Existence and topological stability of Fermi points in multilayered graphene

We study the existence and topological stability of Fermi points in a graphene layer and stacks with many layers. We show that the discrete symmetries (spacetime inversion) stabilize the Fermi points in monolayer, bilayer and multilayer graphene with orthorhombic stacking. The bands near $k=0$ and $\epsilon=0$ in multilayers with the Bernal stacking depend on the parity of the number of layers, and Fermi points are unstable when the number of layers is odd. The low energy changes in the electronic structure induced by commensurate perturbations which mix the two Dirac points are also investigated.Comment: 6 pages, 6 figures. Expanded version as will appear in PR

Symmetry-based approach to electron-phonon interactions in graphene

We use the symmetries of monolayer graphene to write a set of constraints that must be satisfied by any electron-phonon interaction hamiltonian. The explicit solution as a series expansion in the momenta gives the most general, model-independent couplings between electrons and long wavelength acoustic and optical phonons. As an application, the possibility of describing elastic strains in terms of effective electromagnetic fields is considered in detail, with an emphasis on group theory conditions and the role of time reversal symmetry.Comment: 11 pages, 1 figure. Treatment of ripples in suspended graphene sheets included. Revised journal version with improved presentation and two new appendice

Topological phonon analysis of the 2D buckled honeycomb lattice: an application to real materials

By means of group theory, topological quantum chemistry, first-principles and Monte Carlo calculations, we analyze the topology of the 2D buckled honeycomb lattice phonon spectra. Taking the pure crystal structure as an input, we show that eleven distinct phases are possible, five of which necessarily have non-trivial topology according to topological quantum chemistry. Another four of them are also identified as topological using Wilson loops in an analytical model that includes all the symmetry allowed force constants up to third nearest neighbors, making a total of nine topological phases. We then compute the ab initio phonon spectra for the two-dimensional crystals of Si, Ge, P, As and Sb in this structure and construct its phase diagram. Despite the large proportion of topological phases found in the analytical model, all of the crystals lie in a trivial phase. By analyzing the force constants space using Monte Carlo calculations, we elucidate why topological phonon phases are physically difficult to realize in real materials with this crystal structure

Non-Abelian anomalies and hadronic fluids

By using differential geometry methods, we study the role of non-Abelian anomalies in relativistic fluids. We obtain closed expressions for the covariant currents derived from the Chern-Simons effective action. Our results are also applied to the Wess-Zumino-Witten action that accounts for the interaction of Goldstone bosons with external electromagnetic fields. We particularize these results to QCD with two light flavors.Plan Nacional de Altas Energias Spanish MINECO FPA2015-64041-C2-1-P FPA2015-64041-C2-2-PBasque Government IT979-16Spanish MINEICOEuropean Union (EU) FIS2017-85053-C2-1-PJunta de Andalucia FQM-225Spanish MINEICO Ramon y Cajal Program RYC-2016-20678Universidad del Pais Vasco UPV/EHU, Bilbao, Spai

Effective theory for the Goldstone field in the BCS-BEC crossover at T=0

We perform a detailed study of the effective Lagrangian for the Goldstone mode of a superfluid Fermi gas at zero temperature in the whole BCS-BEC crossover. By using a derivative expansion of the response functions, we derive the most general form of this Lagrangian at the next to leading order in the momentum expansion in terms of four coefficient functions. This involves the elimination of all the higher order time derivatives by careful use of the leading order field equations. In the infinite scattering length limit where conformal invariance is realized, we show that the effective Lagrangian must contain an unnoticed invariant combination of higher spatial gradients of the Goldstone mode, while explicit couplings to spatial gradients of the trapping potential are absent. Across the whole crossover, we determine all the coefficient functions at the one-loop level, taking into account the dependence of the gap parameter on the chemical potential in the mean-field approximation. These results are analytically expressed in terms of elliptic integrals of the first and second kind. We discuss the form of these coefficients in the extreme BCS and BEC regimes and around the unitary limit, and compare with recent work by other authors.Comment: 27 pages. 4 references added, typos corrected, expanded Section III

