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Low-energy electrons near Dirac/Weyl nodal points mimic massless relativisticfermions. However, as they are not constrained by Lorentz invariance, they canexhibit tipped-over type-II Dirac/Weyl cones which provide highly anisotropicphysical properties and responses, creating unique possibilities. Recently,they have been observed in several quantum and classical systems. Yet, there isstill no simple and deterministic strategy to realize them since their nodalpoints are accidental degeneracies, unlike symmetry-guaranteed type-Icounterparts. Here, we propose a band-folding scheme for constructing type-IIDirac points, and we use a tight-binding analysis to unveil its generality anddeterministic nature. Through realizations in acoustics, type-II Dirac pointsare experimentally visualized and investigated using near-field mappings. As adirect effect of tipped-over Dirac cones, strongly tilted kink statesoriginating from their valley-Hall properties are also observed. Thisdeterministic scheme could serve as platform for further investigations ofintriguing physics associated with various strongly Lorentz-violating nodalpoints.

Deterministic scheme for two-dimensional type-II Dirac points and experimental realization in acoustics