Realizing Landau levels with open equifrequency contours around band singularities

Charged particles in a magnetic field undergo circular motion and result in quantized energy levels known as Landau levels (LLs). LLs around band singularites are particularly interesting due to their nontrivial topological properties. To date, through the introduction of the artificial magnetic field, LLs have been observed in systems only with closed equifrequency contours (EFCs) around band singularities, i.e. type-I Dirac or Weyl systems. Here, we demonstrate the existence of LLs with open EFCs around band singularities through combined action of artificial electric (E) and magnetic (B) fields, whereas they cannot be generated by B only. We construct an artificial platform of inhomogeneous metasurfaces of the two-dimensional type-II Dirac system with open EFCs, create suitable artificial gauge fields of E&B, and observe the emergence of E&B-induced LLs experimentally. This work presents a new insight for realizing LLs, and provides a platform for controlling optical waves propagating using artificial gauge fields.