60 research outputs found
Berry-phase description of Topological Crystalline Insulators
We study a class of translational-invariant insulators with discrete
rotational symmetry. These insulators have no spin-orbit coupling, and in some
cases have no time-reversal symmetry as well, i.e., the relevant symmetries are
purely crystalline. Nevertheless, topological phases exist which are
distinguished by their robust surface modes. Like many well-known topological
phases, their band topology is unveiled by the crystalline analog of Berry
phases, i.e., parallel transport across certain non-contractible loops in the
Brillouin zone. We also identify certain topological phases without any robust
surface modes -- they are uniquely distinguished by parallel transport along
bent loops, whose shapes are determined by the symmetry group. Our findings
have experimental implications in cold-atom systems, where the crystalline
Berry phase has been directly measured.Comment: Latest version is accepted to PR
Wilson-Loop Characterization of Inversion-Symmetric Topological Insulators
The ground state of translationally-invariant insulators comprise bands which
can assume topologically distinct structures. There are few known examples
where this distinction is enforced by a point-group symmetry alone. In this
paper we show that 1D and 2D insulators with the simplest point-group symmetry
- inversion - have a classification. In 2D, we identify a relative
winding number that is solely protected by inversion symmetry. By analysis of
Berry phases, we show that this invariant has similarities with the first Chern
class (of time-reversal breaking insulators), but is more closely analogous to
the invariant (of time-reversal invariant insulators). Implications of
our work are discussed in holonomy, the geometric-phase theory of polarization,
the theory of maximally-localized Wannier functions, and in the entanglement
spectrum.Comment: The updated version is accepted in Physical Review
Topo-fermiology
The modern semiclassical theory of a Bloch electron in a magnetic field now
encompasses the orbital magnetic moment and the geometric phase. These two
notions are encoded in the Bohr-Sommerfeld quantization condition as a phase
() that is subleading in powers of the field; is measurable
in the phase offset of the de Haas-van Alphen oscillation, as well as of
fixed-bias oscillations of the differential conductance in tunneling
spectroscopy. In some solids and for certain field orientations,
are robustly integer-valued owing to the symmetry of the extremal orbit, i.e.,
they are the topological invariants of magnetotransport. Our comprehensive
symmetry analysis identifies solids in any (magnetic) space group for which
is a topological invariant, as well as identifies the
symmetry-enforced degeneracy of Landau levels. The analysis is simplified by
our formulation of ten (and only ten) symmetry classes for closed,
Fermi-surface orbits. Case studies are discussed for graphene, transition metal
dichalchogenides, 3D Weyl and Dirac metals, and crystalline and
topological insulators. In particular, we point out that a phase offset
in the fundamental oscillation should \emph{not} be viewed as a smoking gun for
a 3D Dirac metal.Comment: Update: (i) Generalized Lifshitz-Kosevich formulae (for the
oscillatory magnetization and density of states) which apply also in magnetic
solids. (ii) Case studies on Bi2Se3 and Na3Bi. A phase offset in the
fundamental oscillation should not be viewed as a smoking gun for a 3D Dirac
metal. (iii) A zero-sum rule for is derived for bulk orbits in
time-reversal-symmetric metal
Effect of Electron-Electron Interactions on Rashba-like and Spin-Split Systems
The role of electron-electron interactions is analyzed for Rashba-like and
spin-split systems within a tight-binding single-band Hubbard model with
on-site and all nearest-neighbor matrix elements of the Coulomb interaction. By
Rashba-like systems we refer to the Dresselhaus and Rashba spin-orbit coupled
phases; spin-split systems have spin-up and spin-down Fermi surfaces shifted
relative to each other. Both systems break parity but preserve time-reversal
symmetry. They belong to a class of symmetry-breaking ground states that
satisfy: (i) electron crystal momentum is a good quantum number (ii) these
states have no net magnetic moment and (iii) their distribution of `polarized
spin' in momentum space breaks the lattice symmetry. In this class, the
relevant Coulomb matrix elements are found to be nearest-neighbor exchange ,
pair-hopping and nearest-neighbor repulsion . These ground states lower
their energy most effectively through , hence we name them Class states.
The competing effects of on the direct and exchange energies determine
the relative stability of Class states. We show that the spin-split and
Rashba-like phases are the most favored ground states within Class because
they have the minimum anisotropy in `polarized spin'. On a square lattice we
find that the spin-split phase is always favored for near-empty bands; above a
critical filling, we predict a transition from the paramagnetic to the
Rashba-like phase at and a second transition to the spin-split state
at . An energetic comparison with ferromagnetism highlights the
importance of the role of in the stability of Class states. We discuss
the relevance of our results to (i) the and phases proposed by
Wu and Zhang in the Fermi Liquid formalism and (ii) experimental observations
of spin-orbit splitting in \emph{Au}(111) surface states
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