Parity Anomaly in the non-linear response of Nodal-Line Semimetals

Abstract

Nodal-line semimetals are topological semimetals characterized by one-dimensional band-touching loops protected by the combined symmetry of inversion $\mathcal{P}$ and time-reversal $\mathcal{T}$ in absence of spin-orbit coupling. These nodal loops can be understood as a one-parameter family of Dirac points exhibiting the parity anomaly associated to $\mathcal{P}\ast \mathcal{T}$ symmetry. We find that the parity anomaly also appears in the non-linear optical response of these systems in an analogous way to the linear response transport. We analyze the presence of a tilting term in the Hamiltonian as an element that does not spoil $\mathcal{P}\ast \mathcal{T}$ symmetry: while it is $\mathcal{P}\ast \mathcal{T}$-symmetric, it breaks separately both $\mathcal{P}$ and $\mathcal{T}$ symmetries, allowing for the potential experimental observability of the linear and non-linear Hall conductivities in appropriate nodal-line semimetals.

11 pages, 5 figures. Version similar to the published one in PRB

References in corpus (12)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological response in Weyl semimetals and the chiral anomaly
• 3D Dirac semimetals: current materials, design principles and predictions of new materials
• The Berry curvature dipole in Weyl semimetal materials: an ab initio study
• Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals
• Rules for Phase Shifts of Quantum Oscillations in Topological Nodal-line Semimetals
• Correlation and transport phenomena in topological nodal-loop semimetals
• Surface and 3D quantum Hall effects from engineering of exceptional points in nodal-line semimetals
• Quantum anomalies in nodal line semimetals
• Quantum Oscillations in Nodal Line Systems
• Topological and trivial magnetic oscillations in nodal loop semimetals
• Magnetic field-Induced Nonlinear Optical Responses in Inversion Symmetric Dirac Semimetals

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• Strain Effects on Band Structure and Dirac Nodal-line Morphology of ZrSiSe
• Giant nonlinear response due to unconventional oscillation in Nodal-line semimetals
• Elastic gauge fields and zero-field 3D quantum Hall effect in hyperhoneycomb lattices
• Unconventional thermoelectric transport in tilted Weyl semimetals
• Kerr effect in tilted nodal loop semimetals
• Delocalization of topological surface states by diagonal disorder in nodal loop semimetals
• Electrochemical transport in Dirac nodal-line semimetals
• Two-dimensional Dirac nodal-line semimetal protected by symmetry
• Collective excitations and screening in two-dimensional tilted nodal-line semimetals
• Time dependent electric transport in nodal-loop semimetals
• Quantum Hall effect and optical magneto-conductivity of two-dimensional topological nodal-line semimetals
• Soliton Fermionic number from the heat kernel expansion