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The geometric phase of an electronic wave function, also known as Berry phase, is the fundamental basis of the topological properties in solids. This phase can be tuned by modulating the band structure of a material, providing a way to drive a topological phase transition. However, despite significant efforts in designing and understanding topological materials, it remains still challenging to tune a given material across different topological phases while tracing the impact of the Berry phase on its quantum transport properties. Here, we report these two effects in a magnetotransport study of ZrTe₅. By tuning the band structure with uniaxial strain, we use quantum oscillations to directly map a weak-to-strong topological insulator phase transition through a gapless Dirac semimetal phase. Moreover, we demonstrate the impact of the strain-tunable spin-dependent Berry phase on the Zeeman effect through the amplitude of the quantum oscillations. We show that such a spin-dependent Berry phase, largely neglected in solid-state systems, is critical in modeling quantum oscillations in Dirac bands of topological materials.

 

Droplet microfluidics offers exquisite control over the flows of multiple fluids in microscale, enabling fabrication of advanced microparticles with precisely tunable structures and compositions in a high throughput manner. The combination of these remarkable features with proper materials and fabrication methods has enabled high efficiency, direct encapsulation of actives in microparticles whose features and functionalities can be well controlled. These microparticles have great potential in a wide range of bio-related applications including drug delivery, cell-laden matrices, biosensors and even as artificial cells. In this review, we briefly summarize the materials, fabrication methods, and microparticle structures produced with droplet microfluidics. We also provide a comprehensive overview of their recent uses in biomedical applications. Finally, we discuss the existing challenges and perspectives to promote the future development of these engineered microparticles. 

Hafnium pentatelluride (HfTe₅) has attracted extensive interest due to its exotic electronic, optical, and thermal properties. As a highly anisotropic crystal (layered structure with in‐plane chains), it has highly anisotropic electrical‐transport properties, but the anisotropy of its thermal‐transport properties has not been established. Here, accurate experimental measurements and theoretical calculations are combined to resolve this issue. Time‐domain thermoreflectance measurements find a highly anisotropic thermal conductivity, 28:1:8, with values of 11.3 ± 2.2, 0.41 ± 0.04, and 3.2 ± 2.0 W m^-1K^-1along the in‐planea‐axis, through‐planeb‐axis, and in‐planec‐axis, respectively. This anisotropy is even larger than what was recently established for ZrTe₅(12:1:6), but the individual values are somewhat higher, even though Zr has a smaller atomic mass than Hf. Density‐functional‐theory calculations predict thermal conductivities in good agreement with the experimental data, provide comprehensive insights into the results, and reveal the origin of the apparent anomaly of the relative thermal conductivities of the two pentatellurides. These results establish that HfTe₅and ZrTe₅, and by implication their alloys, have highly anisotropic and ultralow through‐plane thermal conductivities, which can provide guidance for the design of materials for new directional‐heat‐management applications and potentially other thermal functionalities.