Collective transport and optical absorption near the stripe criticality

There are by now several experimental evidences that the peculiar properties of the cuprates are controlled by a Quantum Critical Point (QCP), located near (actually slightly above) the optimal doping δ = δopt [1]. Already several years ago some of us proposed [2] that the pseudogap region of the underdoped cuprates is characterized by the pronounced tendency to form (local) spatial ordering (the so-called “stripe”) phase below some Charge-Ordering (CO) temperature TCO(δ). This last temperature can therefore be related to the temperature T ∗(δ) at which the pseudogap forms. As a schematic model, we adopted the Hubbard-Holstein model in the presence of long-range Coulombic forces. With reasonable parameters for the cuprates, for infinite Hubbard repulsion and for moderate electronphonon coupling there occurs a mean-field zerotemperature charge-density wave instability with a finite modulating wavevector qc and below a rather large critical doping (δ (0) c ∼ 0.2 − 0.3) (see Ref. [3] and references therein). This meanfield CO instability extends at finite temperatures below a doping dependent temperature T (0) CO(δ), which rapidly increases towards electronic energy scales upon underdoping. We then considered how (δ (0) c and T (0) CO(δ) are modified by dynamical charge fluctuations. The critical doping δc is reduced towards optimal doping and T (0) CO(δ) is reduced to lower values TCO(δ) (typically a few hundreds of Kelvin and vanishing at the COQCP at δc). Owing to the dynamical character of the charge fluctuations, TCO (and the related