functions.models.peierls_factor

peierls_factor(nphi, dx, y_cart, dy_cart, A_UC)

The Peierls factor.

The Peierls factor in Landau gauge \(\\\mathbf{A}=-By\hat{\\\mathbf{e}}_x\) is given by

\[\begin{split}e^{\\\mathrm{i}\theta_{ij}} = \exp\left[ -\frac{2\pi\\\mathrm{i}n_\phi}{A} \Delta X \left( Y_i + \frac{\Delta Y}{2} \right) \right],\end{split}\]

where \(\theta_{ij}\) is the Peierls phase from site \(i=(X_i, Y_i)\). to \(j=(X_j, Y_j)\), \(\Delta X = X_j - X_i\), \(\Delta Y = Y_j - Y_i\), \(n_\phi\) is the flux density, and \(A\) is the area factor to make the expression dimensionless. [Peierls33]

Parameters:

• nphi (float) – The flux density.

• dx (float) – The change in x-coordinates.

• y_cart (int) – The initial y-coordinate in units of a2[1].

• dy_cart (int) – The change in y-coordinates in units of a2[1].

• A_UC (float) – The unit cell area in units of a2 (possibly scaled by a periodicity factor).

Returns:

factor – The Peierls factor.

Return type:

complex