12,177 research outputs found
Oscillatory integral operators with homogeneous polynomial phases in several variables
We obtain decay estimates in for oscillatory integral
operators whose phase functions are homogeneous polynomials of degree m and
satisfy various genericity assumptions. The decay rates obtained are optimal in
the case of (2+2)--dimensions for any m while, in higher dimensions, the result
is sharp for m sufficiently large. The proof for large follows from
essentially algebraic considerations. For cubics in (2+2)--dimensions, the
proof involves decomposing the operator near the conic zero variety of the
determinant of the Hessian of the phase function, using an elaboration of the
general approach of Phong and Stein [1994].Comment: 39 pages, 2 figures; minor corrections; to appear in Journal of
Functional Analysi
Efficient Topological Materials Discovery Using Symmetry Indicators
Although the richness of spatial symmetries has led to a rapidly expanding
inventory of possible topological crystalline (TC) phases of electrons,
physical realizations have been slow to materialize due to the practical
difficulty to ascertaining band topology in realistic calculations. Here, we
integrate the recently established theory of symmetry indicators of band
topology into first-principle band-structure calculations, and test it on a
databases of previously synthesized crystals. The combined algorithm is found
to efficiently unearth topological materials and predict topological properties
like protected surface states. On applying our algorithm to just 8 out of the
230 space groups, we already discover numerous materials candidates displaying
a diversity of topological phenomena, which are simultaneously captured in a
single sweep. The list includes recently proposed classes of TC insulators that
had no previous materials realization as well as other topological phases,
including: (i) a screw-protected 3D TC insulator, \b{eta}-MoTe2, with gapped
surfaces except for 1D helical "hinge" states; (ii) a rotation-protected TC
insulator BiBr with coexisting surface Dirac cones and hinge states; (iii)
non-centrosymmetric Z2 topological insulators undetectable using the
well-established parity criterion, AgXO (X=Na,K,Rb); (iv) a Dirac semimetal
MgBi2O6; (v) a Dirac nodal-line semimetal AgF2; and (vi) a metal with
three-fold degenerate band crossing near the Fermi energy, AuLiMgSn. Our work
showcases how the recent theoretical insights on the fundamentals of band
structures can aid in the practical goal of discovering new topological
materials
- …