
Temperature Dependence of In-plane Resistivity and Inverse Hall Angle in NLED Holographic Model
Qing-Yu Gan,Peng Wang,Hai-Tang Yang
Communications in Theoretical Physics ›› 2019, Vol. 71 ›› Issue (5) : 577-589.
Temperature Dependence of In-plane Resistivity and Inverse Hall Angle in NLED Holographic Model
In the strange metal phase of the high-
high-Tc cuprates / DC conductivity / NLED holographic model {{custom_keyword}} /
Fig. 3 (Color online) The overlap between T-linear |
Fig. 9 (Color online) The overlap between T-linear |
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[4] |
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[5] |
We use the AdS/CFT correspondence to compute the conductivity of massive N=2 hypermultiplet fields at finite baryon number density in an N=4 SU(N_c) super-Yang-Mills theory plasma in the large N_c, large 't Hooft coupling limit. The finite baryon density provides charge carriers analogous to electrons in a metal. An external electric field then induces a finite current which we determine directly. Our result for the conductivity is good for all values of the mass, external field and density, modulo statements about the yet-incomplete phase diagram. In the appropriate limits it agrees with known results obtained from analyzing small fluctuations around equilibrium. For large mass, where we expect a good quasi-particle description, we compute the drag force on the charge carriers and find that the answer is unchanged from the zero density case. Our method easily generalizes to a wide class of systems of probe branes in various backgrounds.
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[6] |
We show that a simple gravitational theory can provide a holographically dual description of a superconductor. There is a critical temperature, below which a charged condensate forms via a second order phase transition and the (DC) conductivity becomes infinite. The frequency dependent conductivity develops a gap determined by the condensate. We find evidence that the condensate consists of pairs of quasiparticles.
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[9] |
A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti-de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.
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Abstract: These notes are loosely based on lectures given at the CERN Winter School on Supergravity, Strings and Gauge theories, February 2009 and at the IPM String School in Tehran, April 2009. I have focused on a few concrete topics and also on addressing questions that have arisen repeatedly. Background condensed matter physics material is included as motivation and easy reference for the high energy physics community. The discussion of holographic techniques progresses from equilibrium, to transport and to superconductivity.
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[20] |
Four lectures on holography and the AdS/CFT correspondence applied to condensed matter systems. The first lecture introduces the concept of a quantum phase transition. The second lecture discusses linear response theory and Ward identities. The third lecture presents transport coefficients derived from AdS/CFT that should be applicable in the quantum critical region associated to a quantum phase transition. The fourth lecture builds in the physics of a superconducting or superfluid phase transition to the simple holographic model of the third lecture.
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[21] |
We initiate a holographic model building approach to `strange metallic' phenomenology. Our model couples a neutral Lifshitz-invariant quantum critical theory, dual to a bulk gravitational background, to a finite density of gapped probe charge carriers, dually described by D-branes. In the physical regime of temperature much lower than the charge density and gap, we exhibit anomalous scalings of the temperature and frequency dependent conductivity. Choosing the dynamical critical exponent z appropriately we can match the non-Fermi liquid scalings, such as linear resistivity, observed in strange metal regimes. As part of our investigation we outline three distinct string theory realizations of Lifshitz geometries: from F theory, from polarised branes, and from a gravitating charged Fermi gas. We also identify general features of renormalisation group ow in Lifshitz theories, such as the appearance of relevant charge-charge interactions when z 鈮 2. We outline a program to extend this model building approach to other anomalous observables of interest such as the Hall conductivity.
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We construct the hydrodynamics of quantum critical points with Lifshitz scaling. There are new dissipative effects allowed by the lack of boost invariance. The formulation is applicable, in general, to any fluid with an explicit breaking of boost symmetry. We use a Drude model of a strange metal to study the physical effects of the new transport coefficient. It can be measured using electric fields with non-zero gradients, or via the heat production when an external force is turned on. The resistivity is proportional to the drag coefficient, scaling arguments fix it to be linear in the temperature.
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[24] |
We use the DBI action from string theory and holography to study the magneto-resistance at quantum criticality with hyperscaling violation. We find and analyze a rich class of scaling behaviors for the magneto-resistance. A special case describes the scaling results found in pnictides by Hayers et al in 2014 (arXiv:1412.6484).
