55 research outputs found
Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe (X=Mo,W)
In recent years, transition metal dichalcogenides (TMDs) have garnered great
interest as topological materials -- monolayers of centrosymmetric
-phase TMDs have been identified as 2D topological insulators (TIs), and
bulk crystals of noncentrosymmetric -phase MoTe and WTe have
been identified as type-II Weyl semimetals. However, ARPES and STM probes of
these TMDs have revealed huge, "arc-like" surface states that overwhelm, and
are sometimes mistaken for, the much smaller topological surface Fermi arcs of
bulk type-II Weyl points. In this letter, we use first-principles calculations
and (nested) Wilson loops to analyze the bulk and surface electronic structure
of both - and -MoTe, finding that -MoTe
(-MoTe gapped with symmetry-preserving distortion) is an
inversion-symmetry-indicated -nontrivial (--) higher-order TI (HOTI) driven by double band
inversion. Both structural phases of MoTe exhibit the same surface features
as WTe, revealing that the large Fermi arcs are in fact not topologically
trivial, but are rather the characteristic split and gapped fourfold surface
states of a HOTI. We also show that, when the effects of SOC are neglected,
-MoTe is a nodal-line semimetal with -nontrivial
monopole nodal lines (MNLSM). This finding confirms that MNLSMs driven by
double band inversion are the weak-SOC limit of HOTIs, implying that MNLSMs are
higher-order topological with flat-band-like hinge states, which
we find to originate from the corner modes of 2D "fragile" TIs.Comment: Final version, 5 pg main text + 18 pg supplement, 4 + 6 figures,
abstract abridged for arXiv posting - see paper for full abstrac
Strong and fragile topological Dirac semimetals with higher-order Fermi arcs
Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s–d-hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- (α) and intermediate-temperature (α″) phases of Cd3As2, KMgBi, and rutile-structure (β′-) PtO2
Topological zero-dimensional defect and flux states in three-dimensional insulators
In insulating crystals, it was previously shown that defects with two fewer dimensions than the bulk can bind topological electronic states. We here further extend the classification of topological defect states by demonstrating that the corners of crystalline defects with integer Burgers vectors can bind 0D higher-order end (HEND) states with anomalous charge and spin. We demonstrate that HEND states are intrinsic topological consequences of the bulk electronic structure and introduce new bulk topological invariants that are predictive of HEND dislocation states in solid-state materials. We demonstrate the presence of first-order 0D defect states in PbTe monolayers and HEND states in 3D SnTe crystals. We relate our analysis to magnetic flux insertion in insulating crystals. We find that π-flux tubes in inversion- and time-reversal-symmetric (helical) higher-order topological insulators bind Kramers pairs of spin-charge-separated HEND states, which represent observable signatures of anomalous surface half quantum spin Hall states
Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
Recent developments in the relationship between bulk topology and surface
crystal symmetry have led to the discovery of materials whose gapless surface
states are protected by crystal symmetries. In fact, there exists only a very
limited set of possible surface crystal symmetries, captured by the 17
"wallpaper groups." We show that a consideration of symmetry-allowed band
degeneracies in the wallpaper groups can be used to understand previous
topological crystalline insulators, as well as to predict new examples. In
particular, the two wallpaper groups with multiple glide lines, and
, allow for a new topological insulating phase, whose surface spectrum
consists of only a single, fourfold-degenerate, true Dirac fermion. Like the
surface state of a conventional topological insulator, the surface Dirac
fermion in this "nonsymmorphic Dirac insulator" provides a theoretical
exception to a fermion doubling theorem. Unlike the surface state of a
conventional topological insulator, it can be gapped into topologically
distinct surface regions while keeping time-reversal symmetry, allowing for
networks of topological surface quantum spin Hall domain walls. We report the
theoretical discovery of new topological crystalline phases in the AB
family of materials in SG 127, finding that SrPb hosts this new
topological surface Dirac fermion. Furthermore, (100)-strained AuY and
HgSr host related topological surface hourglass fermions. We also
report the presence of this new topological hourglass phase in
BaInSb in SG 55. For orthorhombic space groups with two glides, we
catalog all possible bulk topological phases by a consideration of the allowed
non-abelian Wilson loop connectivities, and we develop topological invariants
for these systems. Finally, we show how in a particular limit, these
crystalline phases reduce to copies of the SSH model.Comment: Final version, 6 pg main text + 29 pg supplement, 6 + 13 figure
Magnetic Topological Quantum Chemistry
For over 100 years, the group-theoretic characterization of crystalline
solids has provided the foundational language for diverse problems in physics
and chemistry. However, the group theory of crystals with commensurate magnetic
order has remained incomplete for the past 70 years, due to the complicated
symmetries of magnetic crystals. In this work, we complete the 100-year-old
problem of crystalline group theory by deriving the small corepresentations,
momentum stars, compatibility relations, and magnetic elementary band
corepresentations of the 1,421 magnetic space groups (MSGs), which we have made
freely accessible through tools on the Bilbao Crystallographic Server. We
extend Topological Quantum Chemistry to the MSGs to form a complete, real-space
theory of band topology in magnetic and nonmagnetic crystalline solids -
Magnetic Topological Quantum Chemistry (MTQC). Using MTQC, we derive the
complete set of symmetry-based indicators of electronic band topology, for
which we identify symmetry-respecting bulk and anomalous surface and hinge
states.Comment: Final version, 10 pg main text + 184 pg appendix, 5 + 25 figure
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