5,914 research outputs found
Phase diagram and phonon-induced backscattering in topological insulator nanowires
We present an effective low-energy theory of electron-phonon coupling effects for clean cylindrical topological insulator nanowires. Acoustic phonons are modelled by isotropic elastic continuum theory with stress-free boundary conditions. We take into account the deformation potential coupling between phonons and helical surface Dirac fermions, and also include electron-electron interactions within the bosonization approach. For half-integer values of the magnetic flux along the wire, the low-energy theory admits an exact solution since a topological protection mechanism then rules out phonon-induced -backscattering processes. We determine the zero-temperature phase diagram and identify a regime dominated by superconducting pairing of surface states. As example, we consider the phase diagram of HgTe nanowires. We also determine the phonon-induced electrical resistivity, where we find a quadratic dependence on the flux deviation from the nearest half-integer value
Fidelity and visibility reduction in Majorana qubits by entanglement with environmental modes
We study the dynamics and readout of topological qubits encoded by
zero-energy Majorana bound states in a topological superconductor. We take into
account bosonic modes due to the electromagnetic environment which couple the
Majorana manifold to above-gap continuum quasi-particles. This coupling causes
the degenerate ground state of the topological superconductor to be dressed in
a polaron-like manner by quasi-particle states and bosons, and the system to
become gapless. Topological protection and hence full coherence is only
maintained if the qubit is operated and read out within the low-energy spectrum
of the dressed states. We discuss reduction of fidelity and/or visibility if
this condition is violated by a quantum-dot readout that couples to the bare
(undressed) Majorana modes. For a projective measurement of the bare Majorana
basis, we formulate a Bloch-Redfield approach that is valid for weak
Majorana-environment coupling and takes into account constraints imposed by
fermion-number-parity conservation. Within the Markovian approximation, our
results essentially confirm earlier theories of finite-temperature decoherence
based on Fermi's golden rule. However, the full non-Markovian dynamics reveals,
in addition, the fidelity reduction by a projective measurement. Using a
spinless nanowire model with -wave pairing, we provide quantitative results
characterizing these effects.Comment: 18 pages, 10 figure
Parameter identification in a semilinear hyperbolic system
We consider the identification of a nonlinear friction law in a
one-dimensional damped wave equation from additional boundary measurements.
Well-posedness of the governing semilinear hyperbolic system is established via
semigroup theory and contraction arguments. We then investigte the inverse
problem of recovering the unknown nonlinear damping law from additional
boundary measurements of the pressure drop along the pipe. This coefficient
inverse problem is shown to be ill-posed and a variational regularization
method is considered for its stable solution. We prove existence of minimizers
for the Tikhonov functional and discuss the convergence of the regularized
solutions under an approximate source condition. The meaning of this condition
and some arguments for its validity are discussed in detail and numerical
results are presented for illustration of the theoretical findings
Paraconductivity in Carbon Nanotubes
We report the calculation of paraconductivity in carbon nanotubes above the
superconducting transition temperature. The complex behavior of
paraconductivity depending upon the tube radius, temperature and magnetic field
strength is analyzed. The results are qualitatively compared with recent
experimental observations in carbon nanotubes of an inherent transition to the
superconducting state and pronounced thermodynamic fluctuations above .
The application of our results to single-wall and multi-wall carbon nanotubes
as well as ropes of nanotubes is discussed.Comment: 7 pages, 1 figur
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