274 research outputs found
Magnetic translation algebra with or without magnetic field in the continuum or on arbitrary Bravais lattices in any dimension
The magnetic translation algebra plays an important role in the quantum Hall
effect. Murthy and Shankar, arXiv:1207.2133, have shown how to realize this
algebra using fermionic bilinears defined on a two-dimensional square lattice.
We show that, in any dimension , it is always possible to close the magnetic
translation algebra using fermionic bilinears, whether in the continuum or on
the lattice. We also show that these generators are complete in even, but not
odd, dimensions, in the sense that any fermionic Hamiltonian in even dimensions
that conserves particle number can be represented in terms of the generators of
this algebra, whether or not time-reversal symmetry is broken. As an example,
we reproduce the -sum rule of interacting electrons at vanishing magnetic
field using this representation. We also show that interactions can
significantly change the bare bandwidth of lattice Hamiltonians when
represented in terms of the generators of the magnetic translation algebra.Comment: 14 page
Screening in (d+s)-wave superconductors: Application to Raman scattering
We study the polarization-dependent electronic Raman response of untwinned
YBaCuO superconductors employing a tight-binding band
structure with anisotropic hopping matrix parameters and a superconducting gap
with a mixing of - and s-wave symmetry. Using general arguments we find
screening terms in the B^{\}_{1g} scattering channel which are required by
gauge invariance. As a result, we obtain a small but measurable softening of
the pair-breaking peak, whose position has been attributed for a long time to
twice the superconducting gap maximum. Furthermore, we predict
superconductivity-induced changes in the phonon line shapes that could provide
a way to detect the isotropic s-wave admixture to the superconducting gap.Comment: typos corrected, 6 pages, 3 figure
Influence of higher d-wave gap harmonics on the dynamical magnetic susceptibility of high-temperature superconductors
Using a fermiology approach to the computation of the magnetic susceptibility
measured by neutron scattering in hole-doped high-Tc superconductors, we
estimate the effects on the incommensurate peaks caused by higher d-wave
harmonics of the superconducting order parameter induced by underdoping. The
input parameters for the Fermi surface and d-wave gap are taken directly from
angle resolved photoemission (ARPES) experiments on Bi{2}Sr{2}CaCu{2}O{8+x}
(Bi2212). We find that higher d-wave harmonics lower the momentum dependent
spin gap at the incommensurate peaks as measured by the lowest spectral edge of
the imaginary part in the frequency dependence of the magnetic susceptibility
of Bi2212. This effect is robust whenever the fermiology approach captures the
physics of high-Tc superconductors. At energies above the resonance we observe
diagonal incommensurate peaks. We show that the crossover from parallel
incommensuration below the resonance energy to diagonal incommensuration above
it is connected to the values and the degeneracies of the minima of the
2-particle energy continuum.Comment: 13 pages, 7 figure
Masses and Majorana fermions in graphene
We review the classification of all the 36 possible gap-opening instabilities
in graphene, i.e., the 36 relativistic masses of the two-dimensional Dirac
Hamiltonian when the spin, valley, and superconducting channels are included.
We then show that in graphene it is possible to realize an odd number of
Majorana fermions attached to vortices in superconducting order parameters if a
proper hierarchy of mass scales is in place.Comment: Contribution to the Proceedings of the Nobel symposium on graphene
and quantum matte
Irrational vs. rational charge and statistics in two-dimensional quantum systems
We show that quasiparticle excitations with irrational charge and irrational
exchange statistics exist in tight-biding systems described, in the continuum
approximation, by the Dirac equation in (2+1)-dimensional space and time. These
excitations can be deconfined at zero temperature, but when they are, the
charge re-rationalizes to the value 1/2 and the exchange statistics to that of
"quartons" (half-semions).Comment: 4 pages, 2 figure
Noncommutative geometry for three-dimensional topological insulators
We generalize the noncommutative relations obeyed by the guiding centers in
the two-dimensional quantum Hall effect to those obeyed by the projected
position operators in three-dimensional (3D) topological band insulators. The
noncommutativity in 3D space is tied to the integral over the 3D Brillouin zone
of a Chern-Simons invariant in momentum-space. We provide an example of a model
on the cubic lattice for which the chiral symmetry guarantees a macroscopic
number of zero-energy modes that form a perfectly flat band. This lattice model
realizes a chiral 3D noncommutative geometry. Finally, we find conditions on
the density-density structure factors that lead to a gapped 3D fractional
chiral topological insulator within Feynman's single-mode approximation.Comment: 41 pages, 3 figure
Gaussian field theories, random Cantor sets and multifractality
The computation of multifractal scaling properties associated with a critical
field theory involves non-local operators and remains an open problem using
conventional techniques of field theory. We propose a new description of
Gaussian field theories in terms of random Cantor sets and show how universal
multifractal scaling exponents can be calculated. We use this approach to
characterize the multifractal critical wave function of Dirac fermions
interacting with a random vector potential in two spatial dimensions. We show
that the multifractal scaling exponents are self-averaging.Comment: Extensive modifications of previous version; exact results replace
numerical calculation
- …