dagger = V_dot_D.conj().transpose(0,2,1,3,4)
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V_dot_D = numpy.einsum('kmnab, knoab -> kmoab', dataK.Xbar('Ham', 1)
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[:, :, :, :, None], dataK.D_H[:, :, :, None, :])
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V_dot_D_dagger = V_dot_D.conj().transpose(0, 2, 1, 3, 4)
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V_curly = numpy.einsum('knnab -> knab', V_dot_D + V_dot_D_dagger)
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del2E_H_diag = numpy.einsum('knnab->knab', dataK.Xbar('Ham', 2)).real
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inverse_mass = del2E_H_diag + V_curly
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@ -345,8 +351,10 @@ def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='
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kpts = mpi.bcast(kpts)
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hopping = mpi.bcast(hopping)
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proj_mat = mpi.bcast(proj_mat)
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if calc_velocity: velocities_k = mpi.bcast(velocities_k)
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if calc_inverse_mass: inverse_mass = mpi.bcast(inverse_mass)
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if calc_velocity:
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velocities_k = mpi.bcast(velocities_k)
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if calc_inverse_mass:
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inverse_mass = mpi.bcast(inverse_mass)
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# write interpolated sumk quantities into "things_to_modify"
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things_to_modify['n_k'] = n_kpts
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@ -355,7 +363,8 @@ def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='
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things_to_modify[key] = numpy.full(n_kpts, 1/n_kpts)
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n_inequiv_spin_blocks = sum_k.SP + 1 - sum_k.SO
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for key in ['band_window', 'band_window_optics']:
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things_to_modify[key] = [numpy.full((n_kpts, 2), sum_k.band_window[isp][0]) for isp in range(n_inequiv_spin_blocks)]
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things_to_modify[key] = [numpy.full((n_kpts, 2), sum_k.band_window[isp][0])
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for isp in range(n_inequiv_spin_blocks)]
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things_to_modify['kpts'] = kpts
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things_to_modify['hopping'] = hopping
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things_to_modify['proj_mat'] = proj_mat
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@ -386,6 +395,7 @@ def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='
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# ----------------- transport -----------------------
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def init_spectroscopy(sum_k, code='wien2k', w90_params={}):
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r"""
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Reads all necessary quantities for transport calculations from transport subgroup of the hdf5 archive.
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@ -417,10 +427,12 @@ def init_spectroscopy(sum_k, code='wien2k', w90_params={}):
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if mpi.is_master_node():
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ar = HDFArchive(sum_k.hdf_file, 'r')
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if not (sum_k.transp_data in ar):
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raise IOError("transport_distribution: No %s subgroup in hdf file found! Call convert_transp_input first." % sum_k.transp_data)
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raise IOError(
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"transport_distribution: No %s subgroup in hdf file found! Call convert_transp_input first." % sum_k.transp_data)
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# check if outputs file was converted
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if not ('n_symmetries' in ar['dft_misc_input']):
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raise IOError("transport_distribution: n_symmetries missing. Check if case.outputs file is present and call convert_misc_input() or convert_dft_input().")
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raise IOError(
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"transport_distribution: n_symmetries missing. Check if case.outputs file is present and call convert_misc_input() or convert_dft_input().")
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sum_k = read_transport_input_from_hdf(sum_k)
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@ -432,17 +444,21 @@ def init_spectroscopy(sum_k, code='wien2k', w90_params={}):
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# check some of the input
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pathname = w90_params['pathname'] if 'pathname' in w90_params else './'
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assert all(isinstance(name, str) for name in ['seedname', 'pathname']), f'Check pathname {w90_params["pathname"]} and seedname {w90_params["seedname"]}'
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assert all(isinstance(name, str) for name in [
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'seedname', 'pathname']), f'Check pathname {w90_params["pathname"]} and seedname {w90_params["seedname"]}'
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for file_ending in ['.wout', '_hr.dat', '.chk', '.mmn', '.eig']:
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filename = [pathname, w90_params['seedname'], file_ending]
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assert os.path.isfile(''.join(filename)), f'Filename {"".join(filename)} does not exist!'
