Higher-Order Weyl Semimetals*

We investigate higher-order Weyl semimetals (HOWSMs) having bulk Weyl nodes attached to both surface and hinge Fermi arcs. We identify a new type of Weyl node, that we dub a $2nd$ order Weyl node, that can be identified as a transition in momentum space in which both the Chern number and a higher-order topological invariant change. As a proof of concept we use a model of stacked higher-order quadrupole insulators (QI) to identify three types of WSM phases: $1st$-order, $2nd$-order, and hybrid-order. The model can also realize type-II and hybrid-tilt WSMs with various surface and hinge arcs. Next, we discuss three remarkable results on various mechanisms of gapping out the $2nd$-order Weyl nodes including (i) coupling to a $1st$-order node as well as the nesting of nodes in presence of charge-density wave (CDW) order in (ii) inversion-symmetric and (iii) time-reversal symmetric models of HOWSMs. Moreover, we show that a measurement of charge density in the presence of magnetic flux can help to identify some classes of $2nd$ order WSMs. Finally, we show that periodic driving can be utilized as a way of generating HOWSMs.