### Antiferromagnetic spintronics

Antiferromagnets recently became the hot spot of spintronics, mainly due to their scalability, their robustness against external magnetic fields, and their ultra-fast dynamical characteristic frequency. These advantages make antiferromagnets a promising candidate for next-generation high-density high-speed spintronic device applications. Although the advantages are intriguing, detection and manipulation techniques of conventional ferromagnets usually do not work for pure antiferromagnets since a net magnetic moment is not allowed. However, composite systems interfacing antiferromagnets with other materials can be convenient in detecting and manipulating the antiferromagnetic order. My research in this area focuses on the rich physics in such heterostructures induced by interfacial bonding, thermal remanence effects, impurity pinning and spin-orbit coupling, etc.

*Above figure: three examples of important phenomena in antiferromagnetic heterostructures and thin films. Left: the two-step switching of a FM/AFM/FM heterostructure. Middle: anomalous Hall effect and geometric Hall effect in TI/AFM heterostructure. Right: SOC induced zero-field planar Hall effect in semiconducting MnTe thin films. *

### Non-trivial topology in solid-state matter

My research in this area focuses on topological phenomena in condensed matter. In the past decade, one of the most exciting developments in solid state physics is the recognition of topology in quantized phenomena. Topology is a mathematical concept designed to classify shapes in different spaces. This topological classification is usually given by certain integer numbers that cannot vanish under smooth transformations. Borrowing this concept, physicists recognized that the Landau levels in quantum Hall effect are fundamentally determined by the topology of the Bloch states living in k-space. This understanding had led to many exciting discoveries including quantum spin Hall effect, quantum anomalous Hall effect, topological insulators and topological superconductors. Similarly, a real-space topological object can also be found in solid-state matter: magnetic skyrmions. These discoveries had opened up many possibilities for similar topological phenomena that could be exciting and useful both for fundamental understanding and device applications.

*Above figure: the smallest model of a Chern insulator that hosts quantum anomalous Hall effect due to the k-space Chern number. The band structure of a ribbon that is infinite along x is shown on the left. The wave-function magnitude along y at different kx are shown on the right. The top and the bottom panels correspond to the blue and the green bands, respectively.*

*Above figure: a magnetic skyrmion that possesses a real-space Chern number. The Chern number is 1 or -1 for each magnetic skyrmion. The center of each magnetic skyrmion (blue) is anti-parallel with the ones on the periphery (red), and the spins in between rotate smoothly*

### Quantum transport

When an electronic or spintronic device shrinks down to mesoscopic scale, the transport channel length becomes comparable to the scattering mean free path, therefore the carriers do not suffer from diffusive scattering processes. This preserves the phase of the carriers. The transport behavior therefore enters the regime ruled by quantum mechanics. This leads to many interesting coherent transport phenomena such as resonance tunneling, Feno effect, Aharonov-Bohm effect, etc. I use non-equilibrium Green’s function method (NEGF) to understand the spin and charge transport in this mesoscopic regime. My research in this area includes the transport of spin and charge through topological insulators, magnetic skyrmions and graphene nano-structures, etc.

*Above figure: an illustration of the calculation of multi-terminal quantum transport. Each terminal is treated as a carrier reservoir of its own thermal equilibrium with different Fermi levels. The current injected to terminal m is denoted by the red arrow. The transmission matrix is given by a trace. The model of the device can be arbitrary, from analytical models to first-principles Hamiltonians.*

### Boltzmann semi-classical transport

For devices of macroscopic scales, the transport of carrier is dissipative, and the free flight of carriers can be described by classical physics. The collision events between free-flights occur so frequently, such that tracking the trajectory of a specific particle in space-time becomes meaningless. The over-all outcome of the transport is described by a distribution function that deviates from the equilibrium Fermi-Dirac function, as shown down below. This distribution function can be obtained by solving the semi-classical Boltzmann transport equation. The observables such as current density, Hall angle, spin accumulation, etc., can be evaluated and analyzed. My research in this area uses both analytical k·p model and the full band structure obtained by first principles. I am particularly interested in strong spin-orbit coupled systems.

*Above figure: an illustration of the basic idea of dissipative transport described by Boltzmann transport equation. *