arXiv subjects

Jan Zaanen

Publications and source records attributed to Jan Zaanen.

At least 55 records · Page 3Linked to original sources

arXiv2014

Classification of nematic order in 2+1D: Dislocation melting and $O(2)/Z_N$ lattice gauge theory

Nematic phases, breaking spontaneously rotational symmetry, provide for ubiquitously observed states of matter in both classical and quantum systems. These nematic states may be further classified by their $N$--fold rotational invariance described by cyclic groups $C_N$ in 2+1D. Starting from the space groups of underlying $2d$ crystals, we present a general classification scheme incorporating $C_N$ nematic phases that arise from dislocation-mediated melting and discuss the conventional tensor order parameters. By coupling the $O(2)$ matter fields to the $Z_N$ lattice gauge theory, an unified $O(2)/Z_N$ lattice gauge theory is constructed in order to describe all these nematic phases. This lattice gauge theory is shown to reproduce the $C_N$ nematic-isotropic liquid phase transitions and contains an additional deconfined phase. Finally, using our $O(2)/Z_N$ gauge theory framework, we discuss phase transitions between different $C_N$ nematics.

cond-mat.str-el↗

arXiv2014

Interplay between electronic topology and crystal symmetry: Dislocation-line modes in topological band-insulators

We elucidate the general rule governing the response of dislocation lines in three-dimensional topological band insulators. According to this ${\bf K}\text{-}{\bf b}\text{-}{\bf t}$ rule, the lattice topology, represented by dislocation lines oriented in direction ${\bf t}$ with Burgers vector ${\bf b}$, combines with the electronic-band topology, characterized by the band-inversion momentum ${\bf K}_{\rm inv}$, to produce gapless propagating modes when the plane orthogonal to the dislocation line features a band inversion with a nontrivial ensuing flux $Φ={\bf K}_{\rm inv}\cdot {\bf b}\,\, ({\rm mod\,\,2π})$. Although it has already been discovered by Y. Ran {\it et al.}, Nature Phys. {\bf 5}, 298 (2009), that dislocation lines host propagating modes, the exact mechanism of their appearance in conjunction with the crystal symmetries of a topological state is provided by the ${\bf K}\text{-}{\bf b}\text{-}{\bf t}$ rule . Finally, we discuss possible experimentally consequential examples in which the modes are oblivious for the direction of propagation, such as the recently proposed topologically-insulating state in electron-doped BaBiO$_3$.

cond-mat.mes-hall↗

arXiv2014

How bilayer excitons can greatly enhance thermoelectric efficiency

Currently, one of the major nanotechnological challenges is to design thermoelectric devices that have a high figure of merit. To that end, we propose to use bilayer excitons. Bilayer exciton systems are shown to have an improved thermopower and an enhanced electric counterflow and thermal conductivity, with respect to regular semiconductor-based thermoelectrics. Here we present a roadmap towards experimental realization of a bilayer exciton thermocouple. A bilayer exciton heterostructures of $p$- and $n$-doped Bi$_2$Te$_3$ can have a figure of merit $zT \sim 60$. Another material suggestion is to make a bilayer out of electron-doped SrTiO$_3$ and hole-doped Ca$_3$Co$_4$O$_9$.

cond-mat.mtrl-sci↗

arXiv2014

Electromagnetic properties of viscous charged fluids

We provide a general theoretical framework to describe the electromagnetic properties of viscous charged fluids, consisting for example of electrons in certain solids or plasmas. We confirm that finite viscosity leads to multiple modes of evanescent electromagnetic waves at a given frequency, one of which is characterized by a negative index of refraction, as previously discussed in a simplified model by one of the authors. In particular we explain how optical spectroscopy can be used to probe the viscosity. We concentrate on the impact of this on the coefficients of refraction and reflection at the sample-vacuum interface. Analytical expressions are obtained relating the viscosity parameter to the reflection and transmission coefficients of light. We demonstrate that finite viscosity has the effect to decrease the reflectivity of a metallic surface, while the electromagnetic field penetrates more deeply. While on a phenomenological level there are similarities to the anomalous skin effect, the model presented here requires no particular assumptions regarding the corpuscular nature of the charge liquid. A striking consequence of the branching phenomenon into two degenerate modes is the occurrence in a half-infinite sample of oscillations of the electromagnetic field intensity as a function of distance from the interface.

cond-mat.str-el↗

arXiv2014

BCS instabilities of electron stars to holographic superconductors

We study fermion pairing and condensation towards an ordered state in strongly coupled quantum critical systems with a holographic AdS/CFT dual. On the gravity side this is modeled by a system of charged fermion interacting through a BCS coupling. At finite density such a system has a BCS instability. We combine the relativistic version of mean-field BCS with the semi-classical fluid approximation for the many-body state of fermions. The resulting groundstate is the AdS equivalent of a charged neutron star with a superconducting core. The spectral function of the fermions confirms that the ground state is ordered through the condensation of the pair operator. A natural variant of the BCS star is shown to exist where the gap field couples Stueckelberg-like to the AdS Maxwell field. This enhances the tendency of the system to superconduct.

