Safe Haskell | None |
---|---|

Language | Haskell98 |

- orbMag :: Filling -> Hamiltonian -> Parameterized Magnetization
- dichroism :: Filling -> Hamiltonian -> Parameterized Magnetization
- dichroicIntegrand :: Filling -> Hamiltonian -> Wavevector -> Parameterized Magnetization
- intrinsicOM :: Filling -> Hamiltonian -> Parameterized Magnetization
- integrandMk :: BandIndex -> Hamiltonian -> Wavevector -> Parameterized Magnetization
- bandIntrinsicOM :: BandIndex -> Hamiltonian -> Parameterized Magnetization

# Documentation

orbMag :: Filling -> Hamiltonian -> Parameterized Magnetization Source

Returns the total orbital magnetization due to filling the first n bands.

dichroism :: Filling -> Hamiltonian -> Parameterized Magnetization Source

Returns the gauge-invariant self-rotational orbital magnetization, i.e.
the circular dichroism, of the occupied bands, accomplished by integrating
`dichroicIntegrand`

.

dichroicIntegrand :: Filling -> Hamiltonian -> Wavevector -> Parameterized Magnetization Source

Essentially equation (12) from PRB _77_, 054438 (2008) with alpha, beta set
to x, y respectively so as to give the z-component of the (expectation
value of) the circular dichroism pseudovector. This form takes a double sum over
occupied and then unoccupied states, which improves over the implementation of
`integrandMk`

by allowing for intra-(un)occupied band degeneracies as long as
there is still an electronic band gap.

As is consistent with our API for these types of functions, the
`Filling`

argument should be a positive integer counting the
number of filled bands.

intrinsicOM :: Filling -> Hamiltonian -> Parameterized Magnetization Source

Sums `bandIntrinsicOM`

over the first n bands.

integrandMk :: BandIndex -> Hamiltonian -> Wavevector -> Parameterized Magnetization Source

Gives the gauge-invariant self-rotational orbital magnetism, which is proportional to the circular dichroism for a particular band index. This is m(k) in Xiao et al's semiclassical approach (hence the name).

bandIntrinsicOM :: BandIndex -> Hamiltonian -> Parameterized Magnetization Source

Returns the intrinsic orbital magnetization of the n*th* band, namely
the integral of _m_(k) from (Xiao et al., 2005).