4,484 research outputs found
Entanglement in a second order topological insulator on a square lattice
In a -dimensional topological insulator of order , there are zero
energy states on its corners which have close relationship with its
entanglement behaviors. We studied the bipartite entanglement spectra for
different subsystem shapes and found that only when the entanglement boundary
has corners matching the lattice, exact zero modes exist in the entanglement
spectrum corresponding to the zero energy states caused by the same physical
corners. We then considered finite size systems in which case these corner
states are coupled together by long range hybridizations to form a multipartite
entangled state. We proposed a scheme to calculate the quadripartite
entanglement entropy on the square lattice, which is well described by a
four-sites toy model and thus provides another way to identify the higher order
topological insulators from the multipartite entanglement point of view.Comment: 5 pages, 3 figure
Electronic structure near an impurity and terrace on the surface of a 3-dimensional topological insulator
Motivated by recent scanning tunneling microscopy experiments on surfaces of
BiSb\cite{yazdanistm,gomesstm} and
BiTe,\cite{kaptunikstm,xuestm} we theoretically study the electronic
structure of a 3-dimensional (3D) topological insulator in the presence of a
local impurity or a domain wall on its surface using a 3D lattice model. While
the local density of states (LDOS) oscillates significantly in space at
energies above the bulk gap, the oscillation due to the in-gap surface Dirac
fermions are very weak. The extracted modulation wave number as a function of
energy satisfies the Dirac dispersion for in-gap energies and follows the
border of the bulk continuum above the bulk gap. We have also examined
analytically the effects of the defects by using a pure Dirac fermion model for
the surface states and found that the LDOS decays asymptotically faster at
least by a factor of 1/r than that in normal metals, consistent with the
results obtained from our lattice model.Comment: 7 pages, 5 figure
Vortex State in Na_xCoO_2.yH_2O: p_x\pm ip_y-wave versus d_{x^2-y^2}\pm id_{xy}-wave Pairing
Based on an effective Hamiltonian specified in the triangular lattice with
possible - or -wave pairing, which has
close relevance to the newly discovered NaCoOHO, the
electronic structure of the vortex state is studied by solving the
Bogoliubov-de Gennes equations. It is found that -wave is favored
for the electron doping as the hopping integral . The lowest-lying vortex
bound states are found to have respectively zero and positive energies for
- and -wave superconductors, whose vortex
structures exhibit the intriguing six-fold symmetry. In the presence of strong
on-site repulsion, the antiferromagnetic and ferromagnetic orders are induced
around the vortex cores for the former and the latter, respectively, both of
which cause the splitting of the LDOS peaks due to the lifting of spin
degeneracy. STM and NMR measurements are able to probe the new features of
vortex states uncovered in this work.Comment: 4 pages, 4 figures, The slightly shorter version was submitted to PR
Anderson Impurity in Helical Metal
We use a trial wave function to study the spin-1/2 Kondo effect of a helical
metal on the surface of a three-dimensional topological insulator. While the
impurity spin is quenched by conduction electrons, the spin-spin correlation of
the conduction electron and impurity is strongly anisotropic in both spin and
spatial spaces. As a result of strong spin-orbit coupling, the out-of-plane
component of the impurity spin is found to be fully screened by the orbital
angular momentum of the conduction electrons.Comment: The published versio
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