Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect

We show that Horava-Lifshitz gravity theory can be employed as a covariant framework to build an effective field theory for the fractional quantum Hall effect that respects all the spacetime symmetries such as non-relativistic diffeomorphism invariance and anisotropic Weyl invariance as well as the gauge symmetry. The key to this formalism is a set of correspondence relations that maps all the field degrees of freedom in the Horava-Lifshitz gravity theory to external background (source) fields among others in the effective action of the quantum Hall effect, according to their symmetry transformation properties. We originally derive the map as a holographic dictionary, but its form is independent of the existence of holographic duality. This paves the way for the application of Horava-Lifshitz holography on fractional quantum Hall effect. Using the simplest holographic Chern-Simons model, we compute the low energy effective action at leading orders and show that it captures universal electromagnetic and geometric properties of quantum Hall states, including the Wen-Zee shift, Hall viscosity, angular momentum density and their relations. We identify the shift function in Horava-Lifshitz gravity theory as minus of guiding center velocity and conjugate to guiding center momentum. This enables us to distinguish guiding center angular momentum density from the internal one, which is the sum of Landau orbit spin and intrinsic (topological) spin of the composite particles. Our effective action shows that Hall viscosity is minus half of the internal angular momentum density and proportional to Wen-Zee shift, and Hall bulk viscosity is half of the guiding center angular momentum density.Comment: 69 page

Holographic Spontaneous Parity Breaking and Emergent Hall Viscosity and Angular Momentum

We study the spontaneous parity breaking and generating of Hall viscosity and angular momentum in holographic p+ip model, which can describe strongly-coupled chiral superfluid states in many quantum systems. The dual gravity theory, an SU(2) gauge field minimally coupled to Einstein gravity, is parity-invariant but allows a black hole solution with vector hair corresponding to a parity-broken superfluid state. We show that this state possesses a non-vanishing parity-odd transport coefficient -- Hall viscosity -- and an angular momentum density. We first develop an analytic method to solve this model near the critical regime and to take back-reactions into account. Then we solve the equation for the tensor mode fluctuations and obtain the expression for Hall viscosity via Kubo formula. We also show that a non-vanishing angular momentum density can be obtained through the vector mode fluctuations and the corresponding boundary action. We give analytic results of both Hall viscosity and angular momentum density near the critical regime in terms of physical parameters. The near-critical behavior of Hall viscosity is different from that obtained from a gravitational Chern-Simons model. We find that the magnitude of Hall viscosity to angular momentum density ratio is numerically consistent with being equal to 1/2 at large SU(2) coupling corresponding to the probe limit, in agreement with previous results obtained for various quantum fluid systems and from effective theory approaches. In addition, we find the shear viscosity to entropy density ratio remains above the universal bound.Comment: 55 pages, 1 figure. Version 2: angular momentum calculation revised; referenced adde

Angular Momentum Generation from Holographic Chern-Simons Models

We study parity-violating effects, particularly the generation of angular momentum density and its relation to the parity-odd and dissipationless transport coefficient Hall viscosity, in strongly-coupled quantum fluid systems in 2+1 dimensions using holographic method. We employ a class of 3+1-dimensional holographic models of Einstein-Maxwell system with gauge and gravitational Chern-Simons terms coupled to a dynamical scalar field. The scalar can condensate and break the parity spontaneously. We find that when the scalar condensates, a non-vanishing angular momentum density and an associated edge current are generated, and they receive contributions from both gauge and gravitational Chern-Simons terms. The angular momentum density does not satisfy a membrane paradigm form because the vector mode fluctuations from which it is calculated are effectively massive. On the other hand, the emergence of Hall viscosity is a consequence of the gravitational Chern-Simons term alone and it has membrane paradigm form. We present both general analytic results and numeric results which take back-reactions into account. The ratio between Hall viscosity and angular momentum density resulting from the gravitational Chern-Simons term has in general a deviation from the universal 1/2 value obtained from field theory and condensed matter physics.Comment: 27 pages, 4 figures; Section 3.4 added; minor change

Real-time finite-temperature correlators from AdS/CFT

In this paper we use AdS/CFT ideas in conjunction with insights from finite temperature real-time field theory formalism to compute 3-point correlators of ${\cal N}{=}4$ super Yang-Mills operators, in real time and at finite temperature. To this end, we propose that the gravity field action is integrated only over the right and left quadrants of the Penrose diagram of the Anti de Sitter-Schwarzschild background, with a relative sign between the two terms. For concreteness we consider the case of a scalar field in the black hole background. Using the scalar field Schwinger-Keldysh bulk-to-boundary propagators, we give the general expression of a 3-point real-time Green's correlator. We then note that this particular prescription amounts to adapting the finite-temperature analog of Veltman's circling rules to tree-level Witten diagrams, and comment on the retarded and Feynman scalar bulk-to-boundary propagators. We subject our prescription to several checks: KMS identities, the largest time equation and the zero-temperature limit. When specializing to a particular retarded (causal) 3-point function, we find a very simple answer: the momentum-space correlator is given by three causal (two retarded and one advanced) bulk-to-boundary propagators, meeting at a vertex point which is integrated from spatial infinity to the horizon only. This result is expected based on analyticity, since the retarded n-point functions are obtained by analytic continuation from the imaginary time Green's function, and based on causality considerations.Comment: 43 pages, 6 figures Typos fixed, reference added, one set of plots update

Probing resistive switching in HfO2/Al2O3 bilayer oxides using in-situ transmission electron microscopy

In this work, we investigate the resistive switching in hafnium dioxide (HfO2) and aluminum oxide (Al2O3) bilayered stacks using in-situ transmission electron microscopy and X-ray energy dispersive spectroscopy. Conductance of the HfO2/Al2O3 stack changes gradually upon electrical stressing which is related to the formation of extended nanoscale physical defects at the HfO2/Al2O3 interface and the migration and re-crystallization of Al into the oxide bulk. The results suggest two competing physical mechanisms including the redistribution of oxygen ions and the migration of Al species from the Al electrode during the switching process. While the HfO2/Al2O3 bilayered stack appears to be a good candidate for RRAM technology, the low diffusion barrier of the active Al electrode causes severe Al migration in the bi-layered oxides leading to the device to fail in resetting, and thereby, largely limiting the overall switching performance and material reliability