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assert os.path.isfile(
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''.join(filename)), f'Filename {"".join(filename)} does not exist!'
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calc_velocity = w90_params['calc_velocity'] if 'calc_velocity' in w90_params else True
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calc_inverse_mass = w90_params['calc_inverse_mass'] if 'calc_inverse_mass' in w90_params else False
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assert all(isinstance(name, bool) for name in [calc_velocity, calc_inverse_mass]), f'Parameter {calc_velocity} or {calc_inverse_mass} not bool!'
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assert all(isinstance(name, bool) for name in [
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calc_velocity, calc_inverse_mass]), f'Parameter {calc_velocity} or {calc_inverse_mass} not bool!'
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# select contributions to be used
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oc_select = w90_params['oc_select'] if 'oc_select' in w90_params else 'both'
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assert oc_select in ['intra', 'inter', 'both'], '"oc_select" needs to be either ["intra", "inter", "both"]'
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assert oc_select in ['intra', 'inter',
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'both'], '"oc_select" needs to be either ["intra", "inter", "both"]'
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# gauge choice options 'h' for Hamiltonian and 'w' for Wannier
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oc_basis = w90_params['oc_basis'] if 'oc_basis' in w90_params else 'h'
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assert oc_basis in ['h', 'w'], '"oc_basis" needs to be either ["h", "w"]'
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@ -460,7 +476,7 @@ def init_spectroscopy(sum_k, code='wien2k', w90_params={}):
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# recompute sum_k instances on denser grid
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sum_k, _ = recompute_w90_input_on_different_mesh(sum_k, w90_params['seedname'], nk_optics=w90_params['nk_optics'], pathname=pathname,
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calc_velocity=calc_velocity, calc_inverse_mass=calc_inverse_mass, oc_select=oc_select, oc_basis=oc_basis)
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calc_velocity=calc_velocity, calc_inverse_mass=calc_inverse_mass, oc_select=oc_select, oc_basis=oc_basis)
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# k-dependent-projections.
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# to be checked. But this should be obsolete atm, works for both cases
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@ -470,6 +486,8 @@ def init_spectroscopy(sum_k, code='wien2k', w90_params={}):
|
||||
return sum_k
|
||||
|
||||
# Uses .data of only GfReFreq objects.
|
||||
|
||||
|
||||
def transport_distribution(sum_k, beta, directions=['xx'], energy_window=None, Om_mesh=[0.0], with_Sigma=False, n_om=None, broadening=0.0, code='wien2k'):
|
||||
r"""
|
||||
Calculates the transport distribution
|
||||
@ -520,7 +538,8 @@ def transport_distribution(sum_k, beta, directions=['xx'], energy_window=None, O
|
||||
# up and down are equivalent if SP = 0
|
||||
|
||||
# positive om_mesh
|
||||
assert all(Om >= 0.0 for Om in Om_mesh), "transport_distribution: Om_mesh should not contain negative values!"
|
||||
assert all(
|
||||
Om >= 0.0 for Om in Om_mesh), "transport_distribution: Om_mesh should not contain negative values!"
|
||||
# Check if energy_window is sufficiently large and correct
|
||||
if (energy_window[0] >= energy_window[1] or energy_window[0] >= 0 or energy_window[1] <= 0):
|
||||
assert 0, "transport_distribution: energy_window wrong!"
