Nodal-line transition induced Landau gap in strained lattices

In topological semimetals, the bands can cross at points or lines with different dimensionality and connectivity in momentum space. For graphene and other systems hosting zero-dimensional band touching points, inhomogeneous strain is used to shift the nodal points to mimic gauge fields, whereas the one-dimensional nodal lines can transit between topologically distinct structures in strain fields. Such a nodal-line transition can provide a powerful way to engineer the electronic properties. Here we study the strain-induced Landau quantization for diamond lattices, where nodal chains split into separate lines. The nodal-line transition opens a finite Landau gap for the critical chain point with a vanishing Fermi velocity, which is impossible to be opened in the scenario of magnetic fields or nodal-point systems. Besides the unconventional energy quantization near the chain point, the strained diamond lattices exhibit perfect flat bands in three dimensions with a $\sqrt{n}$-scaling $(n$ is an integer). We also investigate the associated edge states and the line-dependent Hall response. Our work provides an avenue towards understanding the profound roles of nodal-line transition in topological matter and paves the way to study the interplay between strain and higher-dimensional nodal manifolds in arbitrary dimensions.