Chiral Chemical Potential
Chiral Chemical Potential (CCP)ΒΆ
Tags #chiral_magnetic_current #CME
Quantum anomalies in Weyl semimetal (for either \(\textbf{E} \cdot \textbf{B} \ne 0\) or \(\nabla T \cdot \textbf{B} \ne 0\)) leads to chiral charge energy pumping between the opposite Chirality nodes. This results in chiral charge and energy imbalance between the Weyl nodes, which manifests in magneto-transport phenomena.
Consider a Weyl semimetal with one pair of Weyl points of opposite Chirality (which act as Berry curvature monopoles), which are separated in the momentum space by \(\delta \textbf{K}\) and in energy space by \(\Delta\). This \(\Delta\) is known as chiral chemical potential and is odd under (\(\mathcal{P}\)) operation.
The nonconservation of chiral charge in the presence of electric field (\(\textbf{E} \cdot \textbf{B} \ne 0\)) is known as electrical Chiral Anomaly.
Schematic of the CCP (\(\delta \mu\)) imbalance in Weyl semimetal
Such a system breaks both the Time reversal symmetry (\(\mathcal{T}\)) and \(\mathcal{P}\) symmetry. This system possesses a dynamic magnetoelectric coupling \(\theta(\textbf{x},t) \textbf{E} \cdot \textbf{B}\), where \(\theta(\textbf{x},t) = (\delta \textbf{K} \cdot \textbf{x} - \Delta T)\). Since \(\delta \textbf{K}\) and \(\Delta\) are respectively odd under Time reversal symmetry and inversion symmetry, this magnetoelectric coupling leads to the anomalous charge current. \(\(j = \frac{e^2}{h} \delta \textbf{K} \times \textbf{E} + \frac{e^2}{h^2} \Delta B\)\) In the absence of \(\mathcal{T}\) symmetry, the spatial gradient \(\theta(\textbf{x},t)\) governs the anomalous charge Hall current. In contrast, the time derivative of \(\theta(\textbf{x},t)\) induces a current along the direction of the applied MF for the inversion-asymmetric Weyl semimetal, which is known as chiral magnetic current.
Time dependent MF can create a response known as Dynamic chiral magnetic effect.