Workshop book - Physikzentrum der RWTH Aachen - RWTH Aachen ...

Posters Tuesday February 5
Poster 28:
Explicit staggered grid finite difference scheme for (2+1)D Dirac fermions
René Hammer
We study the dynamics of Dirac fermion wave packets on magnetically structured
surfaces of topological insulators and propose a gate-controlled Dirac
fermion interferometer based on a solitonic domain wall structure which functions
as a transistor. A preliminary summary of related work can be found
online (arXiv:1205.6941). Work supported by FWF Project P21289-N16
We discuss and compare several algorithms for a numerical solution of the
time-dependent Dirac equation in 2 spatial dimensions which allow the use of
a finite simulation region for open boundary situations. The newly proposed
explicit finite difference schemes use space and time staggering of the grid,
showing a computational complexity growing only linearly with the number
of space-time grid-points. One of them preserves the linear dispersion relation
of the Weyl equation for wave vectors aligned with the grid and yields only
one additional Dirac cone. The second scheme leads to a purely monotonic
free-particle dispersion avoiding an additional cone altogether. We discuss the
energy dispersion relation, the proof of stability, a definition of the norm on
the staggered grid, and the important issue of absorbing boundary conditions.
These schemes are useful for numerical studies of Dirac fermions on topological
insulators, where the surface state energy spectrum can be m! anipulat ed
by perturbations which break time-reversal symmetry introducing an energy
gap. Work supported by FWF Project P21289-N16
René Hammer, Christian Ertler, and Walter Pötz
Poster 29:
Microwave-controlled manipulation of Majorana bound states
Thomas Schmidt
Majorana bound states have been proposed as building blocks for qubits on
which certain operations can be performed in a topologically protected way
using braiding. However, the set of these protected operations is not sufficient
to realize universal quantum computing. We show that the electric field in
a microwave cavity can induce Rabi oscillations between adjacent Majorana
bound states. These oscillations can be used to implement an additional
single-qubit gate. Supplemented with one braiding operation, this gate allows
to perform arbitrary single-qubit operations.
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