Despite much interest in engineering new topological surface (edge) states using structural defects, such topological surface states have not been observed yet. We show that recently imaged tilt boundaries in gated multilayer graphene should support topologically protected gapless edge states. We approach the problem from two perspectives: the microscopic perspective of a tight-binding model and an ab initio calculation on a bilayer, and the symmetry-protected topological (SPT) state perspective for a general multilayer. Hence, we establish the tilt-boundary edge states as the first concrete example of the edge states of symmetry-protected Z-type SPT, protected by no-valley mixing, electron-number conservation, and time-reversal T symmetries. Further, we discuss possible phase transitions between distinct SPTs upon symmetry changes. Combined with a recently imaged tilt-boundary network, our findings may explain the long-standing puzzle of subgap conductance in gated bilayer graphene. This proposal can be tested through future transport experiments on tilt boundaries. In particular, the tilt boundaries offer an opportunity for the in situ imaging of topological edge transport.

Research advancement in magnetoelectronics is challenged by the lack of a table-top magnetic measurement technique with the simultaneous temporal and spatial resolution necessary for characterizing magnetization dynamics in devices of interest, such as magnetic memory and spin torque oscillators. Although magneto-optical microscopy provides superb temporal resolution, its spatial resolution is fundamentally limited by optical diffraction. To address this challenge, we study heat rather than light as a vehicle to stroboscopically transduce a local magnetic moment into an electrical signal while retaining picosecond temporal resolution. Using this concept, we demonstrate spatiotemporal magnetic microscopy using the time-resolved anomalous Nernst effect (TRANE). Experimentally and with supporting numerical calculations, we find that TRANE microscopy has temporal resolution below 30 ps and spatial resolution determined by the area of thermal excitation. Based on these findings, we suggest a route to exceed the limits imposed by far-field optical diffraction.

Measuring local magnetization dynamics and its spatial variation is essential for advancements in spintronics and relevant applications. Here we demonstrate a phase-sensitive imaging technique for studying patterned magnetic structures based on picosecond laser heating. With the timeresolved anomalous Nernst effect (TRANE) and extensions, we simultaneously image the dynamic magnetization and RF driving current density. The stroboscopic detection implemented in TRANE microscopy provides access to both amplitude and phase information of ferromagnetic resonance (FMR) and RF current. Using this approach, we measure the spatial variation of the Oersted driving field angle across a uniform channel. In a spatially nonuniform sample with a cross shape, a strong spatial variation for the RF current as well as FMR precession is observed. We find that both the amplitude and the phase of local FMR precession are closely related to those of the RF current.

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