Ohm's law at strong coupling: S duality and the cyclotron resonance

By S. Hartnoll, Christopher P. Herzog. 2007

257 citations recorded by the source corpus.

We calculate the electrical and thermal conductivities and the thermoelectric coefficient of a class of strongly interacting 2+1-dimensional conformal field theories with anti-de Sitter space duals. We obtain these transport coefficients as a function of charge density, background magnetic field, temperature, and frequency. We show that the thermal conductivity and thermoelectric coefficient are determined by the electrical conductivity alone. At small frequency, in the hydrodynamic limit, we are able to provide a number of analytic formulas for the electrical conductivity. A dominant feature of the conductivity is the presence of a cyclotron pole. We show how bulk electromagnetic duality acts on the transport coefficients.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/afd00dcf9578752c110a7b2e0a4dd1af26d134aa

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Landscape of superconducting membranes (2009, background): “However, one might certainly wish to consider dyonic black holes also (for instance to study phenomena such as the Hall or Nernst effects [46, 47, 49]) for which this term does not vanish.”
Ground states of holographic superconductors (2009, background): “The theory (1) was introduced in [1] with the aim of describing superconducting black holes, following earlier work [2] on black hole phase transitions and [3, 4, 5], among others, on the possible relation between AdS4 vacua and quantum critical behavior.”
Holography of dyonic dilaton black branes (2010, methodology): “From general reasoning based on linear response in magnetohydrodynamics it was argued in [13] (see also [14]) that at small frequency”
The thermoelectric properties of inhomogeneous holographic lattices (2014, unknown): “see also [43–46].”
Building an AdS/CFT superconductor (2008, background): “Phenomena such as the Hall effect [3] and Nernst effect [4, 5, 6] have dual gravitational descriptions.”
Lectures on holographic methods for condensed matter physics (2009, methodology): “The relationship between the conductivities is found to be [76]”
Analytic calculation of properties of holographic superconductors (2010, background): “Phenomena such as the Hall effect [10] and Nernst effect [11–13] have also been shown to have dual gravitational descriptions.”
Causal hydrodynamics of gauge theory plasmas from AdS/CFT duality (2007, unknown): “[22] for a recent application of SAdS4.”
Holographic Quantum Critical Transport without Self-Duality (2010, background): “The holographic relation of EM duality in the bulk and particle-vortex duality in the boundary theory was first noted in [7, 43] and the effect of this bulk transformation on the boundary transport properties was further studied in [44] – see also [39, 45].”
Towards strange metallic holography (2009, background): “[71, 35, 36, 60, 7]) the Maxwell action takes the usual simple quadratic form F (2).”
Quantum oscillations and black hole ringing (2009, background): “Initial studies [2, 3] focused on hydrodynamic aspects at higher temperatures, while many interesting ground states have emerged in later studies at low temperatures.”
Further evidence for lattice-induced scaling (2012, background): “In the absence of a lattice, the three conductivities σ, α and κ̄ are related by Ward identities [23, 21].”
Holographic Superconductors (2008, background): “However, it was shown in [25] that the contact terms are not present in the case of the current-current correlator in this theory.”
Holographic Quantum Matter (2016, background): “In EinsteinMaxwell-dilaton theories one obtains [126; 171; 337; 417]”