195 research outputs found
Topological Edge States and Fractional Quantum Hall Effect from Umklapp Scattering
We study anisotropic lattice strips in the presence of a magnetic field in
the quantum Hall effect regime. At specific magnetic fields, causing resonant
Umklapp scattering, the system is gapped in the bulk and supports chiral edge
states in close analogy to topological insulators. These gaps result in
plateaus for the Hall conductivity exactly at the known fillings n/m (both
positive integers and m odd) for the integer and fractional quantum Hall
effect. For double strips we find topological phase transitions with phases
that support midgap edge states with flat dispersion. The topological effects
predicted here could be tested directly in optical lattices
Fermionic and Majorana Bound States in Hybrid Nanowires with Non-Uniform Spin-Orbit Interaction
We study intragap bound states in the topological phase of a Rashba nanowire
in the presence of a magnetic field and with non-uniform spin orbit interaction
(SOI) and proximity-induced superconductivity gap. We show that fermionic bound
states (FBS) can emerge inside the proximity gap. They are localized at the
junction between two wire sections characterized by different directions of the
SOI vectors, and they coexist with Majorana bound states (MBS) localized at the
nanowire ends. The energy of the FBS is determined by the angle between the SOI
vectors and the lengthscale over which the SOI changes compared to the Fermi
wavelength and the localization length. We also consider double-junctions and
show that the two emerging FBSs can hybridize and form a double quantum
dot-like structure inside the gap. We find explicit analytical solutions of the
bound states and their energies for certain parameter regimes such as weak and
strong SOI. The analytical results are confirmed and complemented by an
independent numerical tight-binding model approach. Such FBS can act as
quasiparticle traps and thus can have implications for topological quantum
computing schemes based on braiding MBSs
Giant spin orbit interaction due to rotating magnetic fields in graphene nanoribbons
We theoretically study graphene nanoribbons in the presence of spatially
varying magnetic fields produced e.g. by nanomagnets. We show both analytically
and numerically that an exceptionally large Rashba spin orbit interaction (SOI)
of the order of 10 meV can be produced by the non-uniform magnetic field. As a
consequence, helical modes exist in armchair nanoribbons that exhibit nearly
perfect spin polarization and are robust against boundary defects. This paves
the way to realizing spin filter devices in graphene nanoribbons in the
temperature regime of a few Kelvins. If a nanoribbon in the helical regime is
in proximity contact to an s-wave superconductor, the nanoribbon can be tuned
into a topological phase sustaining Majorana fermions
Fractional Fermions with Non-Abelian Statistics
We introduce a novel class of low-dimensional topological tight-binding
models that allow for bound states that are fractionally charged fermions and
exhibit non-Abelian braiding statistics. The proposed model consists of a
double (single) ladder of spinless (spinful) fermions in the presence of
magnetic fields. We study the system analytically in the continuum limit as
well as numerically in the tight-binding representation. We find a topological
phase transition with a topological gap that closes and reopens as a function
of system parameters and chemical potential. The topological phase is of the
type BDI and carries two degenerate mid-gap bound states that are localized at
opposite ends of the ladders. We show numerically that these bound states are
robust against a wide class of perturbations
Parafermions in Interacting Nanowire Bundle
We propose a scheme to induce parafermion modes, exotic
zero-energy bound states that possess non-Abelian statistics. We consider a
minimal setup consisting of a bundle of four tunnel coupled nanowires hosting
spinless electrons that interact strongly with each other. The hallmark of our
setup is that it relies only on simple one-dimensional wires, uniform magnetic
fields, and strong interactions, but does not require the presence of
superconductivity or exotic quantum Hall phases
Integer and Fractional Quantum Hall Effect in a Strip of Stripes
We study anisotropic stripe models of interacting electrons in the presence
of magnetic fields in the quantum Hall regime with integer and fractional
filling factors. The model consists of an infinite strip of finite width that
contains periodically arranged stripes (forming supercells) to which the
electrons are confined and between which they can hop with associated magnetic
phases. The interacting electron system within the one-dimensional stripes are
described by Luttinger liquids and shown to give rise to charge and spin
density waves that lead to periodic structures within the stripe with a
reciprocal wavevector 8k_F. This wavevector gives rise to Umklapp scattering
and resonant scattering that results in gaps and chiral edge states at all
known integer and fractional filling factors \nu. The integer and odd
denominator filling factors arise for a uniform distribution of stripes,
whereas the even denominator filling factors arise for a non-uniform stripe
distribution. We calculate the Hall conductance via the Streda formula and show
that it is given by \sigma_H=\nu e^2/h for all filling factors. We show that
the composite fermion picture follows directly from the condition of the
resonant Umklapp scattering
RKKY interaction in carbon nanotubes and graphene nanoribbons
We study Rudermann-Kittel-Kasuya-Yosida (RKKY) interaction in carbon
nanotubes (CNTs) and graphene nanoribbons in the presence of spin orbit
interactions and magnetic fields. For this we evaluate the static spin
susceptibility tensor in real space in various regimes at zero temperature. In
metallic CNTs the RKKY interaction depends strongly on the sublattice and, at
the Dirac point, is purely ferromagnetic (antiferromagnetic) for the localized
spins on the same (different) sublattice, whereas in semiconducting CNTs the
spin susceptibility depends only weakly on the sublattice and is dominantly
ferromagnetic. The spin orbit interactions break the SU(2) spin symmetry of the
system, leading to an anisotropic RKKY interaction of Ising and
Moryia-Dzyaloshinsky form, besides the usual isotropic Heisenberg interaction.
