2,307 research outputs found
Topological superconductors as nonrelativistic limits of Jackiw-Rossi and Jackiw-Rebbi models
We argue that the nonrelativistic Hamiltonian of p_x+ip_y superconductor in
two dimensions can be derived from the relativistic Jackiw-Rossi model by
taking the limit of large Zeeman magnetic field and chemical potential. In
particular, the existence of a fermion zero mode bound to a vortex in the
p_x+ip_y superconductor can be understood as a remnant of that in the
Jackiw-Rossi model. In three dimensions, the nonrelativistic limit of the
Jackiw-Rebbi model leads to a "p+is" superconductor in which spin-triplet
p-wave and spin-singlet s-wave pairings coexist. The resulting Hamiltonian
supports a fermion zero mode when the pairing gaps form a hedgehoglike
structure. Our findings provide a unified view of fermion zero modes in
relativistic (Dirac-type) and nonrelativistic (Schr\"odinger-type)
superconductors.Comment: 7 pages, no figure; published versio
Isolated Flat Bands and Spin-1 Conical Bands in Two-Dimensional Lattices
Dispersionless bands, such as Landau levels, serve as a good starting point
for obtaining interesting correlated states when interactions are added. With
this motivation in mind, we study a variety of dispersionless ("flat") band
structures that arise in tight-binding Hamiltonians defined on hexagonal and
kagome lattices with staggered fluxes. The flat bands and their neighboring
dispersing bands have several notable features: (a) Flat bands can be isolated
from other bands by breaking time reversal symmetry, allowing for an extensive
degeneracy when these bands are partially filled; (b) An isolated flat band
corresponds to a critical point between regimes where the band is electron-like
or hole-like, with an anomalous Hall conductance that changes sign across the
transition; (c) When the gap between a flat band and two neighboring bands
closes, the system is described by a single spin-1 conical-like spectrum,
extending to higher angular momentum the spin-1/2 Dirac-like spectra in
topological insulators and graphene; and (d) some configurations of parameters
admit two isolated parallel flat bands, raising the possibility of exotic
"heavy excitons"; (e) We find that the Chern number of the flat bands, in all
instances that we study here, is zero.Comment: 7 pages. Sec. II slightly expanded. References adde
Topological qubits in graphenelike systems
The fermion-doubling problem can be an obstacle to getting half-a-qubit in
two-dimensional fermionic tight-binding models in the form of Majorana zero
modes bound to the core of superconducting vortices. We argue that the number
of such Majorana zero modes is determined by a Z_2 x Z_2 topological charge for
a family of two-dimensional fermionic tight-binding models ranging from
noncentrosymmetric materials to graphene. This charge depends on the dimension
of the representation (i.e., the number of species of Dirac fermions -- where
the doubling problem enters) and the parity of the Chern number induced by
breaking time-reversal symmetry. We show that in graphene there are as many as
ten order parameters that can be used in groups of four to change the
topological number from even to odd.Comment: 5 pages; 2 figures; 1 tabl
Topological Hubbard model and its high-temperature quantum Hall effect
The quintessential two-dimensional lattice model that describes the
competition between the kinetic energy of electrons and their short-range
repulsive interactions is the repulsive Hubbard model. We study a time-reversal
symmetric variant of the repulsive Hubbard model defined on a planar lattice:
Whereas the interaction is unchanged, any fully occupied band supports a
quantized spin Hall effect. We show that at 1/2 filling of this band, the
ground state develops spontaneously and simultaneously Ising ferromagnetic
long-range order and a quantized charge Hall effect when the interaction is
sufficiently strong. We ponder on the possible practical applications, beyond
metrology, that the quantized charge Hall effect might have if it could be
realized at high temperatures and without external magnetic fields in strongly
correlated materials.Comment: 11 pages, 5 figure
Time-reversal symmetric hierarchy of fractional incompressible liquids
We provide an effective description of fractional topological insulators that
include the fractional quantum spin Hall effect by considering the
time-reversal symmetric pendant to the topological quantum field theories that
encode the Abelian fractional quantum Hall liquids. We explain the hierarchical
construction of such a theory and establish for it a bulk-edge correspondence
by deriving the equivalent edge theory for chiral bosonic fields. Further, we
compute the Fermi-Bose correlation functions of the edge theory and provide
representative ground state wave functions for systems described by the bulk
theory.Comment: 14 page
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