[Show abstract][Hide abstract] ABSTRACT: It is generally thought that adiabatic exchange of two identical particles is
impossible in one spatial dimension. Here we describe a simple protocol that
permits adiabatic exchange of two Majorana fermions in a one-dimensional
topological superconductor wire. The exchange relies on the concept of
``Majorana shuttle'' whereby a $\pi$ domain wall in the superconducting order
parameter which hosts a pair of ancillary Majoranas delivers one zero mode
across the wire while the other one tunnels in the opposite direction. The
method requires some tuning of parameters and does not, therefore, enjoy the
full topological protection. The resulting exchange statistics, however,
remains non-Abelian for a wide range of parameters that characterize the
exchange.
[Show abstract][Hide abstract] ABSTRACT: Most physical systems known to date tend to resist entering the topological phase and must be fine-tuned to reach that phase. Here, we introduce a system in which a key dynamical parameter adjusts itself in response to the changing external conditions so that the ground state naturally favors the topological phase. The system consists of a quantum wire formed of individual magnetic atoms placed on the surface of an ordinary s-wave superconductor. It realizes the Kitaev paradigm of topological superconductivity when the wave vector characterizing the emergent spin helix dynamically self-tunes to support the topological phase. We call this phenomenon a self-organized topological state.
[Show abstract][Hide abstract] ABSTRACT: It has been suggested recently, based on subtle field-theoretical considerations, that the electromagnetic response of Weyl semimetals and the closely related Weyl insulators can be characterized by an axion term θE·B with space and time dependent axion angle θ(r,t). Here we construct a minimal lattice model of the Weyl medium and study its electromagnetic response by a combination of analytical and numerical techniques. We confirm the existence of the anomalous Hall effect expected on the basis of the field theory treatment. We find, contrary to the latter, that chiral magnetic effect (that is, ground state charge current induced by the applied magnetic field) is absent in both the semimetal and the insulator phase. We elucidate the reasons for this discrepancy.
[Show abstract][Hide abstract] ABSTRACT: We show that isolated Weyl nodes can arise in a system of parallel
topological insulator nano-wires arranged in a honeycomb fashion. This
introduces another theoretical example of a topological semi-metal phase with
more than one pair of Weyl nodes and due to the simple form of its Hamiltonian
it can be used to study various interesting phenomena associated with this
phase. Our result emphasizes that depending on the separation of the Weyl nodes
a topological electromagnetic response might or might not emerge and two pairs
might have overall cancelling contributions to the net anomalous Hall
conductivity.
[Show abstract][Hide abstract] ABSTRACT: It has been shown previously that a finite-length topological insulator
nanowire, proximity-coupled to an ordinary bulk s-wave superconductor and
subject to a longitudinal applied magnetic field, realizes a one-dimensional
topological superconductor with an unpaired Majorana fermion (MF) localized at
each end of the nanowire. Here, we study the stability of these MFs with
respect to various perturbations that are likely to occur in a physical
realization of the proposed device. We show that the unpaired Majorana fermions
persist in this system for any value of the chemical potential inside the bulk
band gap of order 300 meV in Bi$_2$Se$_3$ by computing the Majorana number.
From this calculation, we also show that the unpaired Majorana fermions persist
when the magnetic flux through the nanowire cross-section deviates
significantly from half flux quantum. Lastly, we demonstrate that the unpaired
Majorana fermions persist in strongly disordered wires with fluctuations in the
on-site potential ranging in magnitude up to several times the size of the bulk
band gap. These results suggest this solid-state system should exhibit unpaired
Majorana fermions under accessible conditions likely important for experimental
study or future applications.
[Show abstract][Hide abstract] ABSTRACT: The surface of a topological insulator hosts a very special form of a
quasi-two dimensional metallic system when it is embedded in a topologically
trivial medium like the vacuum. The electronic properties of this unusual 2D
metal are distinct in many aspects from both the conventional two-dimensional
electron gas systems in quantum well heterostructures as well as those of a
single layer graphene. In this paper, we study one of these distinct features
i.e., the response of the electronic spins to an applied magnetic field
perpendicular to the surface. We find an unusual behaviour of the spin
magnetization and susceptibility as a function of both the magnetic field and
the chemical potential for a generic topological surface. We propose that this
behavior could be studied by the recently developed experimental technique
called \beta NMR which is highly sensitive to the surface electron spins. We
explain how this technique could be used to probe for spontaneous magnetic
ordering caused by magnetic dopants or interactions discussed in the recent
literature.
[Show abstract][Hide abstract] ABSTRACT: The Lagrangian describing the bulk electromagnetic response of a
three-dimensional strong topological insulator contains a topological `axion'
term of the form '\theta E dot B'. It is often stated (without proof) that the
corresponding action is quantized on periodic space-time and therefore
invariant under '\theta -> \theta +2\pi'. Here we provide a simple, physically
motivated proof of the axion action quantization on the periodic space-time,
assuming only that the vector potential is consistent with single-valuedness of
the electron wavefunctions in the underlying insulator.
Physical Review B 06/2010; 82(23). DOI:10.1103/PHYSREVB.82.233103 · 3.74 Impact Factor