156 research outputs found
Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
Over the past few years, topological insulators have taken center stage in
solid state physics. The desire to tune the topological invariants of the bulk
and thus control the number of edge states has steered theorists and
experimentalists towards periodically driving parameters of these systems. In
such periodically driven setups, by varying the drive sequence the effective
(Floquet) Hamiltonian can be engineered to be topological: then, the principle
of bulk--boundary correspondence guarantees the existence of robust edge
states. It has also been realized, however, that periodically driven systems
can host edge states not predicted by the Floquet Hamiltonian. The exploration
of such edge states, and the corresponding topological phases unique to
periodically driven systems, has only recently begun. We contribute to this
goal by identifying the bulk topological invariants of periodically driven
one-dimensional lattice Hamiltonians with chiral symmetry. We find simple
closed expressions for these invariants, as winding numbers of blocks of the
unitary operator corresponding to a part of the time evolution, and ways to
tune these invariants using sublattice shifts. We illustrate our ideas on the
periodically driven Su-Schrieffer-Heeger model, which we map to a discrete time
quantum walk, allowing theoretical results about either of these systems to be
applied to the other. Our work helps interpret the results of recent
simulations where a large number of Floquet Majorana fermions in periodically
driven superconductors have been found, and of recent experiments on discrete
time quantum walks
Marginal topological properties of graphene: a comparison with topological insulators
The electronic structures of graphene systems and topological insulators have
closely-related features, such as quantized Berry phase and zero-energy edge
states. The reason for these analogies is that in both systems there are two
relevant orbital bands, which generate the pseudo-spin degree of freedom, and,
less obviously, there is a correspondence between the valley degree of freedom
in graphene and electron spin in topological insulators. Despite the
similarities, there are also several important distinctions, both for the bulk
topological properties and for their implications for the edge states --
primarily due to the fundamental difference between valley and spin. In view of
their peculiar band structure features, gapped graphene systems should be
properly characterized as marginal topological insulators, distinct from either
the trivial insulators or the true topological insulators.Comment: This manuscript will be published on the Proceedings of the 2010
Nobel Symposium on Graphene and Quantum Matte
Construction and properties of a topological index for periodically driven time-reversal invariant 2D crystals
We present mathematical details of the construction of a topological
invariant for periodically driven two-dimensional lattice systems with
time-reversal symmetry and quasienergy gaps, which was proposed recently by
some of us. The invariant is represented by a gap-dependent -valued index that is simply related to the Kane-Mele invariants of
quasienergy bands but contains an extra information. As a byproduct, we prove
new expressions for the two-dimensional Kane-Mele invariant relating the latter
to Wess-Zumino amplitudes and the boundary gauge anomaly.Comment: published version ; 56 pages, 15 figure
Phonon assisted dynamical Coulomb blockade in a thin suspended graphite sheet
The differential conductance in a suspended few layered graphene sample is
fou nd to exhibit a series of quasi-periodic sharp dips as a function of bias
at l ow temperature. We show that they can be understood within a simple model
of dyn amical Coulomb blockade where energy exchanges take place between the
charge carriers transmitted trough the sample and a dissipative electromagnetic
envir onment with a resonant phonon mode strongly coupled to the electrons
Edge states of graphene bilayer strip
The electronic structure of the zig-zag bilayer strip is analyzed. The
electronic spectra of the bilayer strip is computed. The dependence of the edge
state band flatness on the bilayer width is found. The density of states at the
Fermi level is analytically computed. It is shown that it has the singularity
which depends on the width of the bilayer strip. There is also asymmetry in the
density of states below and above the Fermi energy.Comment: 9 page
Quantum oscillations and decoherence due to electron-electron interaction in metallic networks and hollow cylinders
We have studied the quantum oscillations of the conductance for arrays of
connected mesoscopic metallic rings, in the presence of an external magnetic
field. Several geometries have been considered: a linear array of rings
connected with short or long wires compared to the phase coherence length,
square networks and hollow cylinders. Compared to the well-known case of the
isolated ring, we show that for connected rings, the winding of the Brownian
trajectories around the rings is modified, leading to a different harmonics
content of the quantum oscillations. We relate this harmonics content to the
distribution of winding numbers. We consider the limits where coherence length
is small or large compared to the perimeter of each ring
constituting the network. In the latter case, the coherent diffusive
trajectories explore a region larger than , whence a network dependent
harmonics content. Our analysis is based on the calculation of the spectral
determinant of the diffusion equation for which we have a simple expression on
any network. It is also based on the hypothesis that the time dependence of the
dephasing between diffusive trajectories can be described by an exponential
decay with a single characteristic time (model A) .
At low temperature, decoherence is limited by electron-electron interaction,
and can be modelled in a one-electron picture by the fluctuating electric field
created by other electrons (model B). It is described by a functional of the
trajectories and thus the dependence on geometry is crucial. Expressions for
the magnetoconductance oscillations are derived within this model and compared
to the results of model A. It is shown that they involve several
temperature-dependent length scales.Comment: 35 pages, revtex4, 25 figures (34 pdf files
Flat bands as a route to high-temperature superconductivity in graphite
Superconductivity is traditionally viewed as a low-temperature phenomenon.
Within the BCS theory this is understood to result from the fact that the
pairing of electrons takes place only close to the usually two-dimensional
Fermi surface residing at a finite chemical potential. Because of this, the
critical temperature is exponentially suppressed compared to the microscopic
energy scales. On the other hand, pairing electrons around a dispersionless
(flat) energy band leads to very strong superconductivity, with a mean-field
critical temperature linearly proportional to the microscopic coupling
constant. The prize to be paid is that flat bands can generally be generated
only on surfaces and interfaces, where high-temperature superconductivity would
show up. The flat-band character and the low dimensionality also mean that
despite the high critical temperature such a superconducting state would be
subject to strong fluctuations. Here we discuss the topological and
non-topological flat bands discussed in different systems, and show that
graphite is a good candidate for showing high-temperature flat-band interface
superconductivity.Comment: Submitted as a chapter to the book on "Basic Physics of
functionalized Graphite", 21 pages, 12 figure
One-dimensional Topological Edge States of Bismuth Bilayers
The hallmark of a time-reversal symmetry protected topologically insulating
state of matter in two-dimensions (2D) is the existence of chiral edge modes
propagating along the perimeter of the system. To date, evidence for such
electronic modes has come from experiments on semiconducting heterostructures
in the topological phase which showed approximately quantized values of the
overall conductance as well as edge-dominated current flow. However, there have
not been any spectroscopic measurements to demonstrate the one-dimensional (1D)
nature of the edge modes. Among the first systems predicted to be a 2D
topological insulator are bilayers of bismuth (Bi) and there have been recent
experimental indications of possible topological boundary states at their
edges. However, the experiments on such bilayers suffered from irregular
structure of their edges or the coupling of the edge states to substrate's bulk
states. Here we report scanning tunneling microscopy (STM) experiments which
show that a subset of the predicted Bi-bilayers' edge states are decoupled from
states of Bi substrate and provide direct spectroscopic evidence of their 1D
nature. Moreover, by visualizing the quantum interference of edge mode
quasi-particles in confined geometries, we demonstrate their remarkable
coherent propagation along the edge with scattering properties that are
consistent with strong suppression of backscattering as predicted for the
propagating topological edge states.Comment: 15 pages, 5 figures, and supplementary materia
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