Photoemission spectra of massless Dirac fermions on the verge of exciton condensation

Angle-resolved photoemission spectroscopy (ARPES) is a powerful probe of electron correlations in two-dimensional layered materials. In this article we demonstrate that ARPES can be used to probe the onset of exciton condensation in spatially separated systems of electrons and holes created by gating techniques in either double-layer graphene or topological-insulator thin films.

Figure 1

The spectral function of a massless-Dirac-fermion double-layer system on the verge of exciton condensation. The spectral function $\mathcal{A}(\mathit{k},\omega )$ (in units of $1/{\varepsilon }_{\mathrm{F}}$, where ${\varepsilon }_{\mathrm{F}}$ is the Fermi energy) evaluated at $\left|\mathit{k}\right|=k_{\mathrm{F}}$ is plotted as a function of $\omega /{\varepsilon }_{\mathrm{F}}$ for different values of $T_{\mathrm{c}}/T$. The single peak at the Fermi energy in the high-temperature limit splits into two peaks as $T\to T_{\mathrm{c}}$ from above. All curves have been evaluated by setting $T=0.1T_{\mathrm{F}}$.

Figure 2

(a) The diagram considered for the self-energy: the upper line refers to the top (hole) layer while the lower line to the bottom (electron) layer. (b) The ladder approximation for the effective interaction $V_{\mathrm{eff}}$, Eq. (4). The thin wavy line is the screened interlayer interaction $V_0({\mathit{k}}_1,{\mathit{k}}_2,\mathit{K})$; $\mathit{K}$ is the center-of-mass momentum and $\mathit{p}$ is an integration variable.

Figure 3

The density-of-states $\nu \left(\omega \right)$ (in units of the noninteracting value ${\nu }_0$) as a function of $\omega$ (in units of and measured from the Fermi energy ${\varepsilon }_{\mathrm{F}}$). The color coding and labeling is identical to Fig. 1. The filled (yellow) circles denote the convolution on the right-hand side of Eq. (10) evaluated at $T/T_{\mathrm{c}}=1.01$.