Band narrowing and Mott localization in isotropically superstrained graphene

We explore the effect of multiorbital electron-electron interactions in a two-dimensional monolayer made of elemental carbon. Using density functional dynamical mean-field theory (DFDMFT), we show that the interplay between one-particle band narrowing and sizable on-site interactions naturally stabilizes the Mott insulating state in isotropically superstrained graphene. Our theory is expected to be a key step to understanding both the ability of graphene to afford large strain deformations and the changes in electronic degrees of freedom of $p$-band Coulomb interacting electrons for the next generation of flexible electronics made of semiconductive graphene.

Figure 1

Crystal structure of natural ($L=0.24669$ nm) and superstrained ($L=0.3759$ nm) graphene, with $L$ being the lattice constant of the system.

Figure 2

GGA orbital-resolved and total DOS of graphene for different values of the lattice constant $L$. Notice the band narrowing and the evolution of the electronic spectrum with increasing $L$. A particularly relevant feature is the metallic state in GGA for $L=0.3759$ nm. This corresponds to a C-C average bond length of 0.217 nm (0.142 nm in natural graphene).

Figure 3

Total energy difference $\delta E\left(L\right)\equiv E_L-E_{0.24669}$ between strained and natural graphene obtained from GGA calculations, showing the nonmonotonic response as a function of the lattice constant $L$. The inset shows the behavior of the external forces, $\delta E^{\prime }\left(L\right)\equiv \frac{d}{dL}\delta E\left(L\right)$, required to stretch graphene. Notice the maximum in $\delta E^{\prime }\left(L\right)$ for strain values around $25\%$, suggesting that a crossover between hard and soft graphene might be achieved in future experiments on superstrained graphene across the critical value $L_c=0.309$ nm.

Figure 4

Electron localization function (ELF) and electronic density gradient (gray field lines) analysis for symmetrical superstrained graphene with $L=0.3759$ nm. Notice the C-C bond between the two carbon atoms. [The ELF color-map range used here goes from 0.0 (purple/black) to 1.0 (white)].

Figure 5

Comparison between GGA (solid line) and GGA+DMFT results of (super)strained graphene with $L=0.3759$ nm. Notice the evolution towards a Mott insulator with increasing on-site Coulomb repulsion $U$. Compared to the GGA results, large spectral weight transfer is visible in the GGA+DMFT spectral functions.

Figure 6

Orbital-resolved spectral functions and imaginary parts of the self-energies of superstrained graphene for two values of $U$ and $J_H=0.4$ eV. A crossover from a selective-Kondo ($U=5.5$ eV) to an incoherent metallic regime (at $U=6.0$ eV) is visible. Notice the evolution of the self-energies near $E_F$ across the correlation-induced Fermi to non-Fermi liquid crossover.

Figure 7

Orbital-resolved GGA+DMFT DOS and imaginary parts of the self-energies of superstrained graphene near the Mott transition point at $6.05\text{eV}\le U_c\le 6.1\text{eV}$. Notice the sharp pole in the planar $p_{x,y}$ self-energies near $E_F$ within the Mott insulating phase of graphene at extreme strain conditions. This behavior is characteristic of selective Mott physics in multiorbital systems.