|
||||
@ -539,7 +558,7 @@ def transport_distribution(sum_k, beta, directions=['xx'], energy_window=None, O
|
||||
# Define mesh for Green's function and in the specified energy window
|
||||
if (with_Sigma == True):
|
||||
omega = numpy.array([round(x.real, 12)
|
||||
for x in sum_k.Sigma_imp[0].mesh])
|
||||
for x in sum_k.Sigma_imp[0].mesh])
|
||||
mesh = None
|
||||
mu = sum_k.chemical_potential
|
||||
n_om = len(omega)
|
||||
@ -549,7 +568,8 @@ def transport_distribution(sum_k, beta, directions=['xx'], energy_window=None, O
|
||||
# Find according window in Sigma mesh
|
||||
ioffset = numpy.sum(
|
||||
omega < energy_window[0] - max(Om_mesh))
|
||||
omega = omega[numpy.logical_and(omega >= energy_window[0] - max(Om_mesh), omega <= energy_window[1] + max(Om_mesh))]
|
||||
omega = omega[numpy.logical_and(
|
||||
omega >= energy_window[0] - max(Om_mesh), omega <= energy_window[1] + max(Om_mesh))]
|
||||
n_om = len(omega)
|
||||
|
||||
# Truncate Sigma to given omega window
|
||||
@ -558,8 +578,8 @@ def transport_distribution(sum_k, beta, directions=['xx'], energy_window=None, O
|
||||
for icrsh in range(sum_k.n_corr_shells):
|
||||
Sigma_save = sum_k.Sigma_imp[icrsh].copy()
|
||||
spn = sum_k.spin_block_names[sum_k.corr_shells[icrsh]['SO']]
|
||||
glist = lambda: [GfReFreq(target_shape=(block_dim, block_dim), window=(omega[
|
||||
0], omega[-1]), n_points=n_om) for block, block_dim in sum_k.gf_struct_sumk[icrsh]]
|
||||
def glist(): return [GfReFreq(target_shape=(block_dim, block_dim), window=(omega[
|
||||
0], omega[-1]), n_points=n_om) for block, block_dim in sum_k.gf_struct_sumk[icrsh]]
|
||||
sum_k.Sigma_imp[icrsh] = BlockGf(
|
||||
name_list=spn, block_list=glist(), make_copies=False)
|
||||
for i, g in sum_k.Sigma_imp[icrsh]:
|
||||
@ -575,7 +595,7 @@ def transport_distribution(sum_k, beta, directions=['xx'], energy_window=None, O
|
||||
omega = numpy.linspace(
|
||||
energy_window[0] - max(Om_mesh), energy_window[1] + max(Om_mesh), n_om)
|
||||
mesh = MeshReFreq(energy_window[0] -
|
||||
max(Om_mesh), energy_window[1] + max(Om_mesh), n_om)
|
||||
max(Om_mesh), energy_window[1] + max(Om_mesh), n_om)
|
||||
mu = 0.0
|
||||
|
||||
dir_to_int = {'x': 0, 'y': 1, 'z': 2}
|
||||
@ -587,13 +607,15 @@ def transport_distribution(sum_k, beta, directions=['xx'], energy_window=None, O
|
||||
|
||||
if mpi.is_master_node():
|
||||
print("Chemical potential: ", mu)
|
||||
print("Using n_om = %s points in the energy_window [%s,%s]" % (n_om, omega[0], omega[-1]), end=' ')
|
||||
print("Using n_om = %s points in the energy_window [%s,%s]" % (
|
||||
n_om, omega[0], omega[-1]), end=' ')
|
||||
print("where the omega vector is:")
|
||||
print(omega)
|
||||
print("Calculation requested for Omega mesh: ", numpy.array(Om_mesh))
|
||||
print("Omega mesh automatically repined to: ", temp_Om_mesh)
