9 research outputs found
Complete zero-energy flat bands of surface states in fully gapped chiral noncentrosymmetric superconductors
Noncentrosymmetric superconductors can support flat bands of zero-energy
surface states in part of their surface Brillouin zone. This requires that they
obey time-reversal symmetry and have a sufficiently strong
triplet-to-singlet-pairing ratio to exhibit nodal lines in the bulk. These
bands are protected by a winding number that relies on chiral symmetry, which
is realized as the product of time-reversal and particle-hole symmetry. We
reveal a way to stabilize a flat band in the entire surface Brillouin zone,
while the bulk dispersion is fully gapped. This idea could lead to a robust
platform for quantum computation and represents an alternative route to
strongly correlated flat bands in two dimensions, besides twisted bilayer
graphene. The necessary ingredient is an additional spin-rotation symmetry that
forces the direction of the spin-orbit-coupling vector not to depend on the
momentum component normal to the surface. We define a winding number which
leads to flat zero-energy surface bands due to bulk-boundary correspondence. We
discuss under which conditions this winding number is nonzero in the entire
surface Brillouin zone and verify the occurrence of zero-energy surface states
by exact numerical diagonalization of the Bogoliubov-de Gennes Hamiltonian for
a slab. In addition, we consider how a weak breaking of the additional symmetry
affects the surface band, employing first-order perturbation theory and a
quasiclassical approximation. We find that the surface states and the bulk gap
persist for weak breaking of the additional symmetry but that the band does not
remain perfectly flat. The broadening of the band strongly depends on the
deviation of the spin-orbit-coupling vector from its unperturbed direction as
well as on the spin-orbit-coupling strength and the triplet-pairing amplitude.Comment: 18 pages, 6 figure
Is the Intrinsic Value of Macroeconomic News Announcements Related to Their Asset Price Impact?
Majorana flat bands at structured surfaces of nodal noncentrosymmetric superconductors
Surfaces of nodal noncentrosymmetric superconductors can host flat bands of
Majorana modes, which provide a promising platform for quantum computation if
one can find methods for manipulating localized Majorana wave packets. We study
the fate of such flat bands when part of the surface is subjected to an
exchange field induced by a ferromagnetic insulator. We use exact
diagonalization to find the eigenstates and eigenenergies of the Bogoliubov-de
Gennes Hamiltonian of a model system, for which an exchange field is applied
along a strip on the surface of a slab. We consider different orientations of
the strip and the applied field. If the spin polarization of the field-free
system along the field direction is sufficiently large perturbation theory
predicts that energies of states which are mostly localized on the
exchange-field strip are shifted away from zero energy by an amount
proportional to the field strength. On the other hand, energies corresponding
to states localized on the field-free strip are only weakly affected by the
field. Exact diagonalization confirms this. Moreover, we discuss a setup with a
small exchange field applied to the previously field-free strip with the goal
of introducing a linear dispersion. By switching this dispersion on and off, a
wave packet could be moved in a certain direction. We find that in our model
system, a linear dispersion can indeed be achieved. The qualitative features of
this dispersion can be predicted from the momentum-dependent spin polarization
of the field-free surface.Comment: 14 pages, 8 figure