Stellar spectroscopy: Fermions and holographic Lifshitz criticality

Electron stars are fluids of charged fermions in Anti-de Sitter spacetime. They are candidate holographic duals for gauge theories at finite charge density and exhibit emergent Lifshitz scaling at low energies. This paper computes in detail the field theory Green's function G^R(w,k) of the gauge-invariant fermionic operators making up the star. The Green's function contains a large number of closely spaced Fermi surfaces, the volumes of which add up to the total charge density in accordance with the Luttinger count. Excitations of the Fermi surfaces are long lived for w <~ k^z. Beyond w ~ k^z the fermionic quasiparticles dissipate strongly into the critical Lifshitz sector. Fermions near this critical dispersion relation give interesting contributions to the optical conductivity.Comment: 38 pages + appendices. 9 figure

Anomalous Zero Sound

We show that the anomalous term in the current, recently suggested by Son and Yamamoto, modifies the structure of the zero sound mode in the Fermi liquid in a magnetic field.Comment: 14 pages, 2 figure

Semi-local quantum liquids

Gauge/gravity duality applied to strongly interacting systems at finite density predicts a universal intermediate energy phase to which we refer as a semi-local quantum liquid. Such a phase is characterized by a finite spatial correlation length, but an infinite correlation time and associated nontrivial scaling behavior in the time direction, as well as a nonzero entropy density. For a holographic system at a nonzero chemical potential, this unstable phase sets in at an energy scale of order of the chemical potential, and orders at lower energies into other phases; examples include superconductors and antiferromagnetic-type states. In this paper we give examples in which it also orders into Fermi liquids of "heavy" fermions. While the precise nature of the lower energy state depends on the specific dynamics of the individual system, we argue that the semi-local quantum liquid emerges universally at intermediate energies through deconfinement (or equivalently fractionalization). We also discuss the possible relevance of such a semi-local quantum liquid to heavy electron systems and the strange metal phase of high temperature cuprate superconductors.Comment: 31 pages, 7 figure

Lattice potentials and fermions in holographic non Fermi-liquids: hybridizing local quantum criticality

We study lattice effects in strongly coupled systems of fermions at a finite density described by a holographic dual consisting of fermions in Anti-de-Sitter space in the presence of a Reissner-Nordstrom black hole. The lattice effect is encoded by a periodic modulation of the chemical potential with a wavelength of order of the intrinsic length scales of the system. This corresponds with a highly complicated "band structure" problem in AdS, which we only manage to solve in the weak potential limit. The "domain wall" fermions in AdS encoding for the Fermi surfaces in the boundary field theory diffract as usually against the periodic lattice, giving rise to band gaps. However, the deep infrared of the field theory as encoded by the near horizon AdS2 geometry in the bulk reacts in a surprising way to the weak potential. The hybridization of the fermions bulk dualizes into a linear combination of CFT1 "local quantum critical" propagators in the bulk, characterized by momentum dependent exponents displaced by lattice Umklapp vectors. This has the consequence that the metals showing quasi-Fermi surfaces cannot be localized in band insulators. In the AdS2 metal regime, where the conformal dimension of the fermionic operator is large and no Fermi surfaces are present at low T/\mu, the lattice gives rise to a characteristic dependence of the energy scaling as a function of momentum. We predict crossovers from a high energy standard momentum AdS2 scaling to a low energy regime where exponents found associated with momenta "backscattered" to a lower Brillioun zone in the extended zone scheme. We comment on how these findings can be used as a unique fingerprint for the detection of AdS2 like "pseudogap metals" in the laboratory.Comment: 42 pages, 5 figures; v2, minor correction, to appear in JHE

Holographic models for undoped Weyl semimetals

We continue our recently proposed holographic description of single-particle correlation functions for four-dimensional chiral fermions with Lifshitz scaling at zero chemical potential, paying particular attention to the dynamical exponent z = 2. We present new results for the spectral densities and dispersion relations at non-zero momenta and temperature. In contrast to the relativistic case with z = 1, we find the existence of a quantum phase transition from a non-Fermi liquid into a Fermi liquid in which two Fermi surfaces spontaneously form, even at zero chemical potential. Our findings show that the boundary system behaves like an undoped Weyl semimetal.Comment: 64 pages, 19 figure

Holographic Superconductors in a Cohesive Phase

We consider a four-dimensional N=2 gauged supergravity coupled to matter fields. The model is obtained by a U(1) gauging of a charged hypermultiplet and therefore it is suitable for the study of holographic superconductivity. The potential has a topologically flat direction and the parameter running on this "moduli space" labels the new superconducting black holes. Zero temperature solutions are constructed and the phase diagram of the theory is studied. The model has rich dynamics. The retrograde condensate is just a special case in the new class of black holes. The calculation of the entanglement entropy makes manifest the properties of a generic solution and the superconductor at zero temperature is in a confined cohesive phase. The parameter running on the topologically flat direction is a marginal coupling in the dual field theory. We prove this statement by considering the way double trace deformations are treated in the AdS/CFT correspondence. Finally, we comment on a possible connection, in the context of gauge/gravity dualities, between the geometry of the scalar manifold in N=2 supergravity models and the space of marginal deformations of the dual field theory.Comment: 32 pages, 11 figures. Introduction rewritten and clarified, comments and details on section 4 added, acknowledgements rectified. To appear in JHE

The holographic quantum effective potential at finite temperature and density

We develop a formalism that allows the computation of the quantum effective potential of a scalar order parameter in a class of holographic theories at finite temperature and charge density. The effective potential is a valuable tool for studying the ground state of the theory, symmetry breaking patterns and phase transitions. We derive general formulae for the effective potential and apply them to determine the phase transition temperature and density in the scaling region.Comment: 27 page

Cooper pairing near charged black holes

We show that a quartic contact interaction between charged fermions can lead to Cooper pairing and a superconducting instability in the background of a charged asymptotically Anti-de Sitter black hole. For a massless fermion we obtain the zero mode analytically and compute the dependence of the critical temperature T_c on the charge of the fermion. The instability we find occurs at charges above a critical value, where the fermion dispersion relation near the Fermi surface is linear. The critical temperature goes to zero as the marginal Fermi liquid is approached, together with the density of states at the Fermi surface. Besides the charge, the critical temperature is controlled by a four point function of a fermionic operator in the dual strongly coupled field theory.Comment: 1+33 pages, 4 figure

The Spin of Holographic Electrons at Nonzero Density and Temperature

We study the Green's function of a gauge invariant fermionic operator in a strongly coupled field theory at nonzero temperature and density using a dual gravity description. The gravity model contains a charged black hole in four dimensional anti-de Sitter space and probe charged fermions. In particular, we consider the effects of the spin of these probe fermions on the properties of the Green's function. There exists a spin-orbit coupling between the spin of an electron and the electric field of a Reissner-Nordstrom black hole. On the field theory side, this coupling leads to a Rashba like dispersion relation. We also study the effects of spin on the damping term in the dispersion relation by considering how the spin affects the placement of the fermionic quasinormal modes in the complex frequency plane in a WKB limit. An appendix contains some exact solutions of the Dirac equation in terms of Heun polynomials.Comment: 27 pages, 11 figures; v2: minor changes, published versio