hep-th↗

arXiv2014

Holographic duality and the resistivity of strange metals

We present a strange metal, described by a holographic duality, which reproduces the famous linear resistivity of the normal state of the copper oxides, in addition to the linear specific heat. This holographic metal reveals a simple and general mechanism for producing such a resistivity, which requires only quenched disorder and a strongly interacting, locally quantum critical state. The key is the minimal viscosity of the latter: unlike in a Fermi-liquid, the viscosity is very small and therefore is important for the electrical transport. This mechanism produces a resistivity proportional to the electronic entropy.

hep-th↗

arXiv2013

Quantum corrected phase diagram of holographic fermions

We study the phases of strongly correlated electron systems in two spatial dimensions in the framework of AdS${}_4$/CFT${}_3$ correspondence. The AdS (gravity) model consists of a Dirac fermion coupled to electromagnetic field and gravity. To classify the ground states of strongly correlated electrons on the CFT side and to construct the full phase diagram of the system, we construct a quantum many-body model of bulk fermion dynamics, based on the WKB approximation to the Dirac equation. At low temperatures, we find a quantum corrected approximation to the electron star where the edge is resolved in terms of wavefunctions extended fully through AdS. At high temperatures, the system exhibits a {\em first} order thermal phase transition to a charged AdS-RN black hole in the bulk and the emergence of local quantum criticality on the CFT side. This change from the third order transition experienced by the semi-classical electron star restores the intuition that the transition between the critical AdS-RN liquid and the finite density Fermi system is of van der Waals liquid-gas type.

hep-th↗

arXiv2013

Determinant quantum Monte Carlo study of exciton condensation in the bilayer Hubbard model

We studied the possibility of exciton condensation in a strongly correlated bilayer extended Hubbard model using Determinant Quantum Monte Carlo. To model both the onsite repulsion U and the interlayer interaction V we introduced a novel update scheme extending the standard Sherman-Morrison update. We observe that the sign problem increases dramatically with the inclusion of the interlayer interaction V, which prohibits at this stage a unequivocal conclusion regarding the presence of exciton condensation. However, enhancement of the interlayer tunneling results suggest that the strongest exciton condensation tendency lies around 10-20 % p/n-doping. Magnetic properties and conductivity turn out to be relatively independent of the interlayer interaction.

cond-mat.str-el↗

arXiv2013

Exciton condensation in strongly correlated electron bilayers

We studied the possibility of exciton condensation in Mott insulating bilayers. In these strongly correlated systems an exciton is the bound state of a double occupied and empty site. In the strong coupling limit the exciton acts as a hard-core boson. Its physics are captured by the exciton t-J model, containing an effective XXZ model describing the exciton dynamics only. Using numerical simulations and analytical mean field theory we constructed the ground state phase diagram. Three homogeneous phases can be distinguished: the antiferromagnet, the exciton checkerboard crystal and the exciton superfluid. For most model parameters, however, we predict macroscopic phase separation between these phases. The exciton superfluid exists only for large exciton hopping energy. Additionally we studied the collective modes and susceptibilities of the three phases. In the superfluid phase we find the striking feature that the bandwidth of the spin-triplet excitations, potentially detectable by resonant inelastic x-ray scattering (RIXS), is proportional to the superfluid density. The superfluid phase mode is visible in the charge susceptibility, measurable by RIXS or electron energy loss spectroscopy (EELS).

cond-mat.str-el↗

arXiv2013

Bose-Fermi competition in holographic metals

We study the holographic dual of a finite density system with both bosonic and fermionic degrees of freedom. There is no evidence for a universal bose-dominated ground state. Instead, depending on the relative conformal weights the preferred groundstate is either pure AdS-Reissner-Nordstrom, a holographic superconductor, an electron star, or a novel mixed state that is best characterized as a hairy electron star.

hep-th↗

arXiv2013

Influence of long-range interactions on charge ordering phenomena on a square lattice

Usually complex charge ordering phenomena arise due to competing interactions. We have studied how such ordered patterns emerge from the frustration of a long-ranged interaction on a lattice. Using the lattice gas model on a square lattice with fixed particle density, we have identified several interesting phases; such as a generalization of Wigner crystals at low particle densities and stripe phases at densities in between rho = 1/3 and rho = 1/2. These stripes act as domain walls in the checkerboard phase present at half-filling. The phases are characterised at zero temperatures using numerical simulations, and mean field theory is used to construct a finite temperature phase diagram.