All these RKKY terms can be made of comparable magnitude by tuning the Fermi
level close to the gap induced by the spin orbit interaction. We further
calculate the spin susceptibility also at finite frequencies and thereby obtain
the spin noise in real space via the fluctuation-dissipation theorem
Majorana Fermions in Ge/Si Hole Nanowires
We consider Ge/Si core/shell nanowires with hole states coupled to an
-wave superconductor in the presence of electric and magnetic fields. We
employ a microscopic model that takes into account material-specific details of
the band structure such as strong and electrically tunable Rashba-type
spin-orbit interaction and factor anisotropy for the holes. In addition,
the proximity-induced superconductivity Hamiltonian is derived starting from a
microscopic model. In the topological phase, the nanowires host Majorana
fermions with localization lengths that depend strongly on both the magnetic
and electric fields. We identify the optimal regime in terms of the directions
and magnitudes of the fields in which the Majorana fermions are the most
localized at the nanowire ends. In short nanowires, the Majorana fermions
hybridize and form a subgap fermion whose energy is split away from zero and
oscillates as a function of the applied fields. The period of these
oscillations could be used to measure the dependence of the spin-orbit
interaction on the applied electric field and the factor anisotropy.Comment: 11 pages, 7 figure
Second Order Topological Superconductivity in -Junction Rashba Layers
We consider a Josephson junction bilayer consisting of two tunnel-coupled
two-dimensional electron gas layers with Rashba spin-orbit interaction,
proximitized by a top and bottom -wave superconductor with phase difference
close to . We show that, in the presence of a finite weak in-plane
Zeeman field, the bilayer can be driven into a second order topological
superconducting phase, hosting two Majorana corner states (MCSs). If
, in a rectangular geometry, these zero-energy bound states are
located at two opposite corners determined by the direction of the Zeeman
field. If the phase difference deviates from by a critical value,
one of the two MCSs gets relocated to an adjacent corner. As the phase
difference increases further, the system becomes trivially gapped. The
obtained MCSs are robust against static and magnetic disorder. We propose two
setups that could realize such a model: one is based on controlling by
magnetic flux, the other involves an additional layer of randomly-oriented
magnetic impurities responsible for the phase shift of in the
proximity-induced superconducting pairing
Finite-size effects in a nanowire strongly coupled to a thin superconducting shell
We study the proximity effect in a one-dimensional nanowire strongly coupled
to a finite superconductor with a characteristic size which is much shorter
than its coherence length. Such geometries have become increasingly relevant in
recent years in the experimental search for Majorana fermions with the
development of thin epitaxial Al shells which form a very strong contact with
either InAs or InSb nanowires. So far, however, no theoretical treatment of the
proximity effect in these systems has accounted for the finite size of the
superconducting film. We show that the finite-size effects become very
detrimental when the level spacing of the superconductor greatly exceeds its
energy gap. Without any fine-tuning of the size of the superconductor (on the
scale of the Fermi wavelength), the tunneling energy scale must be larger than
the level spacing in order to reach the hard gap regime which is seen
ubiquitously in the experiments. However, in this regime, the large tunneling
energy scale induces a large shift in the effective chemical potential of the
nanowire and pushes the topological phase transition to magnetic field
strengths which exceed the critical field of Al.Comment: 14 pages, 9 figure
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