Charged domain-wall dynamics in doped antiferromagnets and spin fluctuations in cuprate superconductors

Abstract

Evidence is accumulating that the electron liquid in the cuprate superconductors is characterized by manyhole correlations of the charged magnetic domain-wall type. Here we focus on the strong-coupling limit where all holes are bound to domain walls. We assert that at high temperatures a classical domain-wall fluid is realized and show that the dynamics of such a fluid is characterized by spatial and temporal crossover scales set by temperature itself. The fundamental parameters of this fluid are such that the domain-wall motions dominate the low-frequency spin fluctuations and we derive predictions for the behavior of the dynamical magnetic susceptibility. We argue that a crossover occurs from a high-temperature classical to a lowtemperature quantum regime, in direct analogy with helium. We discuss some general characteristics of the domain-wall quantum liquid, realized at low temperatures. I. DOMAIN WALLS IN DOPED ANTIFERROMAGNETSSince the discovery of the cuprate superconductors the issue of hole doping in two-dimensional antiferromagnetic insulators has received considerable attention. Especially in the regime of low to moderate doping a number of unusual properties emerge. Here we want to suggest an interpretation of these phenomena in this regime in terms of holes bound to domain walls, separating antiferromagnetic regions -see Fig. 1. Fluctuations prevent these domain walls from freezing into an ordered state and we thus get a spatially and temporally disordered, liquidlike phase of the type sketched in Fig. 2. We associate the dynamics of this liquid state with the anomalous magnetic fluctuations of the cuprates.We are motivated in part by recent studies of the t-J model revealing tendencies towards the formation of such an inhomogeneous state over a large range of parameters.1 It was found, by exact diagonalization of small systems ͑18 -20 sites͒ with four holes, that upon increasing J/t a phase with domain-wall correlations appears before phase separation occurs.2 Earlier, these domain walls were found to be the classical ͑Hartree-Fock͒ saddle points of Hubbard models at finite doping, 3,4 surviving in more sophisticated variational approaches such as the Gutzwiller ansatz 5 and in fixed-node quantum Monte Carlo. 6 We also mention that long-range Coulomb interactions are not as hazardous to this type of ordering as one would expect at first sight. It was recently shown that the mere electrostatics problem, combined with short-range attractive forces already favors the formation of striped charged phases. 7Also some recent experimental developments give support to these domain-wall ideas. As we shall discuss later in more detail, these domain walls have recently been directly observed in doped La 2 NiO 4 , 8 which is a close relative of the cuprates. 9 Indications for the existence of domain walls in lightly doped La 2 CuO 4 were brought forward in the context of magnetic-susceptibility measurements.10 Finally, domain walls were proposed as a possible explanation for the Korringa behavior of the oxygen ...

Singular or non-Fermi liquids

“…An alternative idea from the microscopic characterization of these materials as doped Hubbard models is that a dilute concentration of holes in the Hubbard model is likely to phase separate or form ordered one-dimensional charge-density wave=spin-density wave structures [298,299,86]. There exists both empirical [257] and computational [288] support for this idea at least for a very dilute concentration of holes.…”

Duality in 2+1D quantum elasticity: superconductivity and quantum nematic order

“…The stripe phase can be seen as a higher order commensurate state with the charges stripes to be interpreted as the discommensurations forming a lattice [43]. A case can be made that due to fluctuations the effects of the lattice potential can be much weakened so that at long wavelength the stripe phase might closely approach an effective Gallilean invariance [24,44]. If this is the case, dislocations might become cheap as compared to interstitials, and the conditions might be right for the emergence of quantum nematics.…”

Stripe fractionalization: the quantum spin nematic and the Abrikosov lattice

“…1. On a side, this interpretation actually offers a simple interpretation for the observation that this gap disappears above the superconducting T c : when the phase order disappears the charge fluctuations become relaxational and there is no longer a characteristic charge fluctuation scale protecting the gauge invariance dynamically [10,11], although it might be still around in the statics [12]. In order to nail down the spin nematic one would like to see the characteristic behavior associated with spin waves in the Raman response (intensity $ w 3 ) at energies less than 5 meV where the neutrons seem to indicate there is nothing.…”