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We examine magnetotransport in a holographic Dirac-Born-Infeld model, taking into account the effects of backreaction on the geometry. The theory we consider includes axionic scalars, introduced to break translational symmetry and generate momentum dissipation. The generic structure of the DC conductivity matrix for these theories is extremely rich, and is significantly more complex than that obtained in the probe approximation. We find new classes of black brane solutions, including geometries that exhibit Lifshitz scaling and hyperscaling violation, and examine their implications on the transport properties of the system. Depending on the choice of theory parameters, these backgrounds can lead to metallic or insulating behavior. Negative magnetoresistance is observed in a family of dynoic solutions. Some of the new backreacted geometries also support magnetic-field-induced metal-insulator transitions.Cremonini, Sera; Hoover, Anthony; Li, Li
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We obtain explicit expressions for the thermoelectric transport coefficients of a strongly coupled, planar medium in the presence of an orthogonal magnetic field and momentum-dissipating processes....
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We investigate the holographic DC and Hall conductivity in massive Einstein-Maxwell-Dilaton (EMD) gravity. Two special EMD backgrounds are considered explicitly. One is dyonic Reissner-Nordstr
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Magnetic field and momentum dissipation are key ingredients in describing condensed matter systems. We include them in gauge/gravity and systematically explore the bottom-up panorama of holographic IR effective field theories based on bulk EinsteinMaxwell Lagrangians plus scalars. The class of solutions here examined appears insufficient to capture the phenomenology of charge transport in the cuprates. We analyze in particular the temperature scaling of the resistivity and of the Hall angle. Keeping an open attitude, we illustrate weak and strong points of the approach.
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[32] |
We investigate an Einstein-Maxwell-Dilaton-Axion holographic model and obtain two branches of a charged black hole solution with a dynamic exponent and a hyperscaling violation factor when a magnetic field presents. The magnetothermoelectric DC conductivities are then calculated in terms of horizon data by means of holographic principle. We find that linear temperature dependence resistivity and quadratic temperature dependence inverse Hall angle can be achieved in our model. The well-known anomalous temperature scaling of the Nernst signal and the Seebeck coefficient of cuprate strange metals are also discussed.
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[34] |
We examine transport in a holographic model in which the dynamics of the charged degrees of freedom is described by the non-perturbative Dirac--Born--Infeld (DBI) action. Axionic scalar fields are included to break translational invariance and generate momentum dissipation in the system. Scaling exponents are introduced by using geometries which are non-relativistic and hyperscaling-violating in the infrared. When the momentum relaxation is strong, the theory reproduces the anomalous temperature dependence of the resistivity and Hall angle of the cuprate strange metals,
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Abstract: We present a new black hole solution in the asymptotic Lifshitz spacetime with a hyperscaling violating factor. A novel computational method is introduced to compute the DC thermoelectric conductivities analytically. We find that both the linear-T and quadratic-T contributions to the resistivity can be realized, indicating that a more detailed comparison with experimental phenomenology can be performed in this scenario.
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[36] |
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[37] |
There has been significant interest in the last several years in studying possible gravitational duals, known as Lifshitz spacetimes, to anisotropically scaling field theories by adding matter to distort the asymptotics of an AdS spacetime. We point out that putative ground state for the most heavily studied example of such a spacetime, that with a flat spatial section, suffers from a naked singularity and further point out this singularity is not resolvable by any known stringy effect. We review the reasons one might worry that asymptotically Lifshitz spacetimes are unstable and employ the initial data problem to study the stability of such systems. Rather surprisingly this question, and even the initial value problem itself, for these spacetimes turns out to generically not be well-posed. A generic normalizable state will evolve in such a way to violate Lifshitz asymptotics in finite time. Conversely, enforcing the desired asymptotics at all times puts strong restrictions not just on the metric and fields in the asymptotic region but in the deep interior as well. Generically, even perturbations of the matter field of compact support are not compatible with the desired asymptotics.
