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1. Strain-tuned topological phase transition and unconventional Zeeman effect in ZrTe5 microcrystals

   https://doi.org/10.1038/s43246-022-00316-5  

   Gaikwad, Apurva ; Sun, Song ; Wang, Peipei ; Zhang, Liyuan ; Cano, Jennifer ; Dai, Xi ; Du, Xu ( November 2022 , Communications Materials)

   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.

    

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2. Magneto-transport evidence for strong topological insulator phase in ZrTe5

   https://doi.org/10.1038/s41467-021-27119-5  

   Wang, Jingyue ; Jiang, Yuxuan ; Zhao, Tianhao ; Dun, Zhiling ; Miettinen, Anna L. ; Wu, Xiaosong ; Mourigal, Martin ; Zhou, Haidong ; Pan, Wei ; Smirnov, Dmitry ; et al ( November 2021 , Nature Communications)

   The identification of a non-trivial band topology usually relies on directly probing the protected surface/edge states. But, it is difficult to achieve electronically in narrow-gap topological materials due to the small (meV) energy scales. Here, we demonstrate that band inversion, a crucial ingredient of the non-trivial band topology, can serve as an alternative, experimentally accessible indicator. We show that an inverted band can lead to a four-fold splitting of the non-zero Landau levels, contrasting the two-fold splitting (spin splitting only) in the normal band. We confirm our predictions in magneto-transport experiments on a narrow-gap strong topological insulator, zirconium pentatelluride (ZrTe₅), with the observation of additional splittings in the quantum oscillations and also an anomalous peak in the extreme quantum limit. Our work establishes an effective strategy for identifying the band inversion as well as the associated topological phases for future topological materials research.

    

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3. Quantum interference in superposed lattices

   https://doi.org/10.1073/pnas.2315787121  

   Feng, Yejun ; Wang, Yishu ; Rosenbaum, T. F. ; Littlewood, P. B. ; Chen, Hua ( February 2024 , Proceedings of the National Academy of Sciences)

   Charge transport in solids at low temperature reveals a material’s mesoscopic properties and structure. Under a magnetic field, Shubnikov–de Haas (SdH) oscillations inform complex quantum transport phenomena that are not limited by the ground state characteristics and have facilitated extensive explorations of quantum and topological interest in two- and three-dimensional materials. Here, in elemental metal Cr with two incommensurately superposed lattices of ions and a spin-density-wave ground state, we reveal that the phases of several low-frequency SdH oscillations in${\sigma }_{\mathit{xx}} \left({\rho }_{\mathit{xx}}\right)$and${\sigma }_{\mathit{yy}} \left({\rho }_{\mathit{yy}}\right)$are no longer identical but opposite. These relationships contrast with the SdH oscillations from normal cyclotron orbits that maintain identical phases between${\sigma }_{\mathit{xx}} \left({\rho }_{\mathit{xx}}\right)$and${\sigma }_{\mathit{yy}} \left({\rho }_{\mathit{yy}}\right)$ . We trace the origin of the low-frequency SdH oscillations to quantum interference effects arising from the incommensurate orbits of Cr’s superposed reciprocal lattices and explain the observed$\pi$-phase shift by the reconnection of anisotropic joint open and closed orbits.

    

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4. Edge mode percolation and equilibration in the topological insulator cadmium arsenide

   https://doi.org/10.1038/s41535-023-00602-6  

   Munyan, Simon ; Guo, Binghao ; Huynh, William ; Huang, Victor ; Stemmer, Susanne ( November 2023 , npj Quantum Materials)

   Two-dimensional topological insulators can feature one-dimensional charge transport via edge modes, which offer a rich ground for studying exotic quasi-particles and for quantum materials applications. In this work, we use lateral junction devices, defined by nanoscale finger gates, to study edge mode transport in the two-dimensional topological insulator Cd₃As₂. The finger gate can be tuned to transmit an integer number of quantum Hall edge modes and exhibits full equilibration in the bipolar regime. When the Fermi level of the channel crosses a Landau level, reflected modes percolate through the channel, resulting in an anomalous conductance peak. The device does not fully pinch off when the channel is tuned into the topological gap, which is a sign of remnant modes in the channel. These modes are expected from band inversion, while residual bulk conduction associated with the disorder potential may also play a role.

    

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5. Spin memory of the topological material under strong disorder

   https://doi.org/10.1038/s41535-020-0241-5  

   Korzhovska, Inna ; Deng, Haiming ; Zhao, Lukas ; Deshko, Yury ; Chen, Zhiyi ; Konczykowski, Marcin ; Zhao, Shihua ; Raoux, Simone ; Krusin-Elbaum, Lia ( June 2020 , npj Quantum Materials)

   Robustness to disorder is the defining property of any topological state. The ultimate disorder limits to topological protection are still unknown, although a number of theories