|
||||
|
||||
Gamma_w = {direction: numpy.zeros((len(temp_Om_mesh), n_om), dtype=numpy.float_) for direction in directions}
|
||||
Gamma_w = {direction: numpy.zeros((len(temp_Om_mesh), n_om),
|
||||
dtype=numpy.float_) for direction in directions}
|
||||
|
||||
# Sum over all k-points
|
||||
ikarray = numpy.array(list(range(sum_k.n_k)))
|
||||
@ -612,7 +634,7 @@ def transport_distribution(sum_k, beta, directions=['xx'], energy_window=None, O
|
||||
for iw in range(n_om):
|
||||
A_kw[isp][:, :, iw] = -1.0 / (2.0 * numpy.pi * 1j) * (
|
||||
A_kw[isp][:, :, iw] - numpy.conjugate(numpy.transpose(A_kw[isp][:, :, iw])))
|
||||
#Akw_write[ik] = A_kw[isp].copy() * sum_k.bz_weights[ik]
|
||||
# Akw_write[ik] = A_kw[isp].copy() * sum_k.bz_weights[ik]
|
||||
|
||||
b_min = max(sum_k.band_window[isp][
|
||||
ik, 0], sum_k.band_window_optics[isp][ik, 0])
|
||||
@ -640,17 +662,19 @@ def transport_distribution(sum_k, beta, directions=['xx'], energy_window=None, O
|
||||
for direction in directions:
|
||||
for iw in range(n_om):
|
||||
for iq in range(len(temp_Om_mesh)):
|
||||
if(iw + iOm_mesh[iq] >= n_om or omega[iw] < -temp_Om_mesh[iq] + energy_window[0] or omega[iw] > temp_Om_mesh[iq] + energy_window[1]):
|
||||
if (iw + iOm_mesh[iq] >= n_om or omega[iw] < -temp_Om_mesh[iq] + energy_window[0] or omega[iw] > temp_Om_mesh[iq] + energy_window[1]):
|
||||
continue
|
||||
|
||||
Gamma_w[direction][iq, iw] += (numpy.dot(numpy.dot(numpy.dot(vel_R[v_i, v_i, dir_to_int[direction[0]]], A_kw[isp][A_i, A_i, int(iw + iOm_mesh[iq])]),
|
||||
vel_R[v_i, v_i, dir_to_int[direction[1]]]), A_kw[isp][A_i, A_i, iw]).trace().real * sum_k.bz_weights[ik])
|
||||
vel_R[v_i, v_i, dir_to_int[direction[1]]]), A_kw[isp][A_i, A_i, iw]).trace().real * sum_k.bz_weights[ik])
|
||||
|
||||
for direction in directions:
|
||||
Gamma_w[direction] = (mpi.all_reduce(mpi.world, Gamma_w[direction], lambda x, y: x + y) / sum_k.cell_vol / sum_k.n_symmetries)
|
||||
Gamma_w[direction] = (mpi.all_reduce(mpi.world, Gamma_w[direction],
|
||||
lambda x, y: x + y) / sum_k.cell_vol / sum_k.n_symmetries)
|
||||
|
||||
return Gamma_w, omega, temp_Om_mesh
|
||||
|
||||
|
||||
def transport_function(beta, directions, hopping, velocities, energy_window, n_om, rot_symmetries):
|
||||
r"""
|
||||
Calculates the transport function
|
||||
@ -688,7 +712,8 @@ def transport_function(beta, directions, hopping, velocities, energy_window, n_o
|
||||
mpi.report('Computing transport function...')
|
||||
|
||||
# check that velocities are computed on the FBZ
|
||||
assert numpy.shape(rot_symmetries)[0] == 1, 'Using symmetries currently not implemented for transport function.'
|
||||
assert numpy.shape(rot_symmetries)[
|
||||
0] == 1, 'Using symmetries currently not implemented for transport function.'