cond-mat.stat-mech↗

arXiv2013

Enhancement of spin propagation due to interlayer exciton condensation

We show that an interlayer exciton condensate doped into a strongly correlated Mott insulator exhibits a remarkable enhancement of the bandwidth of the magnetic excitations (triplons). This triplon is visible in the dynamical magnetic susceptibility and can be measured using resonant inelastic X-ray scattering. The bandwidth of the triplon scales with the exciton superfluid density, but only in the limit of strong correlations. As such the triplon bandwidth acts as a probe of exciton-spin interactions in the condensate.

cond-mat.str-el↗

arXiv2013

Deconfining the rotational Goldstone mode: the superconducting nematic liquid crystal in 2+1D

The Goldstone theorem states that there should be a massless mode for each spontaneously broken symmetry generator. There is no such rotational mode in crystals, however superconducting quantum nematics should carry rotational Goldstone modes. By generalization of thermal 2D defect mediated melting theory into a 2+1D quantum duality, the emergence of the rotational mode at the quantum phase transition from the solid to the nematic arises as a deconfinement phenomenon, with the unusual property that the stiffness of the rotational mode originates entirely in the dual dislocation condensate.

cond-mat.str-el↗

arXiv2013

Dynamics of a single exciton in strongly correlated bilayers

We formulated an effective theory for a single interlayer exciton in a bilayer quantum antiferromagnet, in the limit that the holon and doublon are strongly bound onto one interlayer rung by the Coulomb force. Upon using a rung linear spin wave approximation of the bilayer Heisenberg model, we calculated the spectral function of the exciton for a wide range of the interlayer Heisenberg coupling α=J_{\perp}/Jz. In the disordered phase at large α, a coherent quasiparticle peak appears representing free motion of the exciton in a spin singlet background. In the Néel phase, which applies to more realistic model parameters, a ladder spectrum arises due to Ising confinement of the exciton. The exciton spectrum is visible in measurements of the dielectric function, such as c-axis optical conductivity measurements.

cond-mat.str-el↗

arXiv2012

The space group classification of topological band insulators

Topological band insulators (TBIs) are bulk insulating materials which feature topologically protected metallic states on their boundary. The existing classification departs from time-reversal symmetry, but the role of the crystal lattice symmetries in the physics of these topological states remained elusive. Here we provide the classification of TBIs protected not only by time-reversal, but also by crystalline symmetries. We find three broad classes of topological states: (a) Gamma-states robust against general time-reversal invariant perturbations; (b) Translationally-active states protected from elastic scattering, but susceptible to topological crystalline disorder; (c) Valley topological insulators sensitive to the effects of non-topological and crystalline disorder. These three classes give rise to 18 different two-dimensional, and, at least 70 three-dimensional TBIs, opening up a route for the systematic search for new types of TBIs.

cond-mat.mes-hall↗

arXiv2012

Zero-energy states bound to a magnetic pi-flux vortex in a two-dimensional topological insulator

We show that the existence of a pair of zero-energy modes bound to a vortex carrying a pi-flux is a generic feature of the topologically non-trivial phase of the M-B model, which was introduced to describe the topological band insulator in HgTe quantum wells. We explicitly find the form of the zero-energy states of the corresponding Dirac equation, which contains a novel momentum-dependent mass term and describes a generic topological transition in a band insulator. The obtained modes are exponentially localized in the vortex-core, with the dependence of characteristic length on the parameters of the model matching the dependence extracted from a lattice version of the model. We consider in full generality the short-distance regularization of the vector potential of the vortex, and show that a particular choice yields the modes localized and simultaneously regular at the origin. Finally, we also discuss a realization of two-dimensional spin-charge separation through the vortex zero-modes.

cond-mat.mes-hall↗

arXiv2012

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/μ, 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.

hep-th↗

arXiv2012

Fluctuations in finite density holographic quantum liquids

We study correlators of the global U(1) currents in holographic models which involve N=4 SYM coupled to the finite density matter in the probe brane sector. We find the spectral density associated with the longitudinal response to be exhausted by the zero sound pole and argue that this could be consistent with the behavior of Fermi liquid with vanishing Fermi velocity. However the transversal response shows an unusual momentum independent behavior. Inclusion of magnetic field leads to a gap in the dispersion relation for the zero sound mode propagating in the plane of magnetic field. For small values of the magnetic field B the gap in the spectrum scales linearly with B, which is consistent with Kohn's theorem for nonrelativistic fermions with pairwise interaction. We do not find signatures of multiple Landau levels expected in Landau Fermi liquid theory. We also consider the influence of generic higher derivative corrections on the form of the spectral function.

hep-th↗