Chiral symmetry of microscopic currents in the quantum Hall effect

The spatial distribution of microscopic currents in two-dimensional electron gas devices is investigated exploiting the nonequilibrium Keldysh Green’s function formalism, within the tight-binding framework. First, we establish a criterion at any selected energy for the occurrence of chiral symmetry, i.e., for the spatial separation of carriers with opposite direction of propagation, in the presence of magnetic fields. Then, in the chiral regime, we show that an exact identity links transport current conductance and persistent current conductance, naturally giving rise to the integer quantum Hall effect. Several profiles of current distributions in quantum wires are examined numerically to illustrate the chiral link between local currents and conductance quantization.

Figure 1

Dispersion curves of an ideal wire with $E_0=-4\mid t\mid ,m^{*}=0.068m$, $t=-0.125\mathrm{eV}$, and $B=5\mathrm{T}$.

Figure 2

(a) Total conductance versus Fermi energy in the presence of disorder. (b) Persistent current distribution up to $E_F=17\mathrm{meV}$, the unit on the grey scale is nA. The arrows are a guide to the eye and indicate schematically the local direction of the currents. Transport (c) and persistent (d) differential conductance distributions at $E_F=17\mathrm{meV}$; transport (e) and persistent (f) conductance distributions at $E_F=21\mathrm{meV}$. For conductances, the unit on the grey scale is $2e^2∕h$.