Commit 6413c295 by Joseph Weston

### whitespace fix

 ... ... @@ -37,7 +37,7 @@ The eigenstates satisfy :math:a^\dagger a | n \rangle = n | n \rangle with the Landau level index :math:n \geq 0, and in coordinate representation are proportional to .. math:: \psi_n (x, y) = \left( \frac{\partial}{ \partial w} - \frac{w^*}{4 l_B^2} \right) w^n e^{-|w|^2/4l_B^2}, ... ... @@ -47,7 +47,7 @@ with :math:w = x + i y. The matrix elements of the ladder operators are \langle n | a | m \rangle = \sqrt{m}~\delta_{n, m-1}, \quad \quad \langle n | a^\dagger | m \rangle = \sqrt{m + 1}~\delta_{n, m+1}. Truncating the basis to the first :math:N Landau levels allows us to approximate the Hamiltonian as a discrete, finite matrix. ... ... @@ -56,16 +56,16 @@ We can now formulate the algorithm that Kwant uses to compute Landau levels. 1. We take a generic continuum Hamiltonian, written in terms of the kinetic momentum :math:\vec{k}. The Hamiltonian must be translationally invariant along the directions perpendicular to the field direction. 2. We substitute the momenta perpendicular to the magnetic field with the ladder operators :math:a and :math:a^\dagger. 3. We construct a kwant.builder.Builder using a special lattice which includes the Landau level index :math:n as a degree of freedom on each site. The directions normal to the field direction are not included in the builder, because they are encoded in the Landau level index. This procedure is automated with kwant.continuum.discretize_landau. This procedure is automated with kwant.continuum.discretize_landau. As an example, let us take the Bernevig-Hughes-Zhang model that we first considered in the discretizer tutorial ":ref:discretize-bhz-model": ... ... @@ -155,7 +155,7 @@ with the Landau levels shown as dashed lines. h = landau_syst.hamiltonian_submatrix(params=params) for ev in scipy.linalg.eigvals(h): ax.axhline(ev, linestyle='--') The dispersion and the Landau levels diverge with increasing energy, because the real space discretization of the ribbon gives a worse approximation to the dispersion at higher energies. ... ... @@ -229,4 +229,4 @@ to construct our heterostructure: .. rubric:: Footnotes .. [#] Wikipedia _ has a nice introduction to Landau quantization. \ No newline at end of file a nice introduction to Landau quantization.