Correlated electronic properties of some graphene nanoribbons: A DMRG study

Abstract

The significant electron-electron interactions that characterize the π-electrons of graphene nanoribbons (GNRs) necessitate going beyond one-electron tight-binding description. Existing theories of electron-electron interactions in GNRs take into account one electron-one hole interactions accurately but miss higher order effects. We report highly accurate density matrix renormalization group (DMRG) calculations of the ground state electronic structure, the relative energies of the lowest one-photon versus two-photon excitations and the charge gaps in three narrow graphene nanoribbons (GNRs) within the correlated Pariser-Parr-Pople model for π-conjugated systems. We have employed the symmetrized DMRG method to investigate the zigzag nanoribbon 3-ZGNR and two armchair nanoribbons 6-AGNR and 5-AGNR, respectively. We predict bulk magnetization of the ground state of 3-ZGNR, and a large spin gap in 6-AGNR in their respective thermodynamic limits. Nonzero charge gaps and semiconducting behavior, with moderate to large exciting binding energies are found for all three nanoribbons, in contradiction to the prediction of tight-binding theory. The lowest two-photon gap in 3-ZGNR vanishes in the thermodynamic limit, while this gap is smaller than the one-photon gap in 5-AGNR. However, in 6-AGNR the one-photon gap is smaller than the two-photon gap and it is predicted to be fluorescent.

Entanglement, excitations, and correlation effects in narrow zigzag graphene nanoribbons

“…In our case, the a priori value of the quantum information loss was set to χ = 10 −4 and the truncation errors were in the order of 10 −6 . This threshold value required block states about 15000-20000 so that, our results are far more accurate than those from previous investigations, [24][25][26] in terms of the truncation procedure. Such a large number of block states is necessary to obtain accurate gap values and correlation functions.…”

“…The QMC studies mainly focused on the correlation between edge atoms and dynamical properties, 22 and the previous DMRG model calculations were restricted to very small systems. 24,26 In the widespread use of mean-field theory, it is important to investigate its reliability by examining the role of enhanced quantum fluctuations, which this approximation neglects. Although a benchmark of mean-field theory was performed for quantum dot-like structures, 21 less is known about the case of zigzag nanoribbons.…”

“…3 The above facts motivated the exploration of the interaction effects with the use of several methods, like density-functional theory (DFT), 7,[9][10][11][12] mean-field approximation, [13][14][15][16][17][18][19][20] quantum Monte Carlo (QMC) [21][22][23] and density-matrix renormalization group algorithm (DMRG). [24][25][26] The DFT and DMRG in Ref. [25] are used in ab-initio calculations, while the other methods are applied in solving the π-band model of graphene, that is, the Hubbard model on a honeycomb ribbon:…”

Correlated Electronic Properties of a Graphene Nanoflake: Coronene

“…Ab initio DMRG calculations for neutral systems employing molecular orbitals have bottlenecks since the calculation of two-electron integrals is computationally expensive, and consequently, these studies employ ∼50 active space orbitals [ 55 ]. On the other hand, DMRG calculations with localized orbitals have been successfully employed for -conjugated systems with several hundred orbitals within the PPP Hamiltonian [ 53 , 56 , 57 , 58 , 59 ]. The ab initio study of arenes using the DMRG method has also revealed that fully-localized orbitals bring about faster convergence of energies compared to canonical Hartree–Fock orbitals or split-localized orbitals [ 55 ], making the localized description the picture of choice.…”

“…The study of these large finite graphene analogues is expected to shed light on the properties in the thermodynamic limit and the effect of electronic correlation in these industrially important two-dimensional systems. Most of the earlier studies on graphene and graphene analogues have been done within a non-interacting model or employing the restricted configuration interaction technique with a few frontier molecular orbitals [ 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 ], while the importance of electron correlation in the electronic and magnetic structures of these systems has been emphasized in recent studies [ 23 , 24 , 52 , 53 ]. In the present paper, we demonstrate the application of the symmetrized DMRG technique in the study of a graphene nanoflake, coronene, within a long-range correlated -electron model.…”