We study the linear optical conductivity of the ${\mathrm{Nb}}_{2n+1}{\mathrm{Si}}_n{\mathrm{Te}}_{4n+2}$ family of layered van der Waals materials, which has recently attracted considerable attention owing to its dimensionality-tunable electronic structure with a quasi-one-dimensional nodal-line state. At zero temperature, we analytically show that the Drude weight exhibits strong anisotropy: Along the transverse direction it is finite at charge neutrality, whereas in the nodal-line direction it vanishes quadratically with Fermi energy. On the other hand, the interband optical conductivity exhibits the same linear frequency dependence along both the longitudinal and transverse directions, with only a direction-dependent slope in the low-frequency regime. We further analyze the leading finite-temperature corrections to the intraband and interband optical conductivities, showing that the zero-temperature results remain valid up to experimentally relevant temperatures.

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• Topological materials
• van der Waals systems
• Linear response theory