kubo_bloch Module Reference

Metric-aware Bloch velocities without eigenvector derivatives or band-gap divisions. More...

Functions/Subroutines
subroutine, public	bloch_current (h, s, dh, ds, d, energies, current, status, coefficients)
	Evaluate v_nm = C^H(dH - E_n*dS)C + i*(E_n-E_m)*C^H*D*C.
subroutine, public	bloch_current_from_frame (h, s, dh, ds, d, energies, c, current, tolerance, residuals, status)
	Evaluate the current in a validated reconstructed eigenframe, without rediagonalization.
pure real(dp) function, public	fermi_slope (ea, eb, mu, kt)
	Stable Fermi divided difference including the intraband and degenerate limits.

Detailed Description

Metric-aware Bloch velocities without eigenvector derivatives or band-gap divisions.

Author

Thomas D. Kuehne, tkueh.nosp@m.ne@c.nosp@m.p2k.o.nosp@m.rg

Function/Subroutine Documentation

bloch_current()

subroutine, public kubo_bloch::bloch_current	(	complex(dp), dimension(:, :), intent(in)	h,
		complex(dp), dimension(:, :), intent(in)	s,
		complex(dp), dimension(:, :, :), intent(in)	dh,
		complex(dp), dimension(:, :, :), intent(in)	ds,
		complex(dp), dimension(:, :, :), intent(in)	d,
		real(dp), dimension(:), intent(out)	energies,
		complex(dp), dimension(:, :, :), intent(out)	current,
		integer, intent(out)	status,
		complex(dp), dimension(:, :), intent(out), optional	coefficients )

Evaluate v_nm = C^H(dH - E_n*dS)C + i*(E_n-E_m)*C^H*D*C.

Parameters

h	Full covariant Hamiltonian, including SOC when applicable
s	Overlap in the same Bloch convention
dh	Cartesian k derivatives of h, in Ha*bohr
ds	Cartesian k derivatives of s, in bohr
d	Cell-gauge image first moments, satisfying D-D^H=-i*dS, in bohr
energies	Generalized spectrum
current	Anti-Hermitian current -i*v in the eigenbasis, including diagonal velocities
status	0 success; -1 invalid data; -2 metric failure; -3 connection failure; positive LAPACK failure
coefficients	Optional complete eigenframe for symmetry reconstruction

Note

For a general k-dependent basis D transforms as B^H*D*B-i*(dB)^H*S*B. The connection terms are essential even when the spectrum is accurately reproduced.

Definition at line 35 of file kubo_bloch.F.

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bloch_current_from_frame()

subroutine, public kubo_bloch::bloch_current_from_frame	(	complex(dp), dimension(:, :), intent(in)	h,
		complex(dp), dimension(:, :), intent(in)	s,
		complex(dp), dimension(:, :, :), intent(in)	dh,
		complex(dp), dimension(:, :, :), intent(in)	ds,
		complex(dp), dimension(:, :, :), intent(in)	d,
		real(dp), dimension(:), intent(in)	energies,
		complex(dp), dimension(:, :), intent(in)	c,
		complex(dp), dimension(:, :, :), intent(out)	current,
		real(dp), intent(in)	tolerance,
		real(dp), dimension(2), intent(out)	residuals,
		integer, intent(out)	status )

Evaluate the current in a validated reconstructed eigenframe, without rediagonalization.

Parameters

h	Target Hamiltonian
s	Target AO metric
dh	Cartesian Hamiltonian derivatives
ds	Cartesian overlap derivatives
d	Cell-gauge image first moments
energies	Source spectrum, including complete degenerate blocks
c	Candidate target eigenframe
current	Target current in exactly the supplied gauge
tolerance	Maximum orthonormality and relative projected-eigenproblem errors
residuals	Metric error and energy-scaled projected-Hamiltonian error
status	0 success; -1 invalid data; -3 connection failure; -4 invalid eigenframe

Definition at line 75 of file kubo_bloch.F.

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fermi_slope()

pure real(dp) function, public kubo_bloch::fermi_slope	(	real(dp), intent(in)	ea,
		real(dp), intent(in)	eb,
		real(dp), intent(in)	mu,
		real(dp), intent(in)	kt )

Stable Fermi divided difference including the intraband and degenerate limits.

Parameters

ea	First energy
eb	Second energy
mu	Chemical potential
kt	Positive temperature in energy units

Returns

(f(ea)-f(eb))/(ea-eb) for unit occupation, nonpositive

Definition at line 162 of file kubo_bloch.F.

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