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arXiv:2308.03862 · Physical review. B./Physical review. B

Hall coefficient and resistivity in the doped bilayer Hubbard model

Yin Shi, Jonathan Schirmer, Long‐Qing Chen

Published Feb 7, 2024• 2 citations
arXivHTMLPDF

Abstract

Abstract Finding and understanding non-Fermi liquid transport behaviors are at the core of condensed matter physics. Most of the existing studies were devoted to the monolayer Hubbard model, which is the simplest model that captures essential features of high-temperature superconductivity. Here we discover a new type of non-Fermi liquid behavior emergent in the hole-doped bilayer Hubbard model, using dynamical mean-field theory with a full consideration of the short-range interlayer electron correlation. We find that at low temperatures, the Hall coefficient has a strong nonmonotonic dependence on temperature, leading to a double or quadruple reversal of its sign depending on the doping level. At the same time, the resistivity exhibits two plateaus rather than linearity in its temperature dependence. We show that these intriguing transport behaviors stem from the formation of coherent interlayer singlets, which scatter off gapped collective modes arising from short-range interlayer antiferromagnetic fluctuations.

DOI
10.1103/physrevb.109.075114

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Abstract Finding and understanding non-Fermi liquid transport behaviors are at the core of condensed matter physics. Most of the existing studies were devoted to the monolayer Hubbard model, which is the simplest model that captures essential features of high-temperature superconductivity. Here we discover a new type of non-Fermi liquid behavior emergent in the hole-doped bilayer Hubbard model, using dynamical mean-field theory with a full consideration of the short-range interlayer electron correlation. We find that at low temperatures, the Hall coefficient has a strong nonmonotonic dependence on temperature, leading to a double or quadruple reversal of its sign depending on the doping level. At the same time, the resistivity exhibits two plateaus rather than linearity in its temperature dependence. We show that these intriguing transport behaviors stem from the formation of coherent interlayer singlets, which scatter off gapped collective modes arising from short-range interlayer antiferromagnetic fluctuations.
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.
Low energy properties of the metallic state of the two-dimensional t - J model are presented for second neighbor hopping with hole-doping ( ) and electron-doping ( ), with various superexchange energy J . We use a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory . These equations reproduce the known low energies features of the large U Hubbard model in infinite dimensions. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity, Hall number and cotangent Hall angle. The spectral features display high thermal sensitivity at modest T for density , implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. The cotangent Hall angle exhibits a T 2 behavior at low T , followed by an interesting kink at higher T . The Hall number exhibits strong renormalization due to correlations. Flipping the sign of changes the curvature of the resistivity versus T curves between convex and concave. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.
A phase diagram of two Mott-Hubbard planes interacting with a short-range Coulomb repulsion is presented. Considering the case of equal amount of doping by holes in one layer as electrons in the other, a holon-doublon interlayer exciton formation is shown to be a natural consequence of Coulomb attraction. Quasiparticle spectrum is gapped and incoherent below a critical doping ${\ensuremath{\delta}}_{c}$ due to the formation of excitons. A spin-liquid-insulator (SLI) phase is thus realized without the lattice frustration. The critical value ${\ensuremath{\delta}}_{c}$ sensitively depends on the interlayer interaction strength. In the $t\text{\ensuremath{-}}J$ model description of each layer with the ddd-wave pairing, ${\ensuremath{\delta}}_{c}$ marks the crossover between SLI and ddd-wave superconductor. The SLI phase, despite being nonsuperconducting and charge gapped, still shows an electromagnetic response similar to that of a superfluid due to the exciton transport. Including antiferromagnetic order in the $t\text{\ensuremath{-}}J$ model introduces magnetically ordered phases at low doping and pushes the spin-liquid phase to a larger interlayer interaction strength and higher doping concentrations.
We investigate the highly incoherent regime of hole-doped two-dimensional Mott-Hubbard insulators at moderately small doping $\ensuremath{\delta}$ and temperatures $\ensuremath{\gtrsim}0.1J,$ where J is the exchange coupling. Within an extended dynamical mean-field theory of the $t\ensuremath{-}J$ model and a generalized noncrossing approximation we calculate the single-particle spectral function, the dynamical susceptibility, and thermodynamic and transport quantities. Short-ranged antiferromagnetic fluctuations lead to strongly incoherent single-particle dynamics, large entropy, and large electrical resistivity. At low doping a pseudogap is found to open up in both the single-particle and spin excitation spectra, leading to a decrease in entropy and resistivity. The Hall coefficient changes sign to positive values upon lowering the doping level and increases inversely proportional to $\ensuremath{\delta}.$
When a van Hove singularity is located in the vicinity of the Fermi level, the electronic scattering rate acquires a nonanalytic contribution. This invalidates basic assumptions of Fermi liquid theory and within treatments based on perturbation theory leads to a non-Fermi liquid self-energy and transport properties. Such anomalies are shown to also occur in the strongly correlated metallic state within dynamical mean-field theory. We consider the Hubbard model on a two-dimensional square lattice with nearest- and next-nearest-neighbor hoppings within the single-site dynamical mean-field theory. At temperatures on the order of the low-energy scale T0{T}_{0}T0​ an unusual maximum emerges in the imaginary part of the self-energy which is renormalized toward the Fermi level for finite doping. At zero temperature this double-well structure is suppressed but an anomalous energy dependence of the self-energy remains. For the frustrated Hubbard model on the square lattice with next-nearest-neighbor hopping, the presence of the van Hove singularity changes the asymptotic low-temperature behavior of the resistivity from a Fermi liquid to non-Fermi liquid dependency as function of doping. The results of this work are discussed regarding their relevance for high-temperature cuprate superconductors.
A path-integral field-theoretic derivation of electromagnetic linear response for the two-dimensional Hubbard model is given. We find, remarkably, that changes in the Fermi-surface topology associated with incommensurate planar spin-density-wave saddle points induce a change in sign of the Hall coefficient at dopings ${\mathrm{\ensuremath{\delta}}}_{\mathit{H}}$=0.02--0.5 for U/t=2--10. The change in sign is not affected by short-range magnetic domains. We delinate from first principles an anomalous temperature dependence of the Hall carrier density at dopings close to ${\mathrm{\ensuremath{\delta}}}_{\mathit{H}}$. An additional anisotropic component to the usual dc conductivity is nonvanishing for certain types of spirals. The paper extends the Bloch-Boltzmann theory to the case of untraditional Fermi liquids where the damping of the quasiparticles is \ensuremath{\Gamma}(\ensuremath{\epsilon})\ensuremath{\sim}max(kB{\mathit{k}}_{\mathit{B}}kB​T,\ensuremath{\epsilon}).