Abstract
We study the chiral vortical conductivity in a holographic Weyl semimetal model, which describes a topological phase transition from the strongly coupled topologically nontrivial phase to a trivial phase. We focus on the temperature dependence of the chiral vortical conductivity where the mixed gauge-gravitational anomaly plays a crucial role. After a proper renormalization of the chiral vortical conductivity by the anomalous Hall conductivity and temperature squared, we find that at low temperature in both the Weyl semimetal phase and the quantum critical region this renormalized ratio stays as universal constants. More intriguingly, this ratio in the quantum critical region depends only on the emergent Lifshitz scaling exponent at the quantum critical point.
Highlights
Quantum anomaly induced macroscopic transport physics has attracted much attention recently
The anomalous transports play a crucial role in the dynamics of many different real physical systems involving chiral fermions, ranging from the quark gluon plasma created at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) [3], to neutron stars [4,5], to the more recently discovered Weyl semimetals [2,6]
The strongly coupled Weyl semimetal can be studied within the framework of holography [24,25], in which the Ward identities of the dual system are the same as those from weakly coupled field theory, there is no notion of band structure
Summary
Quantum anomaly induced macroscopic transport physics has attracted much attention recently. The strongly coupled Weyl semimetal can be studied within the framework of holography [24,25], in which the Ward identities of the dual system are the same as those from weakly coupled field theory, there is no notion of band structure It was shown in [24,25] that in the holographic Weyl semimetal model, there is a quantum phase transition between the topologically nontrivial phase and a trivial phase by tuning the ratio between the mass parameter and the time-reversal symmetry breaking parameter. In the following we use Kubo formulas to calculate the chiral vortical conductivity in different phases of holographic Weyl semimetals. Weyl semimetal phase: At the leading order the first type of IR solution is an AdS5 with nonvanishing axial gauge field Azðr 1⁄4 0Þ. ΣAHE=b is independent of T=b at low temperatures
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