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 nth band, namely the integral of _m_(k) from (Xiao et al., 2005).