Competing orders and quantum criticality in doped antiferromagnets

Abstract

We use a number of large-N limits to explore the competition between ground states of square lattice doped antiferromagnets which break electromagnetic U(1), time-reversal, or square lattice space group symmetries. Among the states we find are d-, (s * + id)-, and (d x 2 −y 2 + idxy)-wave superconductors, Wigner crystals, Wigner crystals of hole pairs, orbital antiferromagnets (or staggered-flux states), and states with spin-Peierls and bond-centered charge stripe order. In the vicinity of secondorder quantum phase transitions between the states, we go beyond the large-N limit by identifying the universal quantum field theories for the critical points, and computing the finite temperature, quantum-critical damping of fermion spectral functions. We identify candidate critical points for the recently observed quantum-critical behavior in photoemission experiments on Bi2Sr2CaCu2O 8+δ by Valla et al. (Science 285, 2110(Science 285, (1999). These involve onset of a charge density wave, or of broken time-reversal symmetry with d x 2 −y 2 + idxy or s * + id pairing, in a d-wave superconductor. It is not required (although it is allowed) that the stable state in the doped cuprates to be anything other than the d-wave superconductor-the other states need only be stable nearby in parameter space. At finite temperatures, fluctuations associated with these nearby states lead to the observed fermion damping in the vicinity of the nodal points in the Brillouin zone. The cases with broken time-reversal symmetry are appealing because the order parameter is not required to satisfy any special commensurability conditions. The observed absence of inelastic damping of quasiparticles with momenta (π, k), (k, π) (with 0 ≤ k ≤ π) also appears very naturally for the case of fluctuations to d x 2 −y 2 + idxy order.

Large-Nsolutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs2CuCl4and to the layered organic superconductors κ-(BEDT-TTF)2X (BEDT-TTF≡bis(ethylene-dithio)tetrathiafulvalene); X≡anion)

“…Neither mean-field approximation can describe the superconducting phase. The fermionic Sp(N) Hubbard-Heisenberg model does support superconducting states, but no non-superconducting metallic phases [37]. Whether or not a single model can be constructed which is exact in a large-N limit and yet encompasses all the relevant phases remains an open problem.…”

“…Here we have also rescaled the interaction strengths J i /2 → J i /N and U/2 → U/N to make each of the terms in the Hamiltonian of order N. At half-filling, the only case we consider here, a further simplification occurs as the term J ij n i n j is simply a constant. There is no possibility of phase separation into hole-rich and hole-poor regions, nor can stripes form [37], as the system is at half-filling. We drop this constant term in the following analysis.…”

Quantum Phase Transitions and Collective Modes in d-Wave Superconductors

“…In case (A) fermion scattering events can be treated as virtual processes, and the critical theory of the quantum phase transition is not fundamentally modified by the presence of the fermions. A perturbative expansion for the fermionic self-energy is well behaved, and the fermion damping will vanish with a super-linear power of temperature (T ) as T → 0 [6]. In contrast, in case (B) the fermions become part of the critical theory, a perturbative expansion in the coupling is infrared singular, and a correct treatment requires a coupled critical theory of bosons and fermions.…”

“…In contrast, in case (B) the fermions become part of the critical theory, a perturbative expansion in the coupling is infrared singular, and a correct treatment requires a coupled critical theory of bosons and fermions. The most efficient quasiparticle scattering is provided by a linear, non-derivative coupling between fermion bilinears and order parameter bosons [6]. If such a coupling is relevant in the renormalization group sense, then one expects quantum-critical damping of the fermions, i.e., the damping rate will vanish linearly with T .…”

“…To explain these unusual properties, two main paradigms have been suggested: either (i) the systems reflect the properties of a fundamentally new [6] of the d-wave superconductor close to a quantum critical point. Superconductivity is present for T < Tc.…”