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Register a new userOptical conductivity of doped Mott insulator: the interplay between correlation and electron-phonon interaction
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Added by
Vittorio Cataudella
Publication date
2009
fields
Physics
and research's language is
English
Authors
Giulio Dr. De Filippis
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The optical conductivity (OC) of cuprates is studied theoretically in the low density limit of the t-t-J-Holstein model. By developing a limited phonon basis exact diagonalization (LPBED) method capable of treating the lattice of largest size 4x4 ever considered, we are able to discern fine features of the mid-infrared (MIR) part of the OC revealing three-peak structure. The two lowest peaks are observed in experiments and the highest one is tacitly resolved in moderately doped cuprates. Comparison of OC with the results of semianalytic approaches and detailed analysis of the calculated isotope effect indicate that the middle-energy MIR peak is of mostly magnetic origin while the lowest MIR band originates from the scattering of holes by phonons.
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Raman scattering experiments on stoichiometric, Mott-insulating LaTiO$_3$ over a wide range of excitation energies reveal a broad electronic continuum which is featureless in the paramagnetic state, but develops a gap of $sim 800$ cm$^{-1}$ upon cooling below the Neel temperature $T_N = 146$ K. In the antiferromagnetic state, the spectral weight below the gap is transferred to well-defined spectral features due to spin and orbital excitations. Low-energy phonons exhibit pronounced Fano anomalies indicative of strong interaction with the electron system for $T > T_N$, but become sharp and symmetric for $T < T_N$. The electronic continuum and the marked renormalization of the phonon lifetime by the onset of magnetic order are highly unusual for Mott insulators and indicate liquid-like correlations between spins and orbitals.
Systems with strong electron-phonon couplings typically exhibit various forms of charge order, while strong electron-electron interactions lead to magnetism. We use determinant quantum Monte Carlo (DQMC) calculations to solve a model on a square lattice with a caricature of these interactions. In the limit where electron-electron interactions dominate it has antiferromagnetic (AF) order, while where electron-phonon coupling dominates there is columnar valence-bond solid (VBS) order. We find a novel intervening phase that hosts coexisting nematic and antiferromagnetic orders. We have also found evidence of a Landau-forbidden continuous quantum phase transition with an emergent $O(4)$ symmetry between the VBS and the nematic antiferromagnetic phases.
We examined the temperature (T) evolution of the optical conductivity spectra of Sr$_3$Ir$_2$O$_7$ over a wide range of 10-400 K. The system was barely insulating, exhibiting a small indirect bandgap of $sim$0.1 eV. The low-energy features of the optical d-d excitation (${hbar}{omega}$ $<$ 0.3 eV) evolved drastically, whereas such evolution was not observed for the O K-edge X-ray absorption spectra. This suggests that the T evolution in optical spectra is not caused by a change in the bare (undressed) electronic structure, but instead, presumably originates from an abundance of phonon-assisted indirect excitations. Our results showed that the low-energy excitations were dominated by phonon-absorption processes which involve, in particular, the optical phonons. This implies that phonon-assisted processes significantly facilitate the charge dynamics in barely insulating Sr$_3$Ir$_2$O$_7$.
We demonstrate that most features ascribed to strong correlation effects in various spectroscopies of the cuprates are captured by a calculation of the self-energy incorporating effects of spin and charge fluctuations. The self energy is calculated over the full doping range of electron-doped cuprates from half filling to the overdoped system. The spectral function reveals four subbands, two widely split incoherent bands representing the remnant of the split Hubbard bands, and two additional coherent, spin- and charge-dressed in-gap bands split by a spin-density wave, which collapses in the overdoped regime. The incoherent features persist to high doping, producing a remnant Mott gap in the optical spectra, while transitions between the in-gap states lead to pseudogap features in the mid-infrared.
We introduce the notion of superstructure Mottness to describe the Mott and Wigner-Mott transition in doped strongly correlated electron systems at commensurate filling fractions away from one electron per site. We show that superstructure Mottness emerges in an inhomogeneous electron system when the superstructure contains an odd number of electrons per supercell. We argue that superstructure Mottness exists even in the absence of translation symmetry breaking by a superlattice, provided that the extended or intersite Coulomb interaction is strong. In the latter case, superstructure Mottness offers a unifying framework for the Mott and Wigner physics and a nonperturbative, strong coupling description of the Wigner-Mott transition. We support our proposal by studying a minimal single-band ionic Hubbard $t$-$U$-$V$-$Delta$ model with nearest neighbor Coulomb repulsion $V$ and a two-sublattice ionic potential $Delta$. The model is mapped onto a Hubbard model with two effective ``orbitals representing the two sites within the supercell, the intra and interorbital Coulomb repulsion $U$ and $U^prime sim V$, and a crystal field splitting $Delta$. Charge order on the original lattice corresponds to orbital order. Developing a cluster Gutzwiller approximation, we study the effects and the interplay between $V$ and $Delta$ on the Mott and Wigner-Mott transitions at quarter-filling. We provide the mechanism by which the superlattice potential enhances the correlation effects and the tendency towards local moment formation, construct and elucidate the phase diagram in the unifying framework of superstructure Mottness.
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