4,403 research outputs found
Effects of electron scattering on the topological properties of nanowires: Majorana fermions from disorder and superlattices
We focus on inducing topological state from regular, or irregular scattering
in (i) p-wave superconducting wires and (ii) Rashba wires proximity coupled to
an s-wave superconductor. We find that contrary to common expectations the
topological properties of both systems are fundamentally different: In p-wave
wires, disorder generally has a detrimental effect on the topological order and
the topological state is destroyed beyond a critical disorder strength. In
contrast, in Rashba wires, which are relevant for recent experiments, disorder
can {\it induce} topological order, reducing the need for quasiballistic
samples to obtain Majorana fermions. Moreover, we find that the total phase
space area of the topological state is conserved for long disordered Rashba
wires, and can even be increased in an appropriately engineered superlattice
potential.Comment: 5 pages, 3 figs, RevTe
Robustness of edge states in graphene quantum dots
We analyze the single particle states at the edges of disordered graphene
quantum dots. We show that generic graphene quantum dots support a number of
edge states proportional to circumference of the dot over the lattice constant.
Our analytical theory agrees well with numerical simulations. Perturbations
breaking electron-hole symmetry like next-nearest neighbor hopping or edge
impurities shift the edge states away from zero energy but do not change their
total amount. We discuss the possibility of detecting the edge states in an
antidot array and provide an upper bound on the magnetic moment of a graphene
dot.Comment: Added figure 6, extended discussion (version as accepted by Physical
Review B
Graphene Rings in Magnetic Fields: Aharonov-Bohm Effect and Valley Splitting
We study the conductance of mesoscopic graphene rings in the presence of a
perpendicular magnetic field by means of numerical calculations based on a
tight-binding model. First, we consider the magnetoconductance of such rings
and observe the Aharonov-Bohm effect. We investigate different regimes of the
magnetic flux up to the quantum Hall regime, where the Aharonov-Bohm
oscillations are suppressed. Results for both clean (ballistic) and disordered
(diffusive) rings are presented. Second, we study rings with smooth mass
boundary that are weakly coupled to leads. We show that the valley degeneracy
of the eigenstates in closed graphene rings can be lifted by a small magnetic
flux, and that this lifting can be observed in the transport properties of the
system.Comment: 12 pages, 9 figure
Interfaces Within Graphene Nanoribbons
We study the conductance through two types of graphene nanostructures:
nanoribbon junctions in which the width changes from wide to narrow, and curved
nanoribbons. In the wide-narrow structures, substantial reflection occurs from
the wide-narrow interface, in contrast to the behavior of the much studied
electron gas waveguides. In the curved nanoribbons, the conductance is very
sensitive to details such as whether regions of a semiconducting armchair
nanoribbon are included in the curved structure -- such regions strongly
suppress the conductance. Surprisingly, this suppression is not due to the band
gap of the semiconducting nanoribbon, but is linked to the valley degree of
freedom. Though we study these effects in the simplest contexts, they can be
expected to occur for more complicated structures, and we show results for
rings as well. We conclude that experience from electron gas waveguides does
not carry over to graphene nanostructures. The interior interfaces causing
extra scattering result from the extra effective degrees of freedom of the
graphene structure, namely the valley and sublattice pseudospins.Comment: 19 pages, published version, several references added, small changes
to conclusion
One-loop surface tensions of (supersymmetric) kink domain walls from dimensional regularization
We consider domain walls obtained by embedding the 1+1-dimensional
-kink in higher dimensions. We show that a suitably adapted dimensional
regularization method avoids the intricacies found in other regularization
schemes in both supersymmetric and non-supersymmetric theories. This method
allows us to calculate the one-loop quantum mass of kinks and surface tensions
of kink domain walls in a very simple manner, yielding a compact d-dimensional
formula which reproduces many of the previous results in the literature. Among
the new results is the nontrivial one-loop correction to the surface tension of
a 2+1 dimensional N=1 supersymmetric kink domain wall with chiral domain-wall
fermions.Comment: 23 pages, LATeX; v2: 25 pages, 2 references added, extended
discussion of renormalization schemes which dispels apparent contradiction
with previous result
Majorana bound states without vortices in topological superconductors with electrostatic defects
Vortices in two-dimensional superconductors with broken time-reversal and
spin-rotation symmetry can bind states at zero excitation energy. These
socalled Majorana bound states transform a thermal insulator into a thermal
metal and may be used to encode topologically protected qubits. We identify an
alternative mechanism for the formation of Majorana bound states, akin to the
way in which Shockley states are formed on metal surfaces: An atomic-scale
electrostatic line defect can have a pair of Majorana bound states at the end
points. The Shockley mechanism explains the appearance of a thermal metal in
vortex-free lattice models of chiral p-wave superconductors and (unlike the
vortex mechanism) is also operative in the topologically trivial phase.Comment: 8 pages, 7 figures; the appendices are included as supplemental
material in the published versio
Theory of the topological Anderson insulator
We present an effective medium theory that explains the disorder-induced
transition into a phase of quantized conductance, discovered in computer
simulations of HgTe quantum wells. It is the combination of a random potential
and quadratic corrections proportional to p^2 sigma_z to the Dirac Hamiltonian
that can drive an ordinary band insulator into a topological insulator (having
an inverted band gap). We calculate the location of the phase boundary at weak
disorder and show that it corresponds to the crossing of a band edge rather
than a mobility edge. Our mechanism for the formation of a topological Anderson
insulator is generic, and would apply as well to three-dimensional
semiconductors with strong spin-orbit coupling.Comment: 4 pages, 3 figures (updated figures, calculated DOS
Quantized conductance at the Majorana phase transition in a disordered superconducting wire
Superconducting wires without time-reversal and spin-rotation symmetries can
be driven into a topological phase that supports Majorana bound states. Direct
detection of these zero-energy states is complicated by the proliferation of
low-lying excitations in a disordered multi-mode wire. We show that the phase
transition itself is signaled by a quantized thermal conductance and electrical
shot noise power, irrespective of the degree of disorder. In a ring geometry,
the phase transition is signaled by a period doubling of the magnetoconductance
oscillations. These signatures directly follow from the identification of the
sign of the determinant of the reflection matrix as a topological quantum
number.Comment: 7 pages, 4 figures; v3: added appendix with numerics for long-range
disorde
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