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arXiv:1207.1442 · Physical Review B

Stripe melting and quantum criticality in correlated metals

David F. Mross, T. Senthil

Published Sep 27, 2012• 23 citations
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Abstract

We study theoretically quantum melting transitions of stripe order in a metallic environment, and the associated reconstruction of the electronic Fermi surface. We show that such quantum phase transitions can be continuous in situations where the stripe melting occurs by proliferating pairs of dislocations in the stripe order parameter without proliferating single dislocations. We develop an intuitive picture of such phases as ``stripe loop metals'' where the fluctuating stripes form closed loops of arbitrary size at long distances. We obtain a controlled critical theory of a few different continuous quantum melting transitions of stripes in metals. At such a (deconfined) critical point, the fluctuations of the stripe order parameter are strongly coupled, yet tractable. They also decouple dynamically from the Fermi surface. We calculate many universal properties of these quantum critical points. In particular, we find that the full Fermi surface and the associated Landau quasiparticles remain sharply defined at the critical point. We discuss the phenomenon of Fermi surface reconstruction across this transition and the effect of quantum critical stripe fluctuations on the superconducting instability. We study possible relevance of our results to several phenomena in the cuprates.

DOI
10.1103/physrevb.86.115138

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We study theoretically quantum melting transitions of stripe order in a metallic environment, and the associated reconstruction of the electronic Fermi surface. We show that such quantum phase transitions can be continuous in situations where the stripe melting occurs by proliferating pairs of dislocations in the stripe order parameter without proliferating single dislocations. We develop an intuitive picture of such phases as ``stripe loop metals'' where the fluctuating stripes form closed loops of arbitrary size at long distances. We obtain a controlled critical theory of a few different continuous quantum melting transitions of stripes in metals. At such a (deconfined) critical point, the fluctuations of the stripe order parameter are strongly coupled, yet tractable. They also decouple dynamically from the Fermi surface. We calculate many universal properties of these quantum critical points. In particular, we find that the full Fermi surface and the associated Landau quasiparticles remain sharply defined at the critical point. We discuss the phenomenon of Fermi surface reconstruction across this transition and the effect of quantum critical stripe fluctuations on the superconducting instability. We study possible relevance of our results to several phenomena in the cuprates.
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.
We describe two-dimensional models with a metallic Fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension. The primary examples involve transitions with a topological order parameter associated with dislocations in collinear spin-density-wave (``stripe'') correlations: the suppression of dislocations leads to a fractionalization of spin and charge collective modes, and this transition has been proposed as a candidate for the cuprates near optimal doping. The coupling between the order parameter and long-wavelength volume and shape deformations of the Fermi surface is analyzed by the renormalization group, and a runaway flow to a nonperturbative regime is found in most cases. A phenomenological scaling analysis of simple observable properties of possible second-order quantum critical points is presented, with results quite similar to those near quantum spin-glass transitions and to phenomenological forms proposed by Schr\"oder et al. [Nature (London) 407,407,407, 351 (2000)].
We discuss the quantum phase transition between a quantum nematic metallic state to an electron metallic smectic state in terms of an order-parameter theory coupled to fermionic quasiparticles. Both commensurate and incommensurate smectic (or stripe) cases are studied. Close to the quantum critical point (QCP), the spectrum of fluctuations of the nematic phase has low-energy ``fluctuating stripes.'' We study the quantum critical behavior and find evidence that, contrary to the classical case, the gauge-type of coupling between the nematic and smectic is irrelevant at this QCP. The collective modes of the electron smectic (or stripe) phase are also investigated. The effects of the low-energy bosonic modes on the fermionic quasiparticles are studied perturbatively, for both a model with full rotational symmetry and for a system with an underlying lattice, which has a discrete point group symmetry. We find that at the nematic-smectic critical point, due to the critical smectic fluctuations, the dynamics of the fermionic quasiparticles near several points on the Fermi surface, around which it is reconstructed, are not governed by a Landau Fermi liquid theory. Surprisingly, the quasiparticles in the smectic phase also exhibit non-Fermi liquid behavior. We also present a detailed analysis of the dynamical susceptibilities in the electron nematic phase close to this QCP (the fluctuating stripe regime) and in the electronic smectic phase.
The quantum phase transitions of metals have been extensively studied in the rare-earth "heavy electron" materials, the cuprates, and related compounds. The Fermi surface of the metal often has different shapes in the states well away from the critical point. It has been proposed that these differences can persist up to the critical point, setting up a discontinuous Fermi surface change across a continuous quantum transition. We study square lattice antiferromagnets undergoing a continuous transition from a Neel state to a valence bond solid, and examine the fate of a small density of holes in the two phases. Fermi surfaces of charge e, spin 1/2 quasiparticles appear in both phases, enclosing the usual Luttinger area. However, additional quantum numbers cause the area enclosed by each Fermi surface pocket to jump by a factor of 2 across the transition in the limit of small density. We demonstrate that the electronic spectrum across this transition is described by a critical theory of a localized impurity coupled to a 2+1 dimensional conformal field theory. This critical theory also controls the more complex Fermi surface crossover at fixed density, which likely involves intermediate phases with exotic fractionalized excitations. We suggest that such theories control the electronic spectrum in the pseudogap phase of the cuprates.
Instabilities of quantum critical metals in the limit Nf→0N_f\rightarrow0Nf​→0
We study a model in 2+1 dimensions composed of a Fermi surface of N_f N f flavors of fermions coupled to scalar fluctuations near quantum critical points (QCPs). The N_f\rightarrow0 N f → 0 limit allows us to non-perturbatively calculate the long-range behavior of fermion correlation functions. We use this to calculate charge, spin and pair susceptibilities near different QCPs at zero and finite temperatures, with zero and finite order parameter gaps. While fluctuations smear out the fermionic quasiparticles, we find QCPs where the overall effect of fluctuations leads to enhanced pairing. We also find QCPs where the fluctuations induce spin and charge density wave instabilities for a finite interval of order parameter fluctuation gaps at T=0 T = 0 . We restore a subset of the diagrams suppressed in the N_f\rightarrow0 N f → 0 limit, all diagrams with internal fermion loops with at most 2 vertices, and find that this does not change the long-range behavior of correlators except right at the QCPs.
Using an exact diagonalization method within the dynamical mean-field theory we analyze the stable stripe structures found in the two-dimensional Hubbard model doped by $0.03<\ensuremath{\delta}<0.2$ holes, and discuss a scenario for stripe melting. Our results demonstrate the importance of dynamical correlations which lead to the metallic stripes, in contrast to the Hartree-Fock picture. The spectral functions show a coexistence of the coherent quasiparticles (polaron band) close to the Fermi energy \ensuremath{\mu}, and incoherent states at lower energies. The quasiparticles in the polaron band depend on hole doping, and hybridize strongly with the partly filled mid-gap band within the Mott-Hubbard gap, induced by stripe order. This explains the origin of nondispersive quasiparticles close to the Fermi energy \ensuremath{\mu}, observed near the $X=(\ensuremath{\pi},0)$ and $Y=(0,\ensuremath{\pi})$ points for the samples with coexisting (10) and (01) stripes. We reproduce the gap which opens for charge excitations at the $S=(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ point, observed in the angle-resolved photoemission experiments for ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4},$ and a pseudogap in the integrated spectral density pinned to \ensuremath{\mu}. Finally, we show that large spectral weight close to $\ensuremath{\mu}$ moves from the X to the S point when the second neighbor hopping element increases, and the (01) stripe phase is destabilized by kink fluctuations.