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[38] |
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[39] |
A holographic model of a quantum critical theory at a finite but low temperature, and finite density is studied. The model exhibits non-relativistic z=2 Schr"odinger symmetry and is realized by the Anti-de-Sitter-Schwarzschild black hole in light-cone coordinates. Our approach addresses the electrical conductivities in the presence or absence of an applied magnetic field and contains a control parameter that can be associated to quantum tuning via charge carrier doping or an external field in correlated electron systems. The Ohmic resistivity, the inverse Hall angle, the Hall coefficient and the magnetoresistance are shown to be in good agreement with experimental results of strange metals at very low temperature. The holographic model also predicts new scaling relations in the presence of a magnetic field.
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[40] |
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[41] |
We study the Hall conductivity in holographic models where translational invariance is broken by a lattice. We show that generic holographic theories will display a different temperature dependence in the Hall angle as to the dc conductivity. Our results suggest a general mechanism for obtaining an anomalous scaling of the Hall angle in strongly interacting quantum critical systems.
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[42] |
The linear-
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[43] |
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[44] |
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[45] |
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[46] |
We consider a holographic model consisting of Einstein-Maxwell theory in (d+1) bulk spacetime dimensions with (d-1) massless scalar fields. Momentum relaxation is realised simply through spatially dependent sources for operators dual to the neutral scalars, which can be engineered so that the bulk stress tensor and resulting black brane geometry are homogeneous and isotropic. We analytically calculate the DC conductivity, which is finite. In the d=3 case, both the black hole geometry and shear-mode current-current correlators are those of a sector of massive gravity.
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DOI: https://doi.org/10.1103/PhysRevD.96.106008
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[48] |
Using simple holographic models in D = 4 spacetime dimensions we construct black hole solutions dual to d = 3 CFTs at finite charge density with a Q-lattice deformation. At zero temperature we find new ground state solutions, associated with broken translation invariance in either one or both spatial directions, which exhibit insulating or metallic behaviour depending on the parameters of the holographic theory. For low temperatures and small frequencies, the real part of the optical conductivity exhibits a power-law behaviour. We also obtain an expression for the the DC conductivity at finite temperature in terms of horizon data of the black hole solutions.
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[49] |
We present a class of holographic models that behave effectively as prototypes of Mott insulators, materials where electron-electron interactions dominate transport phenomena. The main ingredient in the gravity dual is that the gauge-field dynamics contains self-interactions by way of a particular type of non-linear electrodynamics. The electrical response in these models exhibits typical features of Mott-like states: i) the low-temperature DC conductivity is unboundedly low; ii) metal-insulator transitions appear by varying various parameters; iii) for large enough self-interaction strength, the conductivity can even decrease with increasing doping (density of carriers), which appears as a sharp manifestation of `traffic-jam'-like behaviour; iv) the insulating state becomes very unstable towards superconductivity at large enough doping. We exhibit some of the properties of the resulting insulator-superconductor transition, which is sensitive to the amount of disorder in a specific way. These models imply a clear and generic correlation between Mott behaviour and significant effects in the nonlinear electrical response. We compute the nonlinear current-voltage curve in our model and find that indeed at large voltage the conductivity is largely reduced.
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Abstract: In an incoherent metal, transport is controlled by the collective diffusion of energy and charge rather than by quasiparticle or momentum relaxation. We explore the possibility of a universal bound
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The presence or absence of a quantum critical point and its location in the phase diagram of high-temperature superconductors have been subjects of intense scrutiny. Clear evidence for quantum criticality, particularly in the transport properties, has proved elusive because the important low-temperature region is masked by the onset of superconductivity. We present measurements of the low- temperature in- plane resistivity of several highly doped La(2-x)Sr(x)CuO(4) single crystals in which the superconductivity had been stripped away by using high magnetic fields. In contrast to other quantum critical systems, the resistivity varies linearly with temperature over a wide doping range with a gradient that scales monotonically with the superconducting transition temperature. It is maximal at a critical doping level (p(c)) similar to 0.19 at which superconductivity is most robust. Moreover, its value at pc corresponds to the onset of quasi- particle incoherence along specific momentum directions, implying that the interaction that first promotes high- temperature superconductivity may ultimately destroy the very quasi- particle states involved in the superconducting pairing.
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We are grateful to Shuxuan Ying and Houwen Wu for useful discussions and valuable comments.
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