Non-Abelian anomalous (super)fluids in thermal equilibrium from differential geometry

We apply differential geometry methods to the computation of the anomalyinduced hydrodynamic equilibrium partition function. Implementing the imaginary-time prescription on the Chern-Simons effective action on a stationary background, we obtain general closed expressions for both the invariant and anomalous part of the partition function. This is applied to the Wess-Zumino-Witten action for Goldstone modes, giving the equilibrium partition function of superfluids. In all cases, we also study the anomalyinduced gauge currents and energy-momentum tensor, providing explicit expressions for them.This work has been supported by Plan Nacional de Altas Energías Spanish MINECO grants FPA2015-64041-C2-1-P, FPA2015-64041-C2-2-P, and by Basque Government grant IT979-16. The research of E.M. is also supported by Spanish MINEICO and European FEDER funds grant FIS2017-85053-C2-1-P, Junta de Andalucía grant FQM-225, as well as by Universidad del País Vasco UPV/EHU through a Visiting Professor appointment and by Spanish MINEICO Ramón y Cajal Progra

Anomalies and WZW-term of two-flavour QCD

The U(2)_R x U(2)_L symmetry of QCD with two massless flavours is subject to anomalies which affect correlation functions involving the singlet currents A^0_\mu or V^0_\mu. These are relevant for pion-photon interactions, because - for two flavours - the electromagnetic current contains a singlet piece. We give the effective Lagrangian required for the corresponding low energy analysis to next-to-leading order, without invoking an expansion in the mass of the strange quark. In particular, the Wess-Zumino-Witten term that accounts for the two-flavour anomalies within the effective theory is written down in closed form.Comment: 17 pages, 1 figur

Local Anomalies, Local Equivariant Cohomology and the Variational Bicomplex

The locality conditions for the vanishing of local anomalies in field theory are shown to admit a geometrical interpretation in terms of local equivariant cohomology, thus providing a method to deal with the problem of locality in the geometrical approaches to the study of local anomalies based on the Atiyah-Singer index theorem. The local cohomology is shown to be related to the cohomology of jet bundles by means of the variational bicomplex theory. Using these results and the techniques for the computation of the cohomology of invariant variational bicomplexes in terms of relative Gel'fand-Fuks cohomology introduced in [6], we obtain necessary and sufficient conditions for the cancellation of local gravitational and mixed anomalies.Comment: 36 pages. The paper is divided in two part

Temperature dependence of the anomalous effective action of fermions in two and four dimensions

The temperature dependence of the anomalous sector of the effective action of fermions coupled to external gauge and pseudo-scalar fields is computed at leading order in an expansion in the number of Lorentz indices in two and four dimensions. The calculation preserves chiral symmetry and confirms that a temperature dependence is compatible with axial anomaly saturation. The result checks soft-pions theorems at zero temperature as well as recent results in the literature for the pionic decay amplitude into static photons in the chirally symmetric phase. The case of chiral fermions is also considered.Comment: RevTex, 19 pages, no figures. References adde

Strain-induced partially flat band, helical snake states, and interface superconductivity in topological crystalline insulators

Topological crystalline insulators in IV-VI compounds host novel topological surface states consisting of multi-valley massless Dirac fermions at low energy. Here we show that strain generically acts as an effective gauge field on these Dirac fermions and creates pseudo-Landau orbitals without breaking time-reversal symmetry. We predict the realization of this phenomenon in IV-VI semiconductor heterostructures, due to a naturally occurring misfit dislocation array at the interface that produces a periodically varying strain field. Remarkably, the zero-energy Landau orbitals form a flat band in the vicinity of the Dirac point, and coexist with a network of snake states at higher energy. We propose that the high density of states of this flat band gives rise to interface superconductivity observed in IV-VI semiconductor multilayers at unusually high temperatures, with non-BCS behavior. Our work demonstrates a new route to altering macroscopic electronic properties to achieve a partially flat band, and paves the way for realizing novel correlated states of matter.Comment: Accepted by Nature Physic