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3D quantum Hall effects in Dirac loops

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Nodal line semimetals describe a class of 3D systems where the low energy bands have Dirac quasiparticles along a closed line in momentum space (Dirac loop) rather than a discrete set of Dirac points [1]. Away from half filling, the Fermi surface is a toroid. In the presence of spin orbit coupling effects, this system can behave as a strong topological insulator, with topologically protected surface states. In spite of being three dimensional, this system has Landau level quantization at finite field for certain field geometries. One conceptually interesting family of lattice models that describes this physics is the family of the hyperhoneycomb lattices, which form 3D structures of crossed 1D chains where all sites have the same planar trigonal connectivity of graphene. In this talk, I will show that Coulomb interactions could drive the system to show an anomalous quantum Hall effect (AQHE) [2], with current loops that produce zero net flux in the 3D unit cell. I will show that in the AQH state, because of lack of inversion symmetry, the Haldane mass has nodes along the nodal line, giving rise to pairs of Weyl points connected by Fermi arcs. I will discuss the anomalous Hall conductivity of this system and the connections with strain field deformations encoded in the elastic Hall viscosity [3].

[1] K. Mullen, B. Uchoa, D. Glatzhofer, Phys. Rev. Lett. 115, 026403 (2015).

[2] S. W. Kim, K. Seo, B. Uchoa, Phys. Rev. B 97 , 201101® (2018).

[3] S. W. Kim, B. Uchoa, arXiv:1901.00574 (2019).

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