Abstract
We present effective field theories for the weakly coupled Weyl-Z2 semimetal, as well as the holographic realization for the strongly coupled case. In both cases, the anomalous systems have both the chiral anomaly and the Z2 anomaly and possess topological quantum phase transitions from the Weyl-Z2 semimetal phases to partly or fully topological trivial phases. We find that the topological phase transition is characterized by the anomalous transport parameters, i.e. the anomalous Hall conductivity and the Z2 anomalous Hall conductivity. These two parameters are nonzero at the Weyl-Z2 semimetal phase and vanish at the topologically trivial phases. In the holographic case, the different behavior between the two anomalous transport coefficients is discussed. Our work reveals the novel phase structure of strongly interacting Weyl-Z2 semimetal with two pairs of nodes.
Highlights
In the system, anomalous transport coefficients caused by the anomaly are important to physics in condensed matter physics as well as in high energy physics and astrophysics
We find that the topological phase transition is characterized by the anomalous transport parameters, i.e. the anomalous Hall conductivity and the Z2 anomalous Hall conductivity
In the Z2 Dirac semimetal with two Dirac nodes, similar to the chiral charge the Z2 topological invariant can be defined as CZ2 = (C↑ − C↓) /2, where C↑, ↓ are the chiral charges of the spin-up and spin-down Weyl fermions in the system
Summary
Weyl semimetals are gapless topological states of matter that possess nontrivial chiral charge. The Dirac semimetal with a topological Z2 charge has been constructed in [20] where there are two Dirac nodes separated along a direction in the momentum space.3 They have demonstrated that in Dirac semimetals with two Dirac nodes, there exists a corresponding Z2 anomaly, which is closely analogous to the chiral anomaly. In this paper we focus on a generalization of the Weyl semimetal state, which is a topological semimetal system possessing both the chiral and Z2 topological charges. In this case, in the topological non-trivial phase, the nodes need to possess two non-trivial topological charges, the chiral one and the Z2 one. We analyze its phase structure in a very detailed way and we will check the anomaly by calculating the Ward identities
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