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Physical review. B, Condensed matter

Strongly correlated two-dimensional electrons in the overdoped limit

J. P. Rodriguez, Pascal Lederer

Published Dec 1, 1993• 5 citations
Publisher

Abstract

A square-lattice gauge-theory model for the holon liquid existing in the unconventional metallic phases of strongly interacting two-dimensional electron liquids is introduced. The phase of the holon order parameter couples in a gauge-invariant way to a statistical gauge field, which arises from strong-interaction physics. We find that the superfluid transition that exists in the absence of statistical gauge-field excitations in the holon liquid turns into a crossover phenomenon in the presence of such fluctuations. The corresponding high-temperature phase shows a T-linear resistance, while the low-temperature phase exhibits a ${\mathit{T}}^{2}$ dependence for the resistance. The crossover temperature scale ${\mathit{T}}_{\mathit{c}0}$ vanishes, however, in the limit of maximum statistical fluctuations. While we find that statistical gauge-field excitations are strictly gapless, the residue of the pole corresponding to such excitations becomes exponentially small at temperatures small in comparison to ${\mathit{T}}_{\mathit{c}0}$.

DOI
10.1103/physrevb.48.16051

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A square-lattice gauge-theory model for the holon liquid existing in the unconventional metallic phases of strongly interacting two-dimensional electron liquids is introduced. The phase of the holon order parameter couples in a gauge-invariant way to a statistical gauge field, which arises from strong-interaction physics. We find that the superfluid transition that exists in the absence of statistical gauge-field excitations in the holon liquid turns into a crossover phenomenon in the presence of such fluctuations. The corresponding high-temperature phase shows a T-linear resistance, while the low-temperature phase exhibits a T2{\mathit{T}}^{2}T2 dependence for the resistance. The crossover temperature scale Tc0{\mathit{T}}_{\mathit{c}0}Tc0​ vanishes, however, in the limit of maximum statistical fluctuations. While we find that statistical gauge-field excitations are strictly gapless, the residue of the pole corresponding to such excitations becomes exponentially small at temperatures small in comparison to Tc0{\mathit{T}}_{\mathit{c}0}Tc0​.
Two unrelated problems can be reduced to a model of a Bose gas interacting with a gauge field: (i) the effect of thermal fluctuations on a system of vortices in bulk superconductors in fields Hc1{\mathit{H}}_{\mathit{c}1}Hc1​\ensuremath{\ll}H\ensuremath{\ll}Hc2{\mathit{H}}_{\mathit{c}2}Hc2​, and (ii) charged, spinless excitations in two-dimensional (2D) strongly correlated electron systems. Both problems are important for the theory of high-temperature superconductors. We study this model in three regimes: at finite temperatures, assuming that the gauge field is purely transverse; at T=0, for the purely static (2D Coulomb) interaction; and at T=0, for a weak Coulomb interaction and a strong transverse one. Transverse interactions suppress the temperature of the superfluid transition significantly. A sufficiently strong transvese interaction is shown to produce a phase separation as the temperature decreases (in the absence of Coulomb repulsion). If there is Coulomb repulsion, the ground state does not have off-diagonal long-range order but the superfluid density is not zero unless the Coulomb constant exceeds a critical value. Sufficiently strong coupling to the transverse field destroys superfluidity as well. In the normal state formed at large couplings, the translational invariance is intact. We propose a bosonic ground state that is not superfluid at T=0. We discuss the implications of these results both for vortex liquids and strongly correlated electron systems.
Superconductivity in the strongly correlated electronic systems described by the Hubbard model for slightly less than half-filled band is shown to arise from the condensation of charge + e holons which are bosons. The holon effective mass is found to be very close to that of the band electrons and they have a strong nearest neighbour repulsion induced by the spin fluctuations. They interact with an U(1) part of the collective SU(2) gauge field (named S-gauge field) of the spin system. This results in spontaneous symmetry breaking of the holon field and the appearance of the Anderson-Higgs phenomenon. The interesting possibility of the SU(2) gauge field-spinon coupled system retaining some gapless excitation spectrum inspite of the spontaneous symmetry breaking in the holon field is pointed out.
Recent advances in fluorescence imaging have enabled direct measurements of doublon, singlon, and holon correlation functions in cold-atom experiments. We demonstrate that these correlators provide a powerful probe of the extended crossover from metallic to insulating behavior at intermediate and high temperatures. To this end, we carry out determinantal quantum Monte Carlo simulations of the two-dimensional repulsive Fermi-Hubbard model on a square lattice, varying doping, interaction strength UUU, and temperature TTT. Our results reveal clear signatures of a crossover from the metallic regime at small UUU to the Mott insulating regime at large UUU. Specifically, we note the following: (1) At half-filling, we distinguish three regimes (metallic, non-Fermi-liquid, and Mott insulating) by analyzing the temperature dependence of the thermodynamic density of states $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\kappa}}=\frac{\ensuremath{\partial}n}{\ensuremath{\partial}\ensuremath{\mu}}$ in comparison with the low-energy single-particle density of states $N(\ensuremath{\omega})$. (2) At finite doping, although $N(\ensuremath{\omega})$ remains gapless, a sign change in $\frac{\ensuremath{\partial}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\kappa}}}{\ensuremath{\partial}T}$ marks a transition from insulating to metallic behavior at a critical density ncr(U,T){n}_{\text{cr}}(U,T)ncr​(U,T). (3) These crossovers can also be tracked using experimentally accessible correlators, such as density-density, moment-moment, and doublon-holon correlations, providing valuable diagnostics in settings where direct spectral information is difficult to obtain.
