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arXiv:1908.03450 · Physical review. B./Physical review. B

Bond particle theory for the pseudogap phase of underdoped cuprates

R. Eder

Published Aug 21, 2019• 4 citations
arXivHTMLPDF

Abstract

We present a theory for the lightly doped $t\text{\ensuremath{-}}J$ model that is of possible relevance for the normal state of underdoped cuprates. Starting from an arbitrary dimer covering of the plane, an exact representation of the $t\text{\ensuremath{-}}J$ Hamiltonian in terms of bond bosons and fermions can be derived. Since all dimer coverings must give identical results for observable quantities, we construct an approximate but translationally invariant Hamiltonian by averaging the bond particle Hamiltonian over all possible dimer coverings. Treating the resulting Hamiltonian in the mean-field approximation, we find Fermi pockets centered near $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ with a total area of $x/2$ (with $x$ the hole concentration) and a gapped spin-wave-like band of triplet excitations.

DOI
10.1103/physrevb.100.085133

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We present a theory for the lightly doped t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model that is of possible relevance for the normal state of underdoped cuprates. Starting from an arbitrary dimer covering of the plane, an exact representation of the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J Hamiltonian in terms of bond bosons and fermions can be derived. Since all dimer coverings must give identical results for observable quantities, we construct an approximate but translationally invariant Hamiltonian by averaging the bond particle Hamiltonian over all possible dimer coverings. Treating the resulting Hamiltonian in the mean-field approximation, we find Fermi pockets centered near (\ensuremathπ/2,\ensuremathπ/2)(\ensuremath{\pi}/2,\ensuremath{\pi}/2)(\ensuremathπ/2,\ensuremathπ/2) with a total area of x/2x/2x/2 (with xxx the hole concentration) and a gapped spin-wave-like band of triplet excitations.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping which respects an SU(2)\mathrm{SU}(2)SU(2) symmetry---a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain ddd-wave superconductor, spin gap, strange metal, and Fermi liquid phases. The spin gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The electron spectral function shows small Fermi pockets at low doping which continuously evolve into the large Fermi surface at high doping concentrations.
We present an exact ground state solution of a quantum dimer model introduced by Punk, Allais, and Sachdev [Quantum dimer model for the pseudogap metal, Proc. Natl. Acad. Sci. U.S.A. 112, 9552 (2015).PNASA60027-842410.1073/pnas.1512206112], which features ordinary bosonic spin-singlet dimers as well as fermionic dimers that can be viewed as bound states of spinons and holons in a hole-doped resonating valence bond liquid. Interestingly, this model captures several essential properties of the metallic pseudogap phase in high-T_{c} cuprate superconductors. We identify a line in parameter space where the exact ground state wave functions can be constructed at an arbitrary density of fermionic dimers. At this exactly solvable line the ground state has a huge degeneracy, which can be interpreted as a flat band of fermionic excitations. Perturbing around the exactly solvable line, this degeneracy is lifted and the ground state is a fractionalized Fermi liquid with a small pocket Fermi surface in the low doping limit.
Using continuity, we derive a renormalized Hamiltonian from the parent $t\text{\ensuremath{-}}J$ model to describe the properties of underdoped cuprates. The theory is constrained to agree with the behavior at half filling, which is well described by the Arovas-Auerbach valence bond state in which bosonic spinons are paired into singlets. Spinon states evolve continuously into the doped region preserving their symmetry. We assume that moving holes rapidly destroy magnetic order, which leads to a gap in the spinon spectrum and strongly renormalizes the theory. The spin gap leads to two different types hopping terms for renormalized holes. In one, a fermionic holon hops within the same sublattice accompanied by a singlet backflow, giving rise to a non-Fermi-liquid normal state with novel properties. Spinon singlets condense below a pseudogap temperature ${T}^{\ensuremath{\ast}}$ (<<< spin gap temperature T0{T}^{0}T0), which allows holons to propagate coherently, forming a spinless Fermi liquid, but without an observable holon Fermi surface. Above ${T}^{\ensuremath{\ast}}$, holons are localized. This is the so-called strange metal phase, which is actually a new type of insulator since its resistivity would be infinite at T=0T=0T=0. In the second term a pair of holons belonging to opposite sublattices hop, accompanied by a singlet backflow. In the presence of the singlet condensate holon pairs condense, leading to ddd-wave superconductivity; the symmetry is primarily determined by the symmetry of the valence bond state at half filling. The metal and the superconductor preserve the two-sublattice character of the valence bond state. A careful examination of the nuclear magnetic resonance, tunneling, and transport data shows that the predictions of the theory is consistent with experimental results. Remarkably, the existence of the spin gap provides a natural explanation for the phenomenon of two dimensionality of the normal state in the presence of interplane hopping. The marked asymmetry between hole-doped and electron-doped cuprates is also easily explained.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping that respects an SU(2) symmetry: a symmetry previously known to be important at half filling. The mean-field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain ddd-wave superconductor, spin-gap, strange metal, and Fermi-liquid phases. The spin-gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping that continuously evolve into the large Fermi surface at high-doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low-energy effective theory for the low-lying fluctuations is derived and additional lying modes [which were overlooked in the U(1) theory] are identified.
We outline the basic ideas involved in a recently proposed derivation of a gauge theory for underdoped cuprates in the "spin-gap phase", performed essentially step by step starting from the t-J model, considered as a model Hamiltonian for the CuO_2 layers. The basic tool is the U(1)XSU(2) Chern-Simons bosonization, to which it is dedicated a somewhat detailed discussion. The basic output is a "spin-gap" not vanishing in any direction and an antiferromagnetic correlation length proportional to the inverse square root of doping concentration, in agreement with data deduced from the neutron experiments. The model also exhibits a small half-pocket Fermi surface around (π/2, π/2) and a linear in temperature dependence of in-plane resistivity in certain temperature range.
We outline the basic ideas involved in a recently proposed [17] derivation of a gauge theory for underdoped cuprates in the “spin gap phase”, performed essentially step by step starting from the t — J model, considered as a model Hamiltonian for the CuO2 layers. The basic tool is the U(1) x SU(2) Chern-Simons bosonization, to which it is dedicated a somewhat detailed discussion. The basic output is a “spingap” not vanishing in any direction and an antiferromagnetic correlation length proportional to the inverse square root of doping concentration, in agreement with data deduced from the neutron experiments. The model also exhibits a small half-pocket Fermi surface around (±π/2, ±π/2) and a linear in temperature dependence of in-plane resistivity in certain temperature range.