# "Topological charge pumping effect due to the parity anomaly on the Surface of Three-Dimensional Topological Insulators"

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### Description

## Seminar Annoucement (Theory of Quantum Matter Unit)

__Date/Time__ : Tuesday 12^{th} February / 16:00-17:00

__Venue__ : Meeting Room A613, Level A, Lab 2, Main Campus

__Speaker __: Dr. Hiroaki Ueda, Tokyo Metropolitan University

__Title__ : “Topological charge pumping effect due to the parity anomaly on the Surface of Three-Dimensional Topological Insulators”

__Abstract__:

A topological insulator (TI) is a band insulator whose wave function is characterized by the topological invariant. A TI has a topologically characterized gapless edge (surface) state, and various exotic phenomena have been reported, such as the surface quantum Hall effect and the realization of the monopole dynamics[1]. For a TI in three-space dimensions, the surface state is described by the massive (gapped) (2 + 1)-dimensional Dirac fermion and the nontrivial topological magnetoelectric effect appears when the exchange field is present[1]. The low energy response to the electromagnetic (U(1) gauge) field was shown to be understood by the topological mass (TM) term (Chern-Simons term)[2]. One of the interesting aspects of TM is the quantum anomaly, where quantum fluctuations break the symmetry in the original Lagrangian. In fact, TM breaks the parity symmetry which exists when the Dirac mass is zero: the so-called parity anomaly[2].

In this seminar, we discuss a current dynamics on the surface of a 3-dimensional topological insulator induced by magnetization precession of a ferromagnet attached. In this system, the magnetization of the FM plays the same role as the U(1) gauge field and the Dirac mass[1]. It is found that the magnetization dynamics generates a direct charge current when the precession axis is within the surface plane. This rectification effect is due to the parity anomaly and is topologically protected. The robustness of the rectification effect against first-varying exchange field and impurities is confirmed by explicit calculation. The nontrivial current dynamics driven by the quantum anomaly has a potential applicability to new spintronics devices.

[1] X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. **83**, 1057 (2011).

[2] A. N. Redlich, Phys. Rev. D** 29**, 2366 (1984); S. Coleman and B. Hill, Phys. Lett. B **159**, 184 (1985).

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