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The bulk properties of nodal line materials have been an important researchtopic in recent years. In this paper, we study the orbital magneticsusceptibility and the Hall conductivity of nodal line materials using theformalism with thermal Green's functions and find characteristic singularbehaviors of them. It is shown that, in the vicinity of the gapless nodal line,the orbital magnetic susceptibility shows a $\delta$-function singularity andthe Hall conductivity shows a step function behavior in their chemicalpotential dependences. Furthermore, these singular behaviors are found to showstrong field angle dependences corresponding to the orientation of the nodalline in the momentum space. These singular behaviors and strong angledependences will give clear evidence for the presence of the nodal line and itsorientation and can be used to experimentally detect nodal line materials.

Characteristic singular behaviors of nodal line materials emerging in orbital magnetic susceptibility and Hall conductivity