Exact inversion-subgroup EBR and symmetry-indicator analysis (spinful TR). More...

Functions/Subroutines
subroutine, public	inversion_indicators (odd, pairs, dimension, strong, weak, z4, status)
	Fu–Kane indices and inversion indicator with an explicit sign convention.
subroutine, public	inversion_ebr_signature (odd, pairs, signed_atomic, nonnegative_atomic, coefficients, status)
	Exact signed/nonnegative EBR-signature test for the inversion subgroup.

Detailed Description

Exact inversion-subgroup EBR and symmetry-indicator analysis (spinful TR).

Note: These are symmetry signatures, not a complete topological classification.

Function/Subroutine Documentation

subroutine, public topology_tqc::inversion_indicators	(	integer, dimension(:), intent(in)	odd,
		integer, intent(in)	pairs,
		integer, intent(in)	dimension,
		integer, intent(out)	strong,
		integer, dimension(3), intent(out)	weak,
		integer, intent(out)	z4,
		integer, intent(out)	status )

Fu–Kane indices and inversion indicator with an explicit sign convention.

Parameters

odd	Number of odd Kramers pairs at each TRIM, x-bit fastest
pairs	Number of occupied Kramers pairs
DIMENSION	Two (kz=0 plane) or three (full reciprocal torus)
strong	Plane index in 2D, strong index in 3D
weak	Three weak indices in 3D; -1 (unavailable) in 2D
z4	sum(odd) mod 4 in 3D; -1 (unavailable) in 2D
status	Zero on valid input

Definition at line 28 of file topology_tqc.F.

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subroutine, public topology_tqc::inversion_ebr_signature	(	integer, dimension(:), intent(in)	odd,
		integer, intent(in)	pairs,
		logical, intent(out)	signed_atomic,
		logical, intent(out)	nonnegative_atomic,
		integer, dimension(:, :), intent(out)	coefficients,
		integer, intent(out)	status )

Exact signed/nonnegative EBR-signature test for the inversion subgroup.

Parameters

odd	Odd Kramers pairs, x-bit fastest, 4 or 8 TRIM
pairs	Selected number of Kramers pairs
signed_atomic	Signature belongs to the integer lattice of atomic signatures
nonnegative_atomic	A physical nonnegative EBR-signature decomposition exists
coefficients	Even/odd local-parity EBR coefficients at the 2^d inversion centers
status	Zero on valid input, coefficients valid only if nonnegative_atomic

Note: EBR at r=a/2 has inversion character s*(-1)^(a.k). Fourier inversion determines the differences between even/odd multiplicities exactly. No database or floating-point integer decision is used.

Definition at line 67 of file topology_tqc.F.

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