Tunneling between two systems of interacting chiral fermions

We develop a theory of tunneling between two systems of spinless chiral fermions. This setup can be realized at the edge of a quantum Hall bilayer structure. We find that the differential conductance of such a device in the absence of interactions has an infinitely sharp peak as a function of applied voltage. Interaction between fermions results in broadening of the conductance peak. We focus on the regime of strong interactions, in which the shape of the peak manifests well defined features associated with the elementary excitations of the system.

Figure 1

(a) The schematic representation of the setup under consideration, which can be realized in quantum Hall bilayer devices. (b) The sketch of the free fermion dispersions ${\epsilon }_p^{\left(j\right)}$. In the absence of interactions, current shows steplike behavior as illustrated in the inset.

Figure 2

(a) The dimensionless form of differential conductance defined by $\overline{G}=\partial \overline{\mathcal{I}}/\partial \overline{V}$, where $\overline{\mathcal{I}}=({\hslash }^2{v}_1/{e\left|\gamma \right|}^2)\mathcal{I}$ and $\overline{V}=eV/\left[\mathrm{\Delta }{p}_F\left(0\right)v_1\right]$. The solid blue curve is obtained from Eq. (13) for the choice of parameters $v_2=0.5v_1, v_{12}=0.3v_1, {\eta }_2=0.8{\eta }_1, {\eta }_{12}=0.6{\eta }_1$, and ${\eta }_1{\left[\mathrm{\Delta }{p}_F\left(0\right)\right]}^2/\left(2\pi \hslash v_1\right)=0.005$. The dotted red curve shows the conductance to leading order in small nonlinearity given by Eq. (20) for the same values of parameters as that of the blue curve. (b) The blue and red lines are the plots of the spectra ${\tilde{\varepsilon }}_1\left(q\right)$ and $\mathrm{\Delta }\mu -{\tilde{\varepsilon }}_2(\mathrm{\Delta }{p}_F-q)$. Dashed lines show the linear asymptotes of corresponding bosonic spectra. Only the small shaded triangular region with typical momentum $q^{*}$ contributes to the current (13).