Correlated Topological Insulators and the Fractional Magnetoelectric Effect

Topological insulators are characterized by the presence of gapless surface modes protected by time-reversal symmetry. In three space dimensions the magnetoelectric response is described in terms of a bulk theta term for the electromagnetic field. Here we construct theoretical examples of such phases that cannot be smoothly connected to any band insulator. Such correlated topological insulators admit the possibility of fractional magnetoelectric response described by fractional theta/pi. We show that fractional theta/pi is only possible in a gapped time reversal invariant system of bosons or fermions if the system also has deconfined fractional excitations and associated degenerate ground states on topologically non-trivial spaces. We illustrate this result with a concrete example of a time reversal symmetric topological insulator of correlated bosons with theta = pi/4. Extensions to electronic fractional topological insulators are briefly described.Comment: 4 pages + ref

Topological exciton Fermi surfaces in two-component fractional quantized Hall insulators

A wide variety of two-dimensional electron systems (2DES) allow for independent control of the total andrelative charge density of two-component fractional quantum Hall (FQH) states. In particular, a recent experimenton bilayer graphene (BLG) observed a continuous transition between a compressible and incompressiblephase at total filling νT =12as charge is transferred between the layers, with the remarkable property that theincompressible phase has a finite interlayer polarizability. We argue that this occurs because the topologicalorder of νT =12systems supports a novel type of interlayer exciton that carries Fermi statistics. If the fermionicexcitons are lower in energy than the conventional bosonic excitons (i.e., electron-hole pairs), they can form anemergent neutral Fermi surface, providing a possible explanation of an incompressible yet polarizable state atνT =12. We perform exact diagonalization studies which demonstrate that fermionic excitons are indeed lowerin energy than bosonic excitons. This suggests that a “topological exciton metal” hidden inside a FQH insulatormay have been realized experimentally in BLG. We discuss several detection schemes by which the topologicalexciton metal can be experimentally probed

Quantum spin liquids and the metal-insulator transition in doped semiconductors

We describe a new possible route to the metal-insulator transition in doped semiconductors such as Si:P or Si:B. We explore the possibility that the loss of metallic transport occurs through Mott localization of electrons into a quantum spin liquid state with diffusive charge neutral "spinon" excitations. Such a quantum spin liquid state can appear as an intermediate phase between the metal and the Anderson-Mott insulator. An immediate testable consequence is the presence of metallic thermal conductivity at low temperature in the electrical insulator near the metal-insulator transition. Further we show that though the transition is second order the zero temperature residual electrical conductivity will jump as the transition is approached from the metallic side. However the electrical conductivity will have a non-monotonic temperature dependence that may complicate the extrapolation to zero temperature. Signatures in other experiments and some comparisons with existing data are made.Comment: 4 pages text + 3 pages Appendices, 3 Figures; v2 - References Adde

Fermionic Modular Categories and the 16-fold Way

We study spin and super-modular categories systematically as inspired by fermionic topological phases of matter, which are always fermion parity enriched and modelled by spin TQFTs at low energy. We formulate a $16$-fold way conjecture for the minimal modular extensions of super-modular categories to spin modular categories, which is a categorical formulation of gauging the fermion parity. We investigate general properties of super-modular categories such as fermions in twisted Drinfeld doubles, Verlinde formulas for naive quotients, and explicit extensions of $PSU(2)_{4m+2}$ with an eye towards a classification of the low-rank cases.Comment: Latest post-referee version. Many typos fixed, many explanations expanded, several inconsistencies corrected. 8 figure

Parafermionic edge zero modes in Z_n-invariant spin chains

A sign of topological order in a gapped one-dimensional quantum chain is the existence of edge zero modes. These occur in the Z_2-invariant Ising/Majorana chain, where they can be understood using free-fermion techniques. Here I discuss their presence in spin chains with Z_n symmetry, and prove that for appropriate coupling they are exact, even in this strongly interacting system. These modes are naturally expressed in terms of parafermions, generalizations of fermions to the Z_n case. I show that parafermionic edge zero modes do not occur in the usual ferromagnetic and antiferromagnetic cases, but rather only when the interactions are chiral, so that spatial-parity and time-reversal symmetries are broken.Comment: 22 pages. v2: small changes, added reference

Modeling the excitation of graphene plasmons in periodic grids of graphene ribbons: an analytical approach

We study electromagnetic scattering and subsequent plasmonic excitations in periodic grids of graphene ribbons. To address this problem, we develop an analytical method to describe the plasmon-assisted absorption of electromagnetic radiation by a periodic structure of graphene ribbons forming a diffraction grating for THz and mid-IR light. The major advantage of this method lies in its ability to accurately describe the excitation of graphene surface plasmons (GSPs) in one-dimensional (1D) graphene gratings without the use of both time-consuming, and computationally-demanding full-wave numerical simulations. We thus provide analytical expressions for the reflectance, transmittance and plasmon-enhanced absorbance spectra, which can be readily evaluated in any personal laptop with little-to-none programming. We also introduce a semi-analytical method to benchmark our previous results and further compare the theoretical data with spectra taken from experiments, to which we observe a very good agreement. These theoretical tools may therefore be applied to design new experiments and cutting-edge nanophotonic devices based on graphene plasmonics.The authors thank N. Asger Mortensen for insightful and valuable comments. PADG acknowledges financial support from Fundação para a Ciência e a Tecnologia (Portugal) from grant No. PD/BI/114376/2016. NMRP and YVB acknowledge financial support from the European Commission through the project “GrapheneDriven Revolutions in ICT and Beyond” (Ref. No. 696656). This work was partially supported by the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing UID/FIS/04650/2013. The Center for Nanostructured Graphene is sponsored by the Danish National Research Foundation, Project DNRF103

N = 1 dualities in 2+1 dimensions

We consider minimally supersymmetric QCD in 2+1 dimensions, with Chern-Simons and superpotential interactions. We propose an infrared $SU(N) \leftrightarrow U(k)$ duality involving gauge-singlet fields on one of the two sides. It shares qualitative features both with 3d bosonization and with 4d Seiberg duality. We provide a few consistency checks of the proposal, mapping the structure of vacua and performing perturbative computations in the $\varepsilon$-expansion

Chern-Simons-matter dualities with SO and USp gauge groups

In the last few years several dualities were found between the low-energy behaviors of Chern-Simons-matter theories with unitary gauge groups coupled to scalars, and similar theories coupled to fermions. In this paper we generalize those dualities to orthogonal and symplectic gauge groups. In particular, we conjecture dualities between SO(N)kChern-Simons theories coupled to Nfreal scalars in the fundamental representation, and SO(k)\u2013N + N f / 2theories coupled to Nfreal (Majorana) fermions in the fundamental. For Nf= 0 these are just level-rank dualities of pure Chern-Simons theories, whose precise form we clarify. They lead us to propose new gapped boundary states of topological insulators and superconductors. For k = 1 we get an interesting low-energy duality between Nffree Majorana fermions and an SO(N)1 Chern-Simons theory coupled to Nfscalar fields (with Nf 64 N 12 2)