Abstract
We analyze charge order in hole-doped cuprates within the the spin-fermion model. We show that a magnetically mediated interaction, which is known to give rise to -wave superconductivity and charge order with momentum along zone diagonal, also gives rise to charge order with momenta and consistent with the experiments. We show that an instability towards with or is a threshold phenomenon, but the dimensionless spin-fermion coupling is above the threshold, if the magnetic correlation length exceeds a certain critical value. At a critical , the onset temperature for the charge order terminates at a quantum-critical point distant from the magnetic one. We argue that the charge order with or changes sign under , but . In real space, such an order has both bond and site components; the bond one is larger. We further argue that and are not equivalent, and their symmetric and antisymmetric combinations describe, in real space, incommensurate density modulations and incommensurate bond current, respectively. We derive the Ginzburg-Landau functional for four-component order parameters with or and analyze it first in mean-field theory and then beyond mean field. Within mean field we find two types of charge-density-wave (CDW) states, I and II, depending on system parameters. In state I, density and current modulations emerge with the same or , breaking lattice rotational symmetry, and differ in phase by . The selection of or additionally breaks time-reversal symmetry, such that the total order parameter manifold is . In state II, density and current modulations emerge with different and the order parameter manifold is , where in the two realizations of state II, corresponds to either lattice rotational or time-reversal symmetry breaking. We extend the analysis beyond mean field and argue that discrete symmetries get broken before long-range charge order sets in. For state I, which, we argue, is related to hole-doped cuprates, we show that, upon lowering the temperature, the system first breaks lattice rotational symmetry () at and develops a nematic order, then breaks time-reversal symmetry at and locks the relative phase between density and current fluctuations, and finally breaks symmetry of a common phase of even and odd components of at and develops a true charge order. We argue that at a mean field, is smaller than superconducting , but preemptive composite order lifts and reduces such that at large charge order develops prior to superconductivity. We obtain the full phase diagram and present quantitative comparison of our results with ARPES data for hole-doped cuprates.
19 More- Received 29 June 2014
DOI:https://doi.org/10.1103/PhysRevB.90.035149
©2014 American Physical Society