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arXiv:0709.0902

3/2-Fermi liquid: the secret of high-Tc cuprates

G. Baskaran

Published Sep 6, 2007• 6 citations
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Abstract

Electrical and magnetic properties of underdoped cuprates in the spin gap phase, a precursor to high Tc superconducting state, is riddled with puzzles. We propose a novel reference state to study this phase, where each hole dopant adds one real holon and one real spinon, with Haldane exclusion statistics $g_{\rm h} =1$ and $g_{\rm s} = {1/2}$, to a fairly inert (pseudo gaped) spin liquid vacuum, resulting in a low density spin-charge liquid. Spins and charges interact and form a novel collective state, a \textit{3/2-Fermi liquid}. A holon pairs with a spinon; this hole like fermion composite carries charge +e and a spin-\hlf moment and novel exclusion statistics $g_{\rm hole} = {3/2}$. We explain an anomalous expansion of Fermi sea area by 3/2, seen in recent quantum oscillation experiments at two different dopings.

DOI
10.48550/arxiv.0709.0902

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Electrical and magnetic properties of underdoped cuprates in the spin gap phase, a precursor to high Tc superconducting state, is riddled with puzzles. We propose a novel reference state to study this phase, where each hole dopant adds one real holon and one real spinon, with Haldane exclusion statistics gh=1g_{\rm h} =1gh​=1 and gs=1/2g_{\rm s} = {1/2}gs​=1/2, to a fairly inert (pseudo gaped) spin liquid vacuum, resulting in a low density spin-charge liquid. Spins and charges interact and form a novel collective state, a \textit{3/2-Fermi liquid}. A holon pairs with a spinon; this hole like fermion composite carries charge +e and a spin-\hlf moment and novel exclusion statistics ghole=3/2g_{\rm hole} = {3/2}ghole​=3/2. We explain an anomalous expansion of Fermi sea area by 3/2, seen in recent quantum oscillation experiments at two different dopings.
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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.
A possibility of holon (boson) pair condensation is explored for hole-doped high-Tc{T}_{c}Tc​ cuprates, by using the U(1)U(1)U(1) slave-boson representation of the $t\ensuremath{-}J$ Hamiltonian with the inclusion of hole-hole repulsion. A phase diagram of the hole doped high-Tc{T}_{c}Tc​ cuprates is deduced by allowing both the holon pairing and spinon pairing channels. It is shown that the spin gap size remains nearly unchanged below the holon pair condensation temperature. We find that the s-wave holon pairing under the condition of d-wave spin singlet pairing is preferred, thus allowing d-wave hole pairing.
The Chern-Simons bosonization with $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ gauge field is applied to the two-dimensional $t\ensuremath{-}J$ model in the limit $t\ensuremath{\gg}J,$ to study the normal-state properties of underdoped cuprate superconductors. We prove the existence of an upper bound on the partition function for holons in a spinon background, and we find the optimal spinon configuration saturating the upper bound on average---a coexisting flux phase and s+ids+ids+id-like resonating-valence-bond state. After neglecting the feedback of holon fluctuations on the U(1) field B and spinon fluctuations on the SU(2) field VVV, the holon field is a fermion and the spinon field is a hard-core boson. Within this approximation we show that the B field produces a \ensuremath{\pi} flux phase for the holons, converting them into Dirac-like fermions, while the VVV field, taking into account the feedback of holons produces a gap for the spinons vanishing in the zero-doping limit. The nonlinear-\ensuremath{\sigma} model with a mass term describes the crossover from the short-ranged antiferromagnetic (AF) state in doped samples to long-range AF order in reference compounds. Moreover, we derive a low-energy effective action in terms of spinons, holons and a self-generated U(1) gauge field. Neglecting the gauge fluctuations, the holons are described by the Fermi-liquid theory with a Fermi surface consisting of four ``half-pockets'' centered at (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) and one reproduces the results for the electron spectral function obtained in the mean-field approximation, in agreement with the photoemission data on underdoped cuprates. The gauge fluctuations are not confining due to coupling to holons, but nevertheless yield an attractive interaction between spinons and holons leading to a bound state with electron quantum numbers. The renormalization effects due to gauge fluctuations give rise to non-Fermi-liquid behavior for the composite electron, in certain temperature range showing the linear in T resistivity. This formalism provides a new interpretation of the spin gap in the underdoped superconductors (mainly due to the short-ranged AF order) and predicts that the minimal gap for the physical electron is proportional to the square root of the doping concentration. Therefore the gap does not vanish in any direction. All these predictions can be checked explicitly in experiment.
Spin-charge split pairing in underdoped cuprate superconductors: support from low-TTT specific heat
We calculate the specific heat of a weakly interacting dilute system of bosons on a lattice and show that it is consistent with the measured electronic specific heat in the superconducting state of underdoped cuprates with boson concentration ρ∼x/2ρ\sim x/2ρ∼x/2, where xxx is the hole (dopant) concentration. As usual, the T3T^3T3 term is due to Goldstone phonons. The zero-point energy, through its dependence on the condensate density ρ0(T)ρ_0(T)ρ0​(T), accounts for the anomalous TTT-linear term. These results support the split-pairing mechanism, in which spinons (pure spin) are paired at T∗T^*T∗ and holons (pure charge) form real-space pairs at Tp<T∗T_p < T^*Tp​<T∗, creating a gauge-coupled physical pair of charge +2e+2e+2e and concentration x/2x/2x/2 which Bose condenses below TcT_cTc​, accounting for the observed phases.
The complex interplay between charge and spin dynamics lies at the heart of strongly correlated quantum materials, and it is a fundamental topic in basic research with far-reaching technological perspectives. We explore in this paper the dynamics of holes in a single-band, extended t - J model where the background spins form a Z 2 quantum spin liquid. Using a field theory approach based on a parton construction, we show that while the electrons for most momenta fractionalize into uncorrelated charge-carrying holons and spin-carrying spinons as generally expected for a quantum spin liquid, the spinon-holon scattering cross section diverges for certain momenta, signaling strong correlations. By deriving an effective low-energy Hamiltonian describing this dynamics, we demonstrate that these divergences are due to the formation of long-lived spinon-holon bound states. Since the wave function of these bound states is localized over a few lattice sites, they correspond to well-defined fermions with the same charge and spin as the underlying electrons. We then show that quantum gas microscopy with atoms in optical lattices provides an excellent platform for verifying and probing the internal spatial structure of these emerging fermions. The fermions will furthermore show up as clear quasiparticle peaks in angle-resolved photoemission spectroscopy with an intensity determined by their internal structure. For a nonzero hole concentration, the fermions form hole pockets with qualitatively the same location, shape, and intensity variation in the Brillouin zone as the so-called Fermi arcs observed in the pseudogap phase. Such agreement is remarkable since the Fermi arcs arise from the delicate interplay between the symmetry of the quantum spin liquid and the internal structure of the emerging fermions in a minimal single-band model with no extra degrees of freedom added. Our results, therefore, provide a microscopic mechanism for the conjectured fractionalized Fermi liquid and open up new pathways for exploring the pseudogap phase and high-temperature superconductivity as arising from a quantum spin liquid.