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arXiv:cond-mat/0312615 · Physical Review Letters

Absence of Asymptotic Freedom in Doped Mott Insulators: Breakdown of Strong Coupling Expansions

Philip Phillips, Dimitrios Galanakis, Tudor D. Stanescu

Published Dec 21, 2004• 21 citations
arXivHTMLPDF

Abstract

We show that doped Mott insulators such as the copper-oxide superconductors are asymptotically slaved in that the quasiparticle weight Z near half-filling depends critically on the existence of the high-energy scale set by the upper Hubbard band. In particular, near half-filling, the following dichotomy arises: Z not equal to 0 when the high-energy scale is integrated out but Z=0 in the thermodynamic limit when it is retained. Slavery to the high-energy scale arises from quantum interference between electronic excitations across the Mott gap. Broad spectral features seen in photoemission in the normal state of the cuprates are argued to arise from high-energy slavery.

DOI
10.1103/physrevlett.93.267004

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We show that doped Mott insulators such as the copper-oxide superconductors are asymptotically slaved in that the quasiparticle weight Z near half-filling depends critically on the existence of the high-energy scale set by the upper Hubbard band. In particular, near half-filling, the following dichotomy arises: Z not equal to 0 when the high-energy scale is integrated out but Z=0 in the thermodynamic limit when it is retained. Slavery to the high-energy scale arises from quantum interference between electronic excitations across the Mott gap. Broad spectral features seen in photoemission in the normal state of the cuprates are argued to arise from high-energy slavery.
Abstract How a Mott insulator develops into a weakly coupled metal upon doping is a central question to understanding various emergent correlated phenomena. To analyze this evolution and its connection to the high-Tc cuprates, we study the single-particle spectrum for the doped Hubbard model using cluster perturbation theory on superclusters. Starting from extremely low doping, we identify a heavily renormalized quasiparticle dispersion that immediately develops across the Fermi level, and a weakening polaronic side band at higher binding energy. The quasiparticle spectral weight roughly grows at twice the rate of doping in the low doping regime, but this rate is halved at optimal doping. In the heavily doped regime, we find both strong electron-hole asymmetry and a persistent presence of Mott spectral features. Finally, we discuss the applicability of the single-band Hubbard model to describe the evolution of nodal spectra measured by angle-resolved photoemission spectroscopy (ARPES) on the single-layer cuprate La2−xSrxCuO4 (0 ≤ x ≤ 0.15). This work benchmarks the predictive power of the Hubbard model for electronic properties of high-Tc cuprates.
Though most fermionic Mott insulators order at low temperatures, ordering is ancillary to their insulating behavior. Our emphasis here is on disentangling ordering from the intrinsic strongly correlated physics of a doped half-filled band. To this end, we focus on the two-dimensional Hubbard model. Because the charge gap arises from on-site correlations, we have been refining the nonperturbative approach of Matsumoto and Mancini [Phys. Rev. B 55, 2095 (1997)] which incorporates local physics. Crucial to this method is a self-consistent two-site dynamical cluster expansion which builds in the nearest-neighbor energy scale J. At half-filling, we find that the spectral function possesses a gap of order U and is devoid of any coherent quasiparticle peaks although ordering or charge fractionalization are absent. At low temperatures, local antiferromagnetic correlations emerge. In the doped case, we find that the Fermi surface exceeds the Luttinger volume. The breakdown of Luttinger's theorem in the underdoped regime is traced both to the dynamically generated Mott gap as well to a nonvanishing of the imaginary part of the self-energy at the Fermi level. Spectral weight transfer across the Mott gap also emerges as a ubiquitous feature of a doped Mott insulator and suggests that high- and low-energy scales are inseparable. Additionally in the underdoped regime, we find that a pseudogap exists in the single-particle density of states as well as in the heat capacity. The pseudogap (which is set by the energy scale t2/U){t}^{2}/U)t2/U) is argued to be a ubiquitous feature of a lightly doped Mott state and simply represents the fact that hole transport involves double occupancy. In analogy with the Mott gap and antiferromagnetism, we propose that ordering may also accompany the formation of a pseudogap. We suggest a current pattern within a one-band model that preserves translational but breaks time-reversal symmetry along the canonical x and y axes but not along $x=\ifmmode\pm\else\textpm\fi{}y$ that is consistent with the experimental observations. Finally, we show that the Hall coefficient in a doped Mott insulator must change sign at a doping level x<1/3.x<1/3.x<1/3. The sign change is tied to a termination of strong correlation physics in the doped Mott state.
Since the discovery of half-filled cuprate to be a Mott insulator, the excitation spectra above the chemical potential for the unoccupied states has attracted much research attention. There were many theoretical works using different numerical techniques to study this problem, but many have reached different conclusions. One of the reasons is the lack of very detailed high-resolution experimental results for the theories to be compared with. Recently, the scanning tunneling spectroscopy [P. Cai et al., Nat. Phys. 12, 1047 (2016); C. Ye et al., Nat. Commun. 4, 1365 (2013)] on lightly doped Mott insulator with an antiferromagnetic order found the presence of in-gap states with energy of order half an eV above the chemical potential. The measured spectral properties with doping are not quite consistent with earlier theoretical works. Although the experiment has disorder and localization effect, but for the energy scale we will study here, a model without disorder is sufficed to illustrate the underlying physics. We perform a diagonalization method on top of the variational Monte Carlo calculation to study the evolution of antiferromagnetic Mott state with doped hole concentration in the Hubbard model. Our results found in-gap states that behave similarly with ones reported by STS. These in-gap states acquire a substantial amount of dynamical spectral weight transferred from the upper Hubbard band. The in-gap states move toward chemical potential with increasing spectral weight as doping increases. Our result also provides information about the energy scale of these in-gap states in relation with the Coulomb coupling strength UUU.
We show exactly that the only charged excitations that exist in the strong-coupling limit of the half-filled Hubbard model are gapped composite excitations generated by the dynamics of the charge 2e2e2e boson that appears upon explicit integration of the high-energy scale. At every momentum, such excitations have nonzero spectral weight at two distinct energy scales separated by the on-site repulsion UUU. The result is a gap in the spectrum for the composite excitations accompanied by a discontinuous vanishing of the density of states at the chemical potential when UUU exceeds the bandwidth. Consequently, we resolve the long-standing problem of the cause of the charge gap in a half-filled band in the absence of symmetry breaking.
The local density of states near dopants or impurities has recently been probed by scanning tunneling microscopy in both the parent and very lightly doped compounds of the high-Tc{T}_{c}Tc​ cuprate superconductors. We use a slave-rotor representation of the Hubbard model to compute the local density of states on impurities in a Mott insulator. Our calculation accounts for the following key features of the experimental observation: (i) positions and amplitudes of the in-gap spectral weights of a single impurity; (ii) the spectral weight transfer from the upper Hubbard band to the lower Hubbard band; (iii) the difference between the cases of single and multiple impurities. For multiple impurities, our study explains the complete suppression of spectral weight observed at precisely the Fermi energy and links this property to zeros of the underlying bulk Green's function of the Mott insulating phase.
We consider a single copper oxide plane with infinite Hubbard U on the copper sites and direct oxygen-oxygen and copper-oxygen overlaps as a model for high-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials. Using a slave-boson representation, we find a region of parameter space with a charge-transfer-type metal-insulator transition at zero doping, i.e, half-filling in a mean-field limit. Performing a 1/N expansion we calculate the photoemission and inverse-photoemission spectra near the transition for both the n-type and p-type high-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials using the sudden approximation.