Optical conductivity with holographic lattices

By G. Horowitz, Jorge E Santos, David Tong. 2012

357 citations recorded by the source corpus.

A bstractWe add a gravitational background lattice to the simplest holographic model of matter at finite density and calculate the optical conductivity. With the lattice, the zero frequency delta function found in previous calculations (resulting from translation invariance) is broadened and the DC conductivity is finite. The optical conductivity exhibits a Drude peak with a cross-over to power-law behavior at higher frequencies. Surprisingly, these results bear a strong resemblance to the properties of some of the cuprates.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c1824e7fef3ff77088ff85be716748a6810eedaa

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In Geometry and Topology

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Citations in the corpus

Momentum dissipation and effective theories of coherent and incoherent transport (2014, result): “When translational symmetry is weakly broken at low energies, momentum is almost-conserved, and the AC conductivities of various holographic models like this have been shown to display Drude-like peaks in agreement with memory matrix predictions [5–15].”
Dissecting holographic conductivities (2015, background): “Another question is the sensitivity of our results to the choice of momentum relaxation mechanism: would they be modified if we had instead used random-field disorder [3, 4, 22, 37–39], or homogeneous [19, 40, 41] or inhomogeneous lattices [20, 32, 42] to break translational invariance? Furthermore,”
Charged black branes with hyperscaling violating factor (2012, background): “In this case, the Drude peak will appear from gravity calculations as well [52].”
The AdS/CFT correspondence (2014, background): “ystem, we can either add periodic sources on the boundary which breaks translational invariance, or let the symmetry be broken spontaneously by an instability, resulting in ‘striped phases’ (see e.g. [126,127] for pioneering eorts in these directions). Such systems naturally implement momentum dissi”
The thermoelectric properties of inhomogeneous holographic lattices (2014, methodology): “Such a scaling was reported in [4, 5], based on log-log plots, for the approximate range 2 < ωτ < 8, where τ is obtained from the fit to the Drude peak.”
Holographic Q-lattices (2013, background): “(3)We will comment on the results of [1] in section 4.”
Further evidence for lattice-induced scaling (2012, methodology): “Recent examples include the study of physics in the presence of a background lattice [1, 2, 3, 4, 5, 6], lattices constructed from D-branes [7, 8] as well as spatially modulated phases in which the breaking of translational invariance occurs spontaneously [9, 10, 11, 12, 13].”
Universal Resistivity from Holographic Massive Gravity (2013, background): “This can be done perturbatively, viewing the lattice as an irrelevant operator from the IR perspective [5], or more directly by computing charge transport in the background of a spatially modulated bulk [6, 7, 8, 9] or in the presence of impurities [10, 11].”
Momentum relaxation in holographic massive gravity (2013, background): “nless τrel. ≥ 0 i.e. m2 β ≥ 0. Finally, we note that the DC resistivity ρDC is non-zero at T = 0. This was also noted by taking the low temperature limit in [21]. It was shown in [4] (and conﬁrmed in [1]) that for a theory with a near-horizon AdS2 geometry that is coupled to a lattice with wavevecto”
Thermoelectric DC conductivities from black hole horizons (2014, background): “This is a significant technical simplification since the black holes can be constructed by solving ODEs instead of PDEs2 as in the constructions [15, 18–22].”
General relativity and the cuprates (2013, methodology): “Here G(z) controls the black hole temperature given by T ≡ G(1)/4π = (6 − μ(2)1)/8π and H1,2, S1,2, F and ψ are six functions of x and z, that we determine using the numerical methods described in [1], which were first introduced in [19] and studied in great detail in [20].”
Charge transport in holography with momentum dissipation (2014, methodology): “Unless the thermal pair creation contribution to the DC conductivity is parametrically larger than the dissipative term, we expect coherent transport with a sharp Drude peak (such as were seen in [12, 14, 15] for instance).”
Holographic lattice in Einstein-Maxwell-dilaton gravity (2013, methodology): “Especially, in recent work [6, 7], a holographic lattice model has been constructed in the Einstein-Maxwell theory by introducing a periodic scalar field to simulate the lattice, or directly imposing a periodic condition for the chemical potential on the boundary, which is also called as ionic latti”
Holographic Quantum Matter (2016, background): “This can also be done with scalar fields [392].”
Numerical methods for finding stationary gravitational solutions (2015, methodology): “[234] G.”
A simple holographic model of momentum relaxation (2013, background): “5 An intermediate frequency scaling regime for numerical lattice set-ups was observed in [2, 3].”
Holographic metals and insulators with helical symmetry (2014, methodology): “A first line of research introduced a holographic lattice imprinted by boundary conditions on the bulk charge contribution, [20]–[24].”