Abstract
Homogeneous, zero temperature scaling solutions with Bianchi VII spatial geometry are constructed in Einstein-Maxwell-Dilaton theory. They correspond to quantum critical saddle points with helical symmetry at finite density. Assuming $AdS_{5}$ UV asymptotics, the small frequency/(temperature) dependence of the AC/(DC) electric conductivity along the director of the helix are computed. A large class of insulating and conducting anisotropic phases is found, as well as isotropic, metallic phases. Conduction can be dominated by dissipation due to weak breaking of translation symmetry or by a quantum critical current.
Highlights
DC conductivity of a metal increases as the temperature is lowered, while it decreases for an insulator
They correspond to quantum critical saddle points with helical symmetry at finite density
We are interested in saddle points where the effects of translation symmetry breaking are strong, imprinting some anisotropy between the helix director and the transverse plane, or even between the x2, x3 directions of the transverse plane; and in saddle points where translation symmetry breaking is mediated by irrelevant deformations
Summary
We obtain broad families of extremal backgrounds with helical symmetry, and characterize them by their behaviour under rigid scaling transformations (1.9). When the density deformation is marginal, we obtain only insulating states, where the optical conductivity behaves covariantly at zero temperature and low frequencies as σ(T ω μ) ∼ ω(ζ−2)/z1. Both terms in the DC conductivity have the same temperature dependence, but can be parametrically separated by the ratio of the charge density over k. In the semi-locally critical limit (1.11), the scaling dimension of the mode depends explicitly on k, and there is a region of instability when an irrelevant mode sourced by the magnetic field becomes relevant at small k, see figure 4 The endpoint of this instability can be an insulating phase. It would be interesting to adapt it to our setup, and to work out whether the phases presented here can conduct heat or not
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