43 research outputs found
Geometry-independent tight-binding method for massless Dirac fermions in two dimensions
The Nielsen-Ninomiya theorem, dubbed `fermion-doubling', poses a problem for
the naive discretization of a single (massless) Dirac cone on a two-dimensional
surface. The inevitable appearance of an additional, unphysical fermionic mode
can, for example, be circumvented by introducing an extra dimension to
spatially separate Dirac cones. In this work, we propose a geometry-independent
protocol based on a tight-binding model for a three-dimensional topological
insulator on a cubic lattice. The low-energy theory, below the bulk gap,
corresponds to a Dirac cone on its two-dimensional surface which can have an
arbitrary geometry. We introduce a method where only a thin shell of the
topological insulator needs to be simulated. Depending on the setup, we propose
to gap out the states on the undesired surfaces either by breaking the
time-reversal symmetry or by introducing a superconducting pairing. We show
that it is enough to have a thickness of the topological-insulator shell of
three to nine lattice constants. This leads to an effectively two-dimensional
scaling with minimal and fixed shell thickness. We test the idea by comparing
the spectrum and probability distribution to analytical results for both a
proximitized Dirac mode and a Dirac mode on a sphere which exhibits a
nontrivial spin-connection. The protocol yields a tight-binding model on a
cubic lattice simulating Dirac cones on arbitrary surfaces with only a small
overhead due to the finite thickness of the shell.Comment: 10 pages, 7 figure
Simulating Floquet topological phases in static systems
We show that scattering from the boundary of static, higher-order topological
insulators (HOTIs) can be used to simulate the behavior of (time-periodic)
Floquet topological insulators. We consider D-dimensional HOTIs with gapless
corner states which are weakly probed by external waves in a scattering setup.
We find that the unitary reflection matrix describing back-scattering from the
boundary of the HOTI is topologically equivalent to a (D-1)-dimensional
nontrivial Floquet operator. To characterize the topology of the reflection
matrix, we introduce the concept of `nested' scattering matrices. Our results
provide a route to engineer topological Floquet systems in the lab without the
need for external driving. As benefit, the topological system does not to
suffer from decoherence and heating.Comment: 31 pages, 8 figures. Updated the paper based on the referee reports
at https://scipost.org/submissions/2001.08217
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Anomalous levitation and annihilation in Floquet topological insulators
Anderson localization in two-dimensional topological insulators takes place via the so-called levitation and pair annihilation process. As disorder is increased, extended bulk states carrying opposite topological invariants move towards each other in energy, reducing the size of the topological gap, eventually meeting and localizing. This results in a topologically trivial Anderson insulator. Here, we introduce the anomalous levitation and pair annihilation, a process unique to periodically driven, or Floquet, systems. Due to the periodicity of the quasienergy spectrum, we find it is possible for the topological gap to increase as a function of disorder strength. Thus, after all bulk states have localized, the system remains topologically nontrivial, forming an anomalous Floquet-Anderson insulator (AFAI) phase. We show a concrete example for this process, adding disorder via on-site potential “kicks” to a Chern insulator model. By changing the period between kicks, we can tune which type of (conventional or anomalous) levitation and annihilation occurs in the system. We expect our results to be applicable to generic Floquet topological systems and to provide an accessible way to realize AFAIs experimentally, without the need for multistep driving schemes
Anomalous levitation and annihilation in Floquet topological insulators
Anderson localization in two-dimensional topological insulators takes place
via the so-called levitation and pair annihilation process. As disorder is
increased, extended bulk states carrying opposite topological invariants move
towards each other in energy, reducing the size of the topological gap,
eventually meeting and localizing. This results in a topologically trivial
Anderson insulator. Here, we introduce the anomalous levitation and pair
annihilation, a process unique to periodically-driven, or Floquet systems. Due
to the periodicity of the quasienergy spectrum, we find it is possible for the
topological gap to increase as a function of disorder strength. Thus, after all
bulk states have localized, the system remains topologically nontrivial,
forming an anomalous Floquet Anderson insulator (AFAI) phase. We show a
concrete example for this process, adding disorder via onsite potential "kicks"
to a Chern insulator model. By changing the period between kicks, we can tune
which type of (conventional or anomalous) levitation-and-annihilation occurs in
the system. We expect our results to be applicable to generic Floquet
topological systems and to provide an accessible way to realize AFAIs
experimentally, without the need for multi-step driving schemes.Comment: 5+4 pages, 5+5 figures, v2: this is the final, published versio
Lack of near-sightedness principle in non-Hermitian systems
The non-Hermitian skin effect is a phenomenon in which an extensive number of
states accumulates at the boundaries of a system. It has been associated to
nontrivial topology, with nonzero bulk invariants predicting its appearance and
its position in real space. Here we demonstrate that the non-Hermitian skin
effect is not a topological phenomenon in general: when translation symmetry is
broken by a single non-Hermitian impurity, skin modes are depleted at the
boundary and accumulate at the impurity site, without changing any bulk
invariant. This may occur even for a fully Hermitian bulk
Floquet-Anderson localization in the Thouless pump and how to avoid it
We investigate numerically how onsite disorder affects conduction in the
periodically driven Rice-Mele model, a prototypical realization of the Thouless
pump. Although the pump is robust against disorder in the fully adiabatic
limit, much less is known about the case of finite period time , which is
relevant also in light of recent experimental realizations. We find that at any
fixed period time and nonzero disorder, increasing the system size
always leads to a breakdown of the pump, indicating Anderson localization of
the Floquet states. Our numerics indicate, however, that in a properly defined
thermodynamic limit, where is kept constant, Anderson localization
can be avoided, and the charge pumped per cycle has a well-defined value -- as
long as the disorder is not too strong. The critical exponent is not
universal, rather, its value depends on the disorder strength. Our findings are
relevant for practical, experimental realizations of the Thouless pump, for
studies investigating the nature of its current-carrying Floquet eigenstates,
as well as the mechanism of the full breakdown of the pump, expected if the
disorder exceeds a critical value.Comment: 5+5 pages, 4+6 figure