743 research outputs found
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
Creation of nonlocal spin-entangled electrons via Andreev tunneling, Coulomb blockade and resonant transport
We discuss several scenarios for the creation of nonlocal spin-entangled
electrons which provide a source of electronic Einstein-Podolsky-Rosen (EPR)
pairs. The central idea is to exploit the spin correlations naturally present
in superconductors in form of Cooper pairs. We show that nonlocal
spin-entanglement in form of an effective Heisenberg spin interaction is
induced between electron spins residing on two quantum dots with no direct
coupling between them but each of them being tunnel-coupled to the same
superconductor. We then discuss a nonequilibrium setup where mobile and
nonlocal spin-entanglement can be created by coherent injection of two
electrons in an Andreev tunneling process into two spatially separated quantum
dots and subsequently into two Fermi-liquid leads. The current for injecting
two spin-entangled electrons into different leads shows a resonance whereas
tunneling via the same dot into the same lead is suppressed by the Coulomb
blockade effect of the quantum dots. The Aharonov-Bohm oscillations in the
current are shown to contain h/e and h/2e periods. Finally we discuss a
structure consisting of a superconductor weakly coupled to two separate
Luttinger liquid leads. We show that strong correlations again suppress the
coherent subsequent tunneling of two electrons into the same lead, thus
generating again nonlocal spin-entangled electrons.Comment: 15 pages, 6 figures; proceedings Spintronics conference 2001,
Georgetown-University, Washington D
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
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
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
Spin orbit-induced anisotropic conductivity of a disordered 2DEG
We present a semi-automated computer-assisted method to generate and
calculate diagrams in the disorder averaging approach to disordered 2D
conductors with intrinsic spin-orbit interaction (SOI). As an application, we
calculate the effect of the SOI on the charge conductivity for disordered 2D
systems and rings in the presence of Rashba and Dresselhaus SOI. In an
infinite-size 2D system, anisotropic corrections to the conductivity tensor
arise due to phase-coherence and the interplay of Rashba and Dresselhaus SOI.
The effect is more pronounced in the quasi-onedimensional case, where the
conductivity becomes anisotropic already in the presence of only one type of
SOI. The anisotropy further increases if the time-reversal symmetry of the
Hamiltonian is broken.Comment: 20 pages, 8 figure
Cluster States From Heisenberg Interaction
We show that a special type of entangled states, cluster states, can be
created with Heisenberg interactions and local rotations in 2d steps where d is
the dimension of the lattice. We find that, by tuning the coupling strengths,
anisotropic exchange interactions can also be employed to create cluster
states. Finally, we propose electron spins in quantum dots as a possible
realization of a one-way quantum computer based on cluster states
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