Metastable electron-electron states in double-layer graphene structures

The prototypical exciton model of two interacting Dirac particles in graphene was analyzed in J. Sabio et al., Phys. Rev. B 81, 045428 (2010) and it was found that in one of the electron-hole scattering channels the total kinetic energy vanishes, resulting in a singular behavior. We show that this singularity can be removed by extending the quasiparticle dispersion, thus breaking the symmetry between upper and lower Dirac cones. The dynamics of an electron-electron pair are then mapped onto that of a single particle with negative mass and anisotropic dispersion. We show that the interplay between dispersion and repulsive interaction can result in the formation of bound, Cooper-pair-like, metastable states in double-layered hybrid structures.

Figure 1

Two-body LDOS in a graphene hybrid structure as a function of binding energy $E$ and interparticle distance $r$. The energy dependence shows distinct bound states in the (a) isotropic regime, which peel off into the free particle continuum in the (b) anisotropic regime (Coulomb potential in white). In real space, the wave functions are those of highly localized bound states at (c) ${\epsilon }_1=45\mathrm{meV}$, and have higher anisotropy for (d) less bound states.

Figure 2

Typical trajectories of an electron pair with zero total momentum ${\mathit{p}}_1=-{\mathit{p}}_2$ in separated graphene layers (separation $d=1.3\mathrm{nm}$) with a hBN dielectric spacer $\left({\epsilon }_s=3.9\right)$. The constituent particles are in different colors, and the ticks on the axes correspond to steps of $20\mathrm{nm}$.

Figure 3

Schematic of the momentum-space grid for the example of $N=4$ shells. Shells are colored as follows: red (zeroth shell), orange (first shell), yellow (second shell), and so on. The vector shown has magnitude $p_{\text{max}}$. All results in this paper were generated for $N=33$.