  Nodal chain is a typical topological phase in nodal line semimetals. Here, we
propose a new topological phase -- interlocking nodal chains, in which two sets
of nodal chains are interlocked each other. It includes one- (1D), two- (2D)
and three-dimensional (3D) versions, which can be produced by a three-band
model. The 2D and 3D interlocking nodal chains will evolve into some other
phases, such as double concentric isolated (or intersecting) nodal rings,
coexisting nodal chain and isolated (or intersecting) nodal rings. These phases
exhibit diverse surface states and Landau levels, which implies that there are
rich electronic and magnetic properties associating with them. Moreover, the 2D
interlocking nodal chains and related phase transitions can be realized in a
series of carbon networks under strain. Without strain, topological phase in
the carbon structures is double concentric isolated nodal rings. A larger
tensile strain leads to the phase transiting to an interlocking nodal chain,
while the middle phase is a coexisting phase of a nodal chain and isolated
nodal rings. In addition, stability and synthesis of the carbon networks are
discussed.