|
||||
|
||||
dir_to_int = {'x': 0, 'y': 1, 'z': 2}
|
||||
|
||||
@ -698,15 +723,19 @@ def transport_function(beta, directions, hopping, velocities, energy_window, n_o
|
||||
transp_func = {direction: numpy.zeros(shape=(ws.shape[0])) for direction in directions}
|
||||
|
||||
for ct, w in enumerate(ws):
|
||||
idx = numpy.where(numpy.abs(hopping[:,0,range(orb_1),range(orb_2)].real - w) <= tol)
|
||||
fermi_wg = fermi_dis(hopping[:,0,range(orb_1),range(orb_2)][idx].real - w, beta, 1)/fermi_dis(0., beta, 1)
|
||||
idx = numpy.where(numpy.abs(hopping[:, 0, range(orb_1), range(orb_2)].real - w) <= tol)
|
||||
fermi_wg = fermi_dis(hopping[:, 0, range(orb_1), range(orb_2)]
|
||||
[idx].real - w, beta, 1)/fermi_dis(0., beta, 1)
|
||||
for direction in directions:
|
||||
dir_a, dir_b = [dir_to_int[x] for x in direction]
|
||||
matrix_product = numpy.einsum('kmn, kno -> kmo' , velocities[:,:,:,dir_a], velocities[:,:,:,dir_b])
|
||||
transp_func[direction][ct] = numpy.sum(fermi_wg * matrix_product[:,range(orb_1),range(orb_2)][idx]).real
|
||||
matrix_product = numpy.einsum(
|
||||
'kmn, kno -> kmo', velocities[:, :, :, dir_a], velocities[:, :, :, dir_b])
|
||||
transp_func[direction][ct] = numpy.sum(
|
||||
fermi_wg * matrix_product[:, range(orb_1), range(orb_2)][idx]).real
|
||||
|
||||
return transp_func
|
||||
|
||||
|
||||
def transport_coefficient(Gamma_w, omega, Om_mesh, spin_polarization, direction, iq, n, beta, method=None):
|
||||
r"""
|
||||
Calculates the transport coefficient A_n in a given direction for a given :math:`\Omega`. The required members (Gamma_w, directions, Om_mesh) have to be obtained first
|
||||
@ -747,9 +776,11 @@ def transport_coefficient(Gamma_w, omega, Om_mesh, spin_polarization, direction,
|
||||
A = 0.0
|
||||
# setup the integrand
|
||||
if (Om_mesh[iq] == 0.0):
|
||||
A_int = Gamma_w[direction][iq] * (fermi_dis(omega, beta) * fermi_dis(-omega, beta)) * (omega * beta)**n
|
||||
A_int = Gamma_w[direction][iq] * \
|
||||
(fermi_dis(omega, beta) * fermi_dis(-omega, beta)) * (omega * beta)**n
|
||||
elif (n == 0.0):
|
||||
A_int = Gamma_w[direction][iq] * (fermi_dis(omega, beta) - fermi_dis(omega + Om_mesh[iq], beta)) / (Om_mesh[iq] * beta)
|
||||
A_int = Gamma_w[direction][iq] * (fermi_dis(omega, beta) -
|
||||
fermi_dis(omega + Om_mesh[iq], beta)) / (Om_mesh[iq] * beta)
|
||||
|
||||
# w-integration
|
||||
if method == 'quad':
|
||||
@ -774,6 +805,7 @@ def transport_coefficient(Gamma_w, omega, Om_mesh, spin_polarization, direction,
|
||||
A = numpy.nan
|
||||
return A
|
||||
|
||||
|
||||
def conductivity_and_seebeck(Gamma_w, omega, Om_mesh, SP, directions, beta, method=None):
|
||||
r"""
|
||||
Calculates the Seebeck coefficient and the optical conductivity by calling
|
||||
@ -828,27 +860,37 @@ def conductivity_and_seebeck(Gamma_w, omega, Om_mesh, SP, directions, beta, meth
|
||||
|
||||
for direction in directions:
|
||||
for iq in range(n_q):
|
||||
A0[direction][iq] = transport_coefficient(Gamma_w, omega, Om_mesh, SP, direction, iq=iq, n=0, beta=beta, method=method)
|
||||
