TBit.Magnetic.OrbitalMagnetization

Documentation

orbMag :: Filling -> Hamiltonian -> Parameterized Magnetization

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

dichroism :: Filling -> Hamiltonian -> Parameterized Magnetization

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

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

Sums bandIntrinsicOM over the first n bands.

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

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

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