Quantum dimer model for the pseudogap metal

Abstract

We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, p. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin S = 1=2, charge +e fermionic dimers. The model realizes a "fractionalized Fermi liquid" with no symmetry breaking and small hole pocket Fermi surfaces enclosing a total area determined by p. Exact diagonalization, on lattices of sizes up to 8 × 8, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments.T he recent experimental progress in determining the phase diagram of the hole-doped Cu-based high-temperature superconductors has highlighted the unusual and remarkable properties of the pseudogap (PG) metal (Fig. 1). A characterizing feature of this phase is a depletion of the electronic density of states at the Fermi energy (1, 2), anisotropically distributed in momentum space, that persists up to room temperature.Attempts have been made to explain the pseudogap metal using thermally fluctuating order parameters; we argue below that such approaches are difficult to reconcile with recent transport experiments. Instead, we introduce a new microscopic model that realizes an alternative perspective (3), in which the pseudogap metal is a finite temperature (T) realization of an interesting quantum state: the fractionalized Fermi liquid (FL*). We show that our model is consistent with key features of the pseudogap metal observed by both transport and spectroscopic probes.The crucial observation that motivates our work is the tension between photoemission and transport experiments. In the cuprates, the hole density p is conventionally measured relative to that of the insulating antiferromagnet (AF), which has one electron per site in the Cu d band. Therefore, the hole density relative to a filled Cu band, with two electrons per site, is actually 1 + p. In fact, photoemission experiments at large hole doping observe a Fermi surface enclosing an area determined by the hole density 1 + p (4), in agreement with the Luttinger relation. In contrast, in the pseudogap metal, a mysterious "Fermi arc" spectrum is observed (5-7), with no clear evidence of closed Fermi surfaces. However, despite this unusual spectroscopic feature, transport measurements report vanilla Fermi liquid properties, but associated with carrier density p, rather than 1 + p. The carrier density of p was indicated directly in Hall measurements (8), whereas other early experiments indicated suppression of the Drude weight (9-11). Although the latter could be compatible with a carrier density of 1 + p but with a suppressed kinetic term, the Hall measurements indicate the suppression of the Drude weight is more likely due to a small carrier density. Two recent experiments displaying Fermi liquid behavior at low p are especially notable: (i) the quasiparticle lifetime τðω, TÞ determined from optical conductivity experiments (12) has the Fermi liquidlike dependence 1=τ ∝ ðZωÞ 2 + ðcπk B TÞ 2 , with c an order unity constan...

d-wave superconductivity in boson+fermion dimer models

“…We presented a slave particle formulation of a mixed boson+fermion quantum dimer model recently proposed in the context of high-T c superconductors [10][11][12]. A key finding of this work is that substantial progress can be made using a mean-field analysis that simply assumes a translational and rotational invariant (liquid) state for the bosonic component.…”

“…Recently QDMs have been revisited as models of hightemperature superconductivity [10][11][12]. This was motivated by the need to reconcile transport experiments [13][14][15][16] and photoemission data [17][18][19] in the underdoped region of cuprate superconductors: while photoemission data show Fermi arcs enclosing an area 1 + p (with p being the doping), transport measurements indicate plain Fermi-liquid properties consistent with an area p. In order to resolve this issue and produce a Fermi liquid which encloses an area p, the authors of Refs.…”

“…This was motivated by the need to reconcile transport experiments [13][14][15][16] and photoemission data [17][18][19] in the underdoped region of cuprate superconductors: while photoemission data show Fermi arcs enclosing an area 1 + p (with p being the doping), transport measurements indicate plain Fermi-liquid properties consistent with an area p. In order to resolve this issue and produce a Fermi liquid which encloses an area p, the authors of Refs. [10][11][12] introduced a model for the pseudogap region of the cuprate superconductors which consists of two types of dimers: one spinless bosonic dimer -representing a valence bond between two neighboring spins -and one spin 1/2 fermionic dimer representing a hole delocalized between two sites. Fig.…”

Fractionalized Fermi liquid with bosonic chargons as a candidate for the pseudogap metal

“…As described in Ref. [12], a quantitative connection between the t-J model and a particular dimer model of the Z 2 FL* can be made in certain limiting regimes. In the present paper we work with a more general model of the plain vanilla Z 2 -FL* state, where the parameters are fixed by demanding that the shapes of our Fermi surfaces are consistent with spectroscopic data.…”

Holon Wigner Crystal in a Lightly Doped Kagome Quantum Spin Liquid

“…[1][2][3][4][5][6][7] It has also been proposed that a doped QSL might form an exotic topologically ordered Fermi liquid state (known as an FL * state) [8,9], or various other topologically ordered versions of other familiar phases. [10] More broadly, it has been suggested that a host of behaviors of highly correlated electronic systems can be best understood from the perspective of doped spin-liquids.…”