1,567 research outputs found
Abelianization of BPS Quivers and the Refined Higgs Index
We count Higgs "phase" BPS states of general non-Abelian quiver, possibly
with loops, by mapping the problem to its Abelian, or toric, counterpart and
imposing Weyl invariance later. Precise Higgs index computation is particularly
important for quivers with superpotentials; the Coulomb "phase" index is
recently shown to miss important BPS states, dubbed intrinsic Higgs states or
quiver invariants. We demonstrate how the refined Higgs index is naturally
decomposed to a sum over partitions of the charge. We conjecture, and show in
simple cases, that this decomposition expresses the Higgs index as a sum over a
set of partition-induced Abelian quivers of the same total charge but
generically of smaller rank. Unlike the previous approach inspired by a similar
decomposition of the Coulomb index, our formulae compute the quiver invariants
directly, and thus offer a self-complete routine for counting BPS states.Comment: 38 pages, 13 figure
Emergence of Two-Dimensional Massless Dirac Fermions, Chiral Pseudospins, and Berry's Phase in Potassium Doped Few-Layer Black Phosphorus
Thin flakes of black phosphorus (BP) are a two-dimensional (2D) semiconductor
whose energy gap is predicted being sensitive to the number of layers and
external perturbations. Very recently, it was found that a simple method of
potassium (K) doping on the surface of BP closes its band gap completely,
producing a Dirac semimetal state with a linear band dispersion in the armchair
direction and a quadratic one in the zigzag direction. Here, based on
first-principles density functional calculations, we predict that, beyond the
critical K density of the gap closure, 2D massless Dirac Fermions (i.e., Dirac
cones) emerge in K-doped few-layer BP, with linear band dispersions in all
momentum directions, and the electronic states around Dirac points have chiral
pseudospins and Berry's phase. These features are robust with respect to the
spin-orbit interaction and may lead to graphene-like electronic transport
properties with greater flexibility for potential device applications
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