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Octopus
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Octopus
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Berry-phase routines for periodic dipoles, static polarization, and the finite-field electric enthalpy potential. More...
Berry-phase routines for periodic dipoles, static polarization, and the finite-field electric enthalpy potential.
The module contains two related implementations:
Data Types | |
| type | berry_t |
| Parameters controlling the inner Berry-potential SCF loop. More... | |
Functions/Subroutines | |
| subroutine, public | berry_init (this, namespace) |
| subroutine, public | berry_write_polarization (namespace, space, mesh, st, ions, kpoints, iunit) |
| Compute and write the static modern-theory polarization after SCF. More... | |
| subroutine | berry_polarization_phase (namespace, space, mesh, st, latt, kpoints, berry_phase) |
| Evaluate Berry phases along each periodic reciprocal-lattice direction. More... | |
| subroutine | berry_neighbor_kpoint (namespace, space, mesh, latt, st, neighbor, gvectors, iq, iq_next, det) |
| Advance one step on a Berry-phase k-string and return the link determinant. More... | |
| subroutine | berry_build_kpoint_strings (namespace, space, kpoints, neighbor, gvectors) |
| Tabulate the k-point strings of a full Monkhorst-Pack grid. More... | |
| integer pure function | berry_kpoint_key (space, kpoints, label) |
| Flatten a Monkhorst-Pack grid label into a single index. More... | |
| integer function | berry_occupied_states (namespace, st, iq, iq_next) |
| Return the number of occupied states shared by two neighboring k-points. More... | |
| complex(real64) function | berry_overlap_det (st, namespace, space, mesh, latt, nocc, iq, iq_next, gvector) |
| Determinant of the occupied-manifold overlap matrix for one k-point link. More... | |
| subroutine | berry_overlap_matrix (st, namespace, space, mesh, latt, nocc, iq, iq_next, gvector, matrix) |
| Build the occupied-state overlap matrix for a Berry-phase k-point link. More... | |
| subroutine | berry_write_polarization_info (space, iunit, berry_phase, electronic_dipole, ionic_dipole, total_dipole, electronic_pol, ionic_pol, total_pol, pol_quantum) |
| Write the static polarization information. More... | |
| subroutine | berry_write_total_polarization_info (space, iunit, total_pol) |
| Write the total polarization. More... | |
| subroutine | berry_polarization_units (space, unit_pol, unit_c_m2) |
| Polarization unit. More... | |
| subroutine, public | berry_perform_internal_scf (this, namespace, space, eigensolver, gr, st, hm, iter, ks, ions, ext_partners) |
| Inner self-consistency loop for a static electric field in periodic systems. More... | |
| subroutine, public | calc_dipole (dipole, space, mesh, st, ions) |
| Calculate the total dipole used by the finite-field Berry machinery. More... | |
| real(real64) function, public | berry_dipole (st, namespace, mesh, latt, space, dir) |
| Use the single-point Berry-phase method to calculate a periodic dipole. More... | |
| complex(real64) function | berry_phase_det (st, namespace, mesh, latt, space, dir, ik) |
| Determinant entering the single-point Berry-phase dipole. More... | |
| subroutine, public | berry_potential (st, namespace, space, mesh, latt, e_field, pot) |
| Local potential for electric enthalpy of a uniform field. More... | |
| real(real64) function, public | berry_energy_correction (st, namespace, space, mesh, latt, e_field, vberry) |
| Return the Berry electric-enthalpy correction for the active field. More... | |
| subroutine, public berry_oct_m::berry_init | ( | type(berry_t), intent(inout) | this, |
| type(namespace_t), intent(in) | namespace | ||
| ) |
| subroutine, public berry_oct_m::berry_write_polarization | ( | type(namespace_t), intent(in) | namespace, |
| class(space_t), intent(in) | space, | ||
| class(mesh_t), intent(in) | mesh, | ||
| type(states_elec_t), intent(in) | st, | ||
| type(ions_t), intent(in) | ions, | ||
| type(kpoints_t), intent(in) | kpoints, | ||
| integer, intent(in) | iunit | ||
| ) |
Compute and write the static modern-theory polarization after SCF.
This routine evaluates the electronic Berry phase on full Monkhorst-Pack k-point strings, combines it with the ionic dipole, and writes it. The polarization is only defined modulo the reported polarization quantum.
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Evaluate Berry phases along each periodic reciprocal-lattice direction.
For each direction, the full k-point grid is decomposed into closed one-dimensional strings. The phase accumulated on each string is the argument of the product of occupied-manifold overlap determinants, and the final phase is averaged over the strings transverse to that direction.
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Advance one step on a Berry-phase k-string and return the link determinant.
The input index iq is the electronic-state k/spin index. The routine takes the neighboring real k-point and the reciprocal-lattice vector of the link from the string tables built by berry_build_kpoint_strings, preserves the spin channel for spin-polarized calculations, determines the occupied manifold, and evaluates the corresponding overlap determinant.
| [in] | neighbor | (nkpoints) next k-point on the string |
| [in] | gvectors | (dim, nkpoints) reciprocal vector of that link |
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Tabulate the k-point strings of a full Monkhorst-Pack grid.