A phenomenological description for confinement of fractionalized excitations is proposed in the gauge theory approach for doped Mott insulators. Introducing the Polyakov-loop parameter into an SU(2) gauge theory for the t-J model, we show that electron excitations emerge below the so-called coherence temperature, resulting from confinement of spinons and holons via the formation of the Polyakov loop. Remarkably, such confined electrons turn out to exhibit non-Fermi liquid physics without quantum criticality, yielding the electric resistivity in quantitative agreement with experimental data. The Higgs phase is not allowed due to confinement, suggesting a possible novel mechanism of superconductivity in the strong coupling approach.
We introduce and analyze a metallic phase of two-dimensional (2D)(2\mathrm{D})(2D) electrons, the roton Fermi liquid (RFL), which, in contrast to the Landau--Fermi liquid, supports both gapless fermionic and bosonic quasiparticle excitations. The RFL is accessed using a reformulation of 2D2\mathrm{D}2D electrons consisting of fermionic quasiparticles and hc∕2ehc∕2ehc∕2e vortices interacting with a mutual long-ranged statistical interaction. In the presence of a strong vortex-antivortex (i.e., roton) hopping term, the RFL phase emerges as an exotic yet eminently tractable quantum ground state. The RFL phase exhibits a ``Bose surface'' of gapless roton excitations describing transverse current fluctuations, has off-diagonal quasi-long-ranged order at zero temperature (T=0)(T=0)(T=0), but is not superconducting, having zero superfluid density and no Meissner effect. The electrical resistance vanishes as $T\ensuremath{\rightarrow}0$ with a power of temperature (and frequency), $R(T)\ensuremath{\sim}{T}^{\ensuremath{\gamma}}$ (with $\ensuremath{\gamma}>1$), independent of the impurity concentration. The RFL phase also has a full Fermi surface of quasiparticle excitations just as in a Landau--Fermi liquid. Electrons can, however, scatter anomalously from rotonic ``current fluctuations'' and ``superconducting fluctuations.'' Current fluctuations induced by the gapless rotons scatter anomalously only at ``hot spots'' on the Fermi surface (with tangents parallel to the crystalline axes), while superconducting fluctuations give rise to an anomalous lifetime over the entire Fermi surface except near the (incipient) nodal points (``cold spots''). Fermionic quasiparticles dominate the Hall electrical transport. We also find three dominant instabilities of the RFL phase: an instability to a conventional Fermi-liquid phase driven by vortex condensation, a BCS-type instability toward fermion pairing, and a (nonpairing) superconducting instability. Precisely at the instability into the Fermi-liquid state, the exponent $\ensuremath{\gamma}$ saturates the bound, $\ensuremath{\gamma}=1$, so that $R(T)\ensuremath{\sim}T$. Upon entering the superconducting state the rotons are gapped out, and the anomalous quasiparticle scattering is strongly suppressed. We discuss how the RFL phase might underlie the strange metallic state of the cuprates near optimal doping, and outline a phenomenological picture to accommodate the underdoped pseudogap regime and the overdoped Landau--Fermi-liquid phase.
We develop a description of a quantum liquid phase of interacting bosons confined in two dimensions that possesses relative ddd-wave two-body correlations. We refer to this stable quantum phase as a ddd-wave Bose liquid (DBL). The DBL has no broken symmetries, supports gapless boson excitations that reside on ``Bose surfaces'' in momentum space, and exhibits power-law correlation functions characterized by a manifold of continuously variable exponents. While the DBL can be constructed for bosons moving in the two-dimensional continuum, the state only respects the point group symmetries of the square lattice. On the square lattice, the DBL respects all symmetries and does not require a particular lattice filling. However, lattice effects do allow for the possibility of a second distinct phase, a quasilocal variant we refer to as a ddd-wave local Bose liquid (DLBL). Remarkably, the DLBL has short-range boson correlations and hence no Bose surfaces, despite sharing gapless excitations and other critical signatures with the DBL. Moreover, both phases are metals with a resistance that vanishes as a power of the temperature. We establish these results by constructing a class of many-particle wave functions for the DBL, which are time reversal invariant analogs of Laughlin's quantum Hall wave function for bosons in a half-filled Landau level. A gauge theory formulation leads to a simple mean field theory, and a suitable NNN-flavor generalization enables incorporation of gauge field fluctuations to deduce the properties of the DBL/DLBL in a controlled and systematic fashion. Various equal-time correlation functions thereby obtained are in qualitative accord with the properties inferred from the variational wave functions. We also identify a promising microscopic Hamiltonian that might manifest the DBL or DLBL, and perform a variational energetics study comparing other competing phases, including the superfluid. We suggest how the ddd-wave Bose liquid wave function can be suitably generalized to describe an itinerant non-Fermi-liquid phase of electrons on the square lattice with a no-double-occupancy constraint, a ddd-wave metal phase.