Strongly bound excitons in gapless two-dimensional structures

Common wisdom asserts that bound excitons cannot form in high-dimensional ($d>1$) metallic structures because of their overwhelming screening and the unavoidable resonance with nearby continuous bands. Strikingly we illustrate that this prevalent assumption is not quite true. A key ingredient has been overlooked: Destructive coherent effects are capable of thwarting the formation of resonance. As an example of this general mechanism, we focus on an experimentally relevant material and predict bound excitons in twisted bilayer graphene, which is a two-dimensional gapless structure that exhibits metallic screening. The binding energies calculated by first-principles simulations are surprisingly large. The low-energy effective model reveals that these bound states are produced by a unique destructive coherence between two alike subband resonant excitons. In particular, this coherent effect is not sensitive to the screening and dimensionality, and hence may persist as a general mechanism for creating bound excitons in various metallic structures, opening the door for excitonic applications based on metallic structures.

Figure 1

(a) Low-energy band structure of tBLG. α (light red) is the plane passing both axes of the Dirac cones, whereas β (light blue) is the bisector plane of the two cones. (b) and (c) Schematic formation of exciton ${\mathrm{X}}_{13}$ (b) and ${\mathrm{X}}_{24}$ (c) illustrated on the α plane. The energy bands are labeled with 1 to 4 in ascending energy order. The involved bands are outlined in black, while the states that mainly compose the exciton are enclosed by the ellipses. (d) Bands plotted on the β plane. $E_G^T=\hslash v_F\left|\Delta \mathbf{K}\right|$ is the transition energy gap between the first (second) and third (fourth) band.

Figure 2

(a) and (b) Optical absorbance obtained by the GW + BSE method. The blue dash-dotted curves are the noninteracting spectra, while the red solid ones are the spectra with the e-h interactions included. (c) and (d) e-h attractive energy $E_a^S$ (blue bars, in arbitrary unit) plotted versus the exciton energy ${\Omega }^S$ for graphene (c) and tBLG (d) within an identical energy window from 2.2 to 5.0 eV, where those unusual excitonic effects happen. For references, the absorbance spectra of both structures are also plotted (red dashed curves).

Figure 3

$|{\chi }_S\left({\mathbf{x}}_e,{\mathbf{x}}_h\right){|}^2$ of excitons $R$, $S$, and $A$ in 21.8° tBLG plotted on the top layer (a1)–(c1) and the bottom layer (a2)–(c2) with the hole fixed at the most-probable position on the top sheet. The distribution of the electron is normalized to the maximal probability of the two layers so that it ranges from 0 (blue) to 1 (red). The details within the primitive cell are less important and thus have been smoothed out.

Figure 4

(a) e-h attractive energy from the low-energy effective model. The blue bars mark the exciton states with prominent e-h attractive energies, whereas the gray bars represent the background states of less interest. (b1)–(b3) Modulus squared wave function of exciton $X_1$, $X_2$, and $X_3$.

Figure 5

(a) PDOS $|\langle X_{13,1}|X_f\rangle {|}^2$ ($|\langle X_{24,1}|X_f\rangle {|}^2$) where $X_f$ goes over the full exciton space. (b) Exciton hybridization diagram in tBLG. The outlined circles represent the excitons formed on either the $1\to 3$ or $2\to 4$ transition subspaces, while the gray ellipses represent the continua. The plus (minus) sign indicates the symmetric (antisymmetric) superposition of exciton states.