The labels number the points of the unfolded grid, while the k-points themselves are stored folded into the first Brillouin zone. A neighbor can therefore differ from k - dk by a reciprocal-lattice vector, which is returned in gvectors and enters the overlap of that link as the periodic-gauge factor exp(-i G.r).
The strings run towards decreasing k. Octopus stores the periodic part u_{nk} of the Bloch state in the convention psi_{nk} = exp(-i k.r) u_{nk}, so u_{nk} is the periodic part of the state of wavevector -k in the usual convention, and the Berry phase of King-Smith and Vanderbilt is therefore accumulated along -k in terms of the stored labels. Traversing the string the other way conjugates the overlap of every regular link but not the one that closes the string, and the resulting phase then fails to converge with the number of points on the string.
| [out] | neighbor | (nkpoints, periodic_dim) |
| [out] | gvectors | (dim, nkpoints, periodic_dim) |
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| subroutine, public berry_oct_m::berry_perform_internal_scf | ( | type(berry_t), intent(in) | this, |
| type(namespace_t), intent(in) | namespace, | ||
| type(electron_space_t), intent(in) | space, | ||
| type(eigensolver_t), intent(inout) | eigensolver, | ||
| type(grid_t), intent(in) | gr, | ||
| type(states_elec_t), intent(inout) | st, | ||
| type(hamiltonian_elec_t), intent(inout) | hm, | ||
| integer, intent(in) | iter, | ||
| type(v_ks_t), intent(inout) | ks, | ||
| type(ions_t), intent(in) | ions, | ||
| type(partner_list_t), intent(in) | ext_partners | ||
| ) |
Inner self-consistency loop for a static electric field in periodic systems.
This updates the Berry potential, recomputes the electric enthalpy correction, refreshes the Kohn-Sham potential, and iterates until the Berry-phase dipole stops changing or MaximumIterBerry is reached.
| subroutine, public berry_oct_m::calc_dipole | ( | real(real64), dimension(:), intent(out), contiguous | dipole, |
| class(space_t), intent(in) | space, | ||
| class(mesh_t), intent(in) | mesh, | ||
| type(states_elec_t), intent(in) | st, | ||
| type(ions_t), intent(in) | ions | ||
| ) |
Calculate the total dipole used by the finite-field Berry machinery.
Periodic directions use the single-point Berry-phase dipole and are folded back by the polarization quantum. Non-periodic directions use the ordinary real-space electronic multipole plus the ionic dipole.
TODO: This should be a method of the electronic system directly that can be exposed.
| real(real64) function, public berry_oct_m::berry_dipole | ( | type(states_elec_t), intent(in) | st, |
| type(namespace_t), intent(in) | namespace, | ||
| class(mesh_t), intent(in) | mesh, | ||
| type(lattice_vectors_t), intent(in) | latt, | ||
| class(space_t), intent(in) | space, | ||
| integer, intent(in) | dir | ||
| ) |
Use the single-point Berry-phase method to calculate a periodic dipole.
This is only accurate in the limit of a large supercell. It is implemented only for an orthogonal unit cell.
\[ \mu = - eL/2*\pi Im ln <\Psi|exp(-i(2*\pi/L)x)|\Psi> \]
E Yaschenko, L Fu, L Resca, R Resta, Phys. Rev. B 58, 1222-1229 (1998) The single-point Berry-phase method for dipoles should not be used when there is more than one k-point. In that case, finite differences should be used to construct derivatives with respect to k.
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| subroutine, public berry_oct_m::berry_potential | ( | type(states_elec_t), intent(in) | st, |
| type(namespace_t), intent(in) | namespace, | ||
| class(space_t), intent(in) | space, | ||
| class(mesh_t), intent(in) | mesh, | ||
| type(lattice_vectors_t), intent(in) | latt, | ||
| real(real64), dimension(:), intent(in), contiguous | e_field, | ||
| real(real64), dimension(:,:), intent(out), contiguous | pot | ||
| ) |
Local potential for electric enthalpy of a uniform field.
This is the single-point Berry-phase finite-field potential used by the internal Berry SCF loop.
P Umari et al., Phys Rev Lett 95, 207602 (2005) eqs (3), (7)
\[ E * (e L / 2 \pi) Im e^{i 2 \pi r / L} / z \]
| [in] | e_field | (spacedim) |
| [out] | pot | (meshnp, stdnspin) |
| real(real64) function, public berry_oct_m::berry_energy_correction | ( | type(states_elec_t), intent(in) | st, |
| type(namespace_t), intent(in) | namespace, | ||
| class(space_t), intent(in) | space, | ||
| class(mesh_t), intent(in) | mesh, | ||
| type(lattice_vectors_t), intent(in) | latt, | ||
| real(real64), dimension(:), intent(in), contiguous | e_field, | ||
| real(real64), dimension(:,:), intent(in) | vberry | ||
| ) |
Return the Berry electric-enthalpy correction for the active field.
The correction subtracts the expectation value of the local Berry potential and adds the real dipole-field term, giving the contribution used in the finite-field SCF loop.
| [in] | e_field | (spaceperiodic_dim) |
| [in] | vberry | (meshnp, stdnspin) |
1.9.4