Model building in AdS/CMT: DC conductivity and Hall angle

Abstract

Using the bottom-up approach in a holographic setting, we attempt to study both the transport and thermodynamic properties of a generic system in 3+1 dimensional bulk spacetime. We show the exact 1/T and $T^2$ dependence of the longitudinal conductivity and Hall angle, as seen experimentally in most copper-oxide systems, which are believed to be close to quantum critical point. This particular temperature dependence to conductivities are possible in two different cases: (1) Background solutions with scale invariant and broken rotational symmetry, (2) solutions with pseudo-scaling and unbroken rotational symmetry but only at low density limit. Generically, the study of the transport properties in a scale invariant background solution, using the probe brane approach, at high density and at low temperature limit suggests us to consider only metrics with two exponents. More precisely, the spatial part of the metric components should not be same i.e., $g_{xx}\ne g_{yy}$. In doing so, we have generated the above mentioned behavior to conductivity with a very special behavior to specific heat which at low temperature goes as: $C_V\sim T^3$. However, if we break the scaling symmetry of the background solution by including a nontrivial dilaton, axion or both and keep the rotational symmetry then also we can generate such a behavior to conductivity but only in the low density regime. As far as we are aware, this particular temperature dependence to both the conductivity and Hall angle is being shown for the first time using holography.

1+40 pages; v2: Analysis of pseudo-scaling and rotational invariant solutions are added; v3: Improved presentation; v4: Typos fixed and closer to journal version

References in corpus (21)

• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Effective Holographic Theories for low-temperature condensed matter systems
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Metallic AdS/CFT
• Quantum critical transport, duality, and M-theory
• Ohm's Law at strong coupling: S duality and the cyclotron resonance
• Holography of Dyonic Dilaton Black Branes
• Impure AdS/CFT
• Wilsonian Approach to Fluid/Gravity Duality
• Zero Sound from Holography
• Holographic Quantum Critical Transport without Self-Duality
• Hall Conductivity of Flavor Fields from AdS/CFT
• Quantum criticality and black holes
• From black holes to strange metals
• On Euclidean and Noetherian Entropies in AdS Space
• Strange Metallic Behavior in Anisotropic Background
• AC Transport at Holographic Quantum Hall Transitions
• AdS/QHE: Towards a Holographic Description of Quantum Hall Experiments
• Non-linear, Finite Frequency Quantum Critical Transport from AdS/CFT
• Conductivity at finite 't Hooft coupling from AdS/CFT
• Sum rules, plasma frequencies and Hall phenomenology in holographic plasmas

Cited by in corpus (21)

• DC and Hall conductivity in holographic massive Einstein-Maxwell-Dilaton gravity
• The open string membrane paradigm with external electromagnetic fields
• Holographic model for the anomalous scalings of the cuprates
• Quantum Criticality and DBI Magneto-resistance
• A Holographic Model of Strange Metals
• Inability of linear axion holographic Gubser-Rocha model to capture all the transport anomalies of strange metals
• Probing holographic semi-local quantum liquids with D-branes
• On the hydrodynamics of (2 + 1)-dimensional strongly coupled relativistic theories in an external magnetic field
• A Holographic Model of Quantum Hall Transition
• Taking a critical look at holographic critical matter
• Scaling of the Holographic AC conductivity for non-Fermi liquids at criticality
• Holography of electrically and magnetically charged black branes
• Doped Holographic Superconductors in Gubser-Rocha model
• RG flow of transport quantities
• Approximate strange metallic behavior in AdS
• Temperature Dependence of In-plane Resistivity and Inverse Hall Angle in NLED Holographic Model
• Novel semi-circle law and Hall sliding in a strongly interacting electron liquid
• Duality and modular symmetry in the quantum Hall effect from Lifshitz holography
• A renormalisation group equation for transport co-efficients in (2+1)-dimensions derived from the AdS/CMT correspondence
• Strange metals at finite 't Hooft coupling
• Critical scaling of the AC conductivity and momentum dissipation