Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice

The massless two-dimensional Dirac equation in a perpendicular magnetic field B supports a B -independent ‘zeroth Landau level’, a dispersionless zero-energy-mode protected by chiral symmetry. On a lattice the zero-mode becomes doubly degenerate with states of opposite chirality, which removes the protection and allows for a broadening when the magnetic field is non-uniform. It is known that this fundamental obstruction can be avoided by spatially separating the doubly degenerate states, adjoining + B and − B regions in a system of twice the size. Here we show that the same objective can be achieved without doubling the system size. The key ingredients are 1) a chirality-preserving ‘tangent fermion’ discretization of the Dirac equation; and 2) a boundary condition that ensures the zero-mode contains only states of a single chirality.