Abstract
Using the path integral formulation in Euclidean space, we extended the calculation of the abelian chiral anomalies in the case of Lorentz violating theories by considering a new fermionic correction term provided by the standard model extension, which arises in the continuous Hamiltonian of a weakly tilted Weyl semimetal, and whose cones have opposite tilting. We found that this anomaly is insensitive to the tilting parameter, retaining its well-known covariant form. This independence on the Lorentz violating parameters is consistent with other findings reported in the literature. The initially imposed gauge invariant regularization was consistently recovered at the end of the calculation by the appearance of highly non-trivial combinations of the covariant derivatives, which ultimately managed to give only terms containing the electromagnetic tensor. We emphasize that the value of the anomaly with an arbitrary parameter is not automatically related to the effective action describing the electromagnetic response of such materials.
Highlights
The appearance of fermionic excitations in the continuum Hamiltonians of condensed matter materials, which naturally violate some spacetime symmetries and incorporate contributions similar to those in the fermionic sector of the standard model extension (SME) [1,2], has created the possibility of applying many of the techniques already developed in the search for a fundamental Lorentz violation in the interactions of high energy physics to this area
Such an approach has been fruitful in the case of Weyl semimetals (WSMs) whose electronic Hamiltonians naturally include some of the Lorentz invariance violating (LIV) terms considered in the fermionic sector of the standard model extension (SME) [7]
Motivated by the continuum Hamiltonian of a tilted WSM, whose cones μ have opposite tilting, we considered the LIV parameter dμ ν = δi δν0 vi, where vi is the tilting parameter given by the microscopic structure of the material
Summary
The appearance of fermionic excitations in the continuum Hamiltonians of condensed matter materials, which naturally violate some spacetime symmetries and incorporate contributions similar to those in the fermionic sector of the standard model extension (SME) [1,2], has created the possibility of applying many of the techniques already developed in the search for a fundamental Lorentz violation in the interactions of high energy physics to this area. The topological properties of anomalies have long been recognized in high energy physics and their presence is expected to provide a macroscopic understanding of the underlying topological properties in the electronic design of these materials Such an approach has been fruitful in the case of Weyl semimetals (WSMs) whose electronic Hamiltonians naturally include some of the Lorentz invariance violating (LIV) terms considered in the fermionic sector of the standard model extension (SME) [7]. Using the path integral approach, we deal with the calculation of the anomaly corresponding to the modified axial current responsible for the tilting of the cones around each node, which amounts to discarding the effect of the bμ contribution in a first approximation In this restricted setting, our work is similar to the calculation of the anomaly presented in Ref. The Appendix A summarizes some useful relations used in the calculations
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