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arXiv:1511.00327 · Physical Review B

Electron-electron interactions, topological phase, and optical properties of a charged artificial benzene ring

Isil Ozfidan, Milos Vladisavljevic, Marek Korkusiński, Paweł Hawrylak

Published Dec 8, 2015• 5 citations
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Abstract

We present a theory of the electronic and optical properties of a charged artificial benzene ring (ABR). The ABR is described by the extended Hubbard model solved using exact diagonalization methods in both real and Fourier space as a function of the tunneling matrix element $t$, Hubbard on-site repulsion $U$, and interdot interaction $V$. In the strongly interacting case, we discuss exact analytical results for the spectrum of the hole in a half-filled ABR dressed by the spin excitations of the remaining electrons. The spectrum is interpreted in terms of the appearance of a topological phase associated with an effective gauge field piercing through the ring. We show that the maximally spin-polarized $(S=5/2)$ and maximally spin-depolarized $(S=1/2)$ states are the lowest energy, orbitally nondegenerate, states. We discuss the evolution of the phase diagram and level crossings as interactions are switched off and the ground state becomes spin nondegenerate but orbitally degenerate $S=1/2$. We present a theory of optical absorption spectra and show that the evolution of the ground and excited states, level crossings, and presence of artificial gauge can be detected optically.

DOI
10.1103/physrevb.92.245304

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We present a theory of the electronic and optical properties of a charged artificial benzene ring (ABR). The ABR is described by the extended Hubbard model solved using exact diagonalization methods in both real and Fourier space as a function of the tunneling matrix element ttt, Hubbard on-site repulsion UUU, and interdot interaction VVV. In the strongly interacting case, we discuss exact analytical results for the spectrum of the hole in a half-filled ABR dressed by the spin excitations of the remaining electrons. The spectrum is interpreted in terms of the appearance of a topological phase associated with an effective gauge field piercing through the ring. We show that the maximally spin-polarized (S=5/2)(S=5/2)(S=5/2) and maximally spin-depolarized (S=1/2)(S=1/2)(S=1/2) states are the lowest energy, orbitally nondegenerate, states. We discuss the evolution of the phase diagram and level crossings as interactions are switched off and the ground state becomes spin nondegenerate but orbitally degenerate S=1/2S=1/2S=1/2. We present a theory of optical absorption spectra and show that the evolution of the ground and excited states, level crossings, and presence of artificial gauge can be detected optically.
In this thesis, we develop the methodology for exploring the electronic and optical properties of an artificial benzene ring, both analytically as well as numerically through direct diagonalization using the configuration interaction method. We use the extended Hubbard Hamiltonian to model the interactions with different numbers of electrons, with spin projection and total spin resolved as good quantum numbers. The focus in this work is on the charged case and the emergence of an artificial gauge field and how it can be detected optically. We also examine three other cases of the artificial benzene ring, the single electron case, the charge neutral or half filled case, and the quarter filled case. Ground state properties, excited state spectra, and interactions with light are described.
In this, the second of three articles on the optical absorption of electrons in a half-filled Peierls-distorted chain, we present exact results for strongly correlated tight-binding electrons. In the limit of a strong on-site interaction U, we map the Hubbard model onto the Harris-Lange model which can be solved exactly in one dimension in terms of spinless fermions for the charge excitations. The exact solution allows for an interpretation of the charge dynamics in terms of parallel Hubbard bands with a free-electron dispersion of bandwidth W, separated by the Hubbard interaction U. The spin degrees of freedom enter the expressions for the optical absorption only via a momentum-dependent but static ground-state expectation value. The remaining spin problem can be traced out exactly since the eigenstates of the Harris-Lange model are spin degenerate. This corresponds to the Hubbard model at temperatures large compared with the spin exchange energy. Explicit results are given for the optical absorption in the presence of a lattice distortion δ and a nearest-neighbour interaction V. We find that the optical absorption for V = 0 is dominated by a peak at ω = U and broad but weak absorption bands for |ω - U| ≤ W. For an appreciable nearest-neighbour interaction V < W/2, almost all the spectral weight is transferred to Simpson's exciton band which is eventually Peierls split.
In this second of three articles on the optical absorption of electrons in a halffilled Peierls-distorted chain we present exact results for strongly correlated tight-binding electrons. In the limit of a strong on-site interaction U we map the Hubbard model onto the Harris-Lange model which can be solved exactly in one dimension in terms of spinless fermions for the charge excitations. The exact solution allows for an interpretation of the charge dynamics in terms of parallel Hubbard bands with a free-electron dispersion of band-width W, separated by the Hubbard interaction U. The spin degrees of freedom enter the expressions for the optical absorption only via a momentum dependent but static ground state expectation value. The remaining spin problem can be traced out exactly since the eigenstates of the Harris-Lange model are spindegenerate. This corresponds to the Hubbard model at temperatures large compared to the spin exchange energy.
In this, the last of three articles on the optical absorption of electrons in a half-filled Peierls-distorted chain, we address the dimerized extended Hubbard model in the limit of a large on-site interaction U. When the Hubbard interaction is large compared with both the bandwidth W and the nearest-neighbour interaction V, the charge dynamics are properly described by the Harris-Lange model. This model can be exactly mapped onto a model of free spinless fermions in parallel (Hubbard) bands of width W which are eventually Peierls split. To determine the coherent absorption features at low temperatures, we design and employ the ‘no-recoil approximation’ in which we assume that the momentum transfer to the spin degrees of freedom can only be Δqs = 0 or Δqs = π/a during an optical excitation. We present explicit analytical results for the optical absorption in the presence of a lattice dimerization δ and a nearest-neighbour interaction V for the Néel and dimer state. We find that the coherent part of the optical absorption for and the spin dimerization of the ground state.
The square-lattice extended Hubbard model at half filling is studied by a perturbation scheme. By taking into account the ground state of the mean-field theory as a reference state, the scheme treats the collective fluctuations beyond the mean field as the predominant perturbation. The system at ground state can be a spin-density wave (SDW) or a charge-density wave (CDW) depending on the relative strengths of the on-site electron interaction and the nearest-neighbor interaction. The excitation modes above the ground state are analyzed through diagonalizing an effective Hamiltonian. The energy spectra and the wave functions are self-consistently given by the formalism. By comparing the ground-state energies, we investigate the SDW-CDW transition.
Phase diagrams of the one-dimensional extended Hubbard model with a nearest neighbor interaction VVV and site-off-diagonal (bond-charge XXX and bond-bond WWW) interactions at half-filling are obtained numerically, using the level-crossing approach for finite-size clusters. This analysis is straightforward extension of the preceding work [cond-mat/9909277], where only the XXX term is considered as a site-off-diagonal term. Similarly to the XXX term, the WWW term enlarges bond-charge-density-wave (BCDW) and bond-spin-density-wave (BSDW) phases for W<0W<0W<0 and W>0W>0W>0 cases, respectively. In the strong-coupling region, however, the WWW term causes ferromagnetism for W>0W>0W>0, and shifts the boundary of the phase separation in the U/t≪−1U/t\ll-1U/t≪−1 region, which are different from the roles of the XXX term. In addition, we discuss a parameter region where the BSDW state is the exact ground state, and show that the exactly solvable point appears just on the phase boundary between the BSDW and the ferromagnetic phases.