A1[direction][iq] = transport_coefficient(Gamma_w, omega, Om_mesh, SP, direction, iq=iq, n=1, beta=beta, method=method)
|
||||
A2[direction][iq] = transport_coefficient(Gamma_w, omega, Om_mesh, SP, direction, iq=iq, n=2, beta=beta, method=method)
|
||||
print("A_0 in direction %s for Omega = %.2f %e a.u." % (direction, Om_mesh[iq], A0[direction][iq]))
|
||||
print("A_1 in direction %s for Omega = %.2f %e a.u." % (direction, Om_mesh[iq], A1[direction][iq]))
|
||||
print("A_2 in direction %s for Omega = %.2f %e a.u." % (direction, Om_mesh[iq], A2[direction][iq]))
|
||||
A0[direction][iq] = transport_coefficient(
|
||||
Gamma_w, omega, Om_mesh, SP, direction, iq=iq, n=0, beta=beta, method=method)
|
||||
A1[direction][iq] = transport_coefficient(
|
||||
Gamma_w, omega, Om_mesh, SP, direction, iq=iq, n=1, beta=beta, method=method)
|
||||
A2[direction][iq] = transport_coefficient(
|
||||
Gamma_w, omega, Om_mesh, SP, direction, iq=iq, n=2, beta=beta, method=method)
|
||||
print("A_0 in direction %s for Omega = %.2f %e a.u." %
|
||||
(direction, Om_mesh[iq], A0[direction][iq]))
|
||||
print("A_1 in direction %s for Omega = %.2f %e a.u." %
|
||||
(direction, Om_mesh[iq], A1[direction][iq]))
|
||||
print("A_2 in direction %s for Omega = %.2f %e a.u." %
|
||||
(direction, Om_mesh[iq], A2[direction][iq]))
|
||||
if ~numpy.isnan(A1[direction][iq]):
|
||||
# Seebeck and kappa are overwritten if there is more than one Omega =
|
||||
# 0 in Om_mesh
|
||||
seebeck[direction] = - A1[direction][iq] / A0[direction][iq] * 86.17
|
||||
kappa[direction] = A2[direction][iq] - A1[direction][iq]*A1[direction][iq]/A0[direction][iq]
|
||||
kappa[direction] = A2[direction][iq] - \
|
||||
A1[direction][iq]*A1[direction][iq]/A0[direction][iq]
|
||||
kappa[direction] *= 293178.0
|
||||
|
||||
# factor for optical conductivity: hbar * velocity_Hartree_to_SI * volume_Hartree_to_SI * m_to_cm * 10^-4 final unit
|
||||
convert_to_SI = cst.hbar * (cst.c * cst.fine_structure) **2 * (1/cst.physical_constants['Bohr radius'][0]) **3 * 1e-6
|
||||
convert_to_SI = cst.hbar * (cst.c * cst.fine_structure) ** 2 * \
|
||||
(1/cst.physical_constants['Bohr radius'][0]) ** 3 * 1e-6
|
||||
optic_cond[direction] = beta * convert_to_SI * A0[direction]
|
||||
for iq in range(n_q):
|
||||
print("Conductivity in direction %s for Omega = %.2f %f x 10^4 Ohm^-1 cm^-1" % (direction, Om_mesh[iq], optic_cond[direction][iq]))
|
||||
print("Conductivity in direction %s for Omega = %.2f %f x 10^4 Ohm^-1 cm^-1" %
|
||||
(direction, Om_mesh[iq], optic_cond[direction][iq]))
|
||||
if not (numpy.isnan(A1[direction][iq])):
|
||||
print("Seebeck in direction %s for Omega = 0.00 %f x 10^(-6) V/K" % (direction, seebeck[direction]))
|
||||
print("kappa in direction %s for Omega = 0.00 %f W/(m * K)" % (direction, kappa[direction]))
|
||||
print("Seebeck in direction %s for Omega = 0.00 %f x 10^(-6) V/K" %
|
||||
(direction, seebeck[direction]))
|
||||
print("kappa in direction %s for Omega = 0.00 %f W/(m * K)" %
|
||||
(direction, kappa[direction]))
|
||||
|
||||
return optic_cond, seebeck, kappa
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user