20 research outputs found
Boundaries determine the formation energies of lattice defects in two-dimensional buckled materials
Theoretical Physic
Topological modes bound to dislocations in mechanical metamaterials
Mechanical metamaterials are artificial structures with unusual properties,
such as negative Poisson ratio, bistability or tunable vibrational properties,
that originate in the geometry of their unit cell. At the heart of such unusual
behaviour is often a soft mode: a motion that does not significantly stretch or
compress the links between constituent elements. When activated by motors or
external fields, soft modes become the building blocks of robots and smart
materials. Here, we demonstrate the existence of topological soft modes that
can be positioned at desired locations in a metamaterial while being robust
against a wide range of structural deformations or changes in material
parameters. These protected modes, localized at dislocations, are the
mechanical analogue of topological states bound to defects in electronic
systems. We create physical realizations of the topological modes in prototypes
of kagome lattices built out of rigid triangular plates. We show mathematically
that they originate from the interplay between two Berry phases: the Burgers
vector of the dislocation and the topological polarization of the lattice. Our
work paves the way towards engineering topologically protected nano-mechanical
structures for molecular robotics or information storage and read-out.Comment: 13 pages, 6 figures; changes to text and figures and added analysis
on mode localization; see
http://www.lorentz.leidenuniv.nl/~paulose/dislocation-modes/ for accompanying
video
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.Comment: Accepted in Nature Physic
Higher-order renormalization of graphene many-body theory
We study the many-body theory of graphene Dirac quasiparticles interacting
via the long-range Coulomb potential, taking as a starting point the ladder
approximation to different vertex functions. We test in this way the low-energy
behavior of the electron system beyond the simple logarithmic dependence of
electronic correlators on the high-energy cutoff, which is characteristic of
the large-N approximation. We show that the graphene many-body theory is
perfectly renormalizable in the ladder approximation, as all higher powers in
the cutoff dependence can be absorbed into the redefinition of a finite number
of parameters (namely, the Fermi velocity and the weight of the fields) that
remain free of infrared divergences even at the charge neutrality point. We
illustrate this fact in the case of the vertex for the current density, where a
complete cancellation between the cutoff dependences of vertex and electron
self-energy corrections becomes crucial for the preservation of the gauge
invariance of the theory. The other potentially divergent vertex corresponds to
the staggered (sublattice odd) charge density, which is made cutoff independent
by a redefinition in the scale of the density operator. This allows to compute
a well-defined, scale invariant anomalous dimension to all orders in the ladder
series, which becomes singular at a value of the interaction strength marking
the onset of chiral symmetry breaking (and gap opening) in the Dirac field
theory. The critical coupling we obtain in this way matches with great accuracy
the value found with a quite different method, based on the resolution of the
gap equation, thus reassuring the predictability of our renormalization
approach.Comment: 27 pages, 7 figures, references adde
Condensed matter and AdS/CFT
I review two classes of strong coupling problems in condensed matter physics,
and describe insights gained by application of the AdS/CFT correspondence. The
first class concerns non-zero temperature dynamics and transport in the
vicinity of quantum critical points described by relativistic field theories. I
describe how relativistic structures arise in models of physical interest,
present results for their quantum critical crossover functions and
magneto-thermoelectric hydrodynamics. The second class concerns symmetry
breaking transitions of two-dimensional systems in the presence of gapless
electronic excitations at isolated points or along lines (i.e. Fermi surfaces)
in the Brillouin zone. I describe the scaling structure of a recent theory of
the Ising-nematic transition in metals, and discuss its possible connection to
theories of Fermi surfaces obtained from simple AdS duals.Comment: 39 pages, 12 figures; Lectures at the 5th Aegean summer school, "From
gravity to thermal gauge theories: the AdS/CFT correspondence", and the De
Sitter Lecture Series in Theoretical Physics 2009, University of Groninge
Dynamically induced magnetism in KTaO
Dynamical multiferroicity features entangled dynamic orders: fluctuating
electric dipoles induce magnetization. Hence, the material with paraelectric
fluctuations can develop magnetic signatures if dynamically driven. We identify
the paraelectric KTaO (KTO) as a prime candidate for the observation of the
dynamical multiferroicity. We show that when a KTO sample is exposed to a
circularly polarized laser pulse, the dynamically induced ionic magnetic
moments are of the order of 5\% of the nuclear magneton per unit cell. We
determine the phonon spectrum using ab initio methods and identify T as
relevant soft phonon modes that couple to the external field and induce
magnetic polarization. We also predict a corresponding electron effect for the
dynamically induced magnetic moment which is enhanced by several orders of
magnitude due to the significant mass difference between electron and ionic
nucleus.Comment: 5 pages, 3 figure