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arXiv:cond-mat/9804300 · Physical review. B, Condensed matter

Metallic stripes: Separation of spin, charge, and string fluctuation

Jan Zaanen, Osman Y. Osman, Wim van Saarloos

Published Nov 1, 1998• 33 citations
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Abstract

Inspired by the cuprate stripes, we consider the problem of a one-dimensional metal living on a delocalized trajectory in two dimensional space: the metallic lattice string. A model is constructed with maximal coupling between longitudinal and transversal charge motions, which nevertheless renormalizes into a minimal generalization of the Luttinger liquid: an independent set of string modes has to be added to the long-wavelength theory, with a dynamics governed by the quantum sine-Gordon model.

DOI
10.1103/physrevb.58.r11868

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Inspired by the cuprate stripes, we consider the problem of a one-dimensional metal living on a delocalized trajectory in two dimensional space: the metallic lattice string. A model is constructed with maximal coupling between longitudinal and transversal charge motions, which nevertheless renormalizes into a minimal generalization of the Luttinger liquid: an independent set of string modes has to be added to the long-wavelength theory, with a dynamics governed by the quantum sine-Gordon model.
Recently, experimental evidence has been accumulating that the doped holes in the high-Tc{T}_{c}Tc​ cuprate superconductors form domain walls separating antiferromagnetic domains. These so-called stripes are linelike objects and if these persist in the superconducting state, high-Tc{T}_{c}Tc​ superconductivity is related to a quantum string liquid. In this paper the problem of a single quantum meandering string on a lattice is considered. A kink model is introduced for the string dynamics, which allows us to analyze lattice commensuration aspects. Building on earlier work by den Nijs and Rommelse [Phys. Rev. B 40, 4709 (1989)], this lattice string model can be related both to restricted solid-on-solid models, describing the world-sheet of the string in Euclidean space time, and to one-dimensional quantum spin chains. At zero temperature a strong tendency towards orientational order is found and the remaining directed string problem can be treated in detail. Quantum delocalized strings are found whose long-wavelength wandering fluctuation is described by free field theory and it is argued that the fact that the critical phase of delocalized lattice strings corresponds to a free Gaussian theory is a very general consequence of the presence of a lattice. In addition, the mapping on the surface problem is exploited to show the existence of different types of localized string phases; some of these are characterized by a proliferation of kinks, but the kink flavors are condensed so that the long-wavelength fluctuations of these strings are suppressed. The simplest phase of this kind is equivalent to the incompressible (Haldane) phase of the S=1S=1S=1 spin chain and corresponds to a bond centered string: The average string position is centered on bonds. We also find localized phases of this type that take arbitrary orientations relative to the underlying lattice. The possible relevance of these lattice strings for the stripes in cuprates is discussed.
Recent experiments have shown the existence of an ordered stripe phase in the cuprates, suggesting that the nearby metallic phase is best described as a domain-wall fluid. As a minimal model to describe the melting of charged domain walls we introduce quantum lattice strings. This model is related to a generalized quantum spin chain. The string exhibits a rich phase diagram, containing several rough phases with low-lying excitations as well as gapped ordered phases. In this scenario the occurrence of the stripe phase is related to a transition from the quantum-rough (metal) to the classical flat phase.
The low-energy properties of interacting Fermi systems are highly constrained by conservation laws. They generally simplify the structure of the underlying renormalization group by reducing the number of independent renormalization constants. In one dimension, all properties of normal metallic fixed points are uniquely determined by separate charge and spin conservation for states near the left and right Fermi points, respectively. We construct the general Luttinger-liquid theory of one-dimensional (1D) metals directly from these conservation laws. Luttinger-liquid parameters emerge naturally from the velocities associated with the conserved currents at the Luttinger-liquid fixed point. Instead of bosonization, one may thus use techniques familiar from Fermi-liquid theory, i.e., Feynman diagrams, equations of motion, and Ward identities. The choice of a technique comprising both Fermi- and Luttinger-liquid theory makes the similarities and differences of both theories particularly transparent, and sets the stage for constructing non-Fermi-liquid metallic fixed points in d>1. Several generic properties and asymptotic conservation laws of 2D non-Fermi-liquid metals are discussed.
The problems of charge stripe formation, spin-charge separation, and stability of the antiphase domain wall (ADW) associated with a stripe are addressed using an analytical approach to the t- J(z) model. We show that a metallic stripe together with its ADW is the ground state of the problem in the low doping regime. The stripe is described as a system of spinons and magnetically confined holons strongly coupled to the two dimensional spin environment with holon-spin-polaron elementary excitations filling a one-dimensional band.
I give a brief introduction to Luttinger liquids. Luttinger liquids are paramagnetic one-dimensional metals without Landau quasi-particle excitations. The elementary excitations are collective charge and spin modes, leading to charge-spin separation. Correlation functions exhibit power-law behavior. All physical properties can be calculated, e.g. by bosonization, and depend on three parameters only: the renormalized coupling constant Kρ, and the charge and spin velocities. I also discuss the stability of Luttinger liquids with respect to temperature, interchain coupling, lattice effects and phonons, and list important open problems.
We construct a theory of continuous stripe melting quantum phase transitions in two-dimensional metals and the associated Fermi surface reconstruction. Such phase transitions are strongly coupled but yet theoretically tractable in situations where the stripe ordering is destroyed by proliferating doubled dislocations of the charge stripe order. The resulting non-Landau quantum critical point has strong stripe fluctuations which we show decouple dynamically from the Fermi surface even though static stripe ordering reconstructs the Fermi surface. We discuss connections to various stripe phenomena in the cuprates. We point out several puzzling aspects of old experimental results [G. Aeppli et al., Science 278, 1432 (1997)] on singular stripe fluctuations in the cuprates, and provide a possible explanation within our theory. These results may thus have been the first observation of non-Landau quantum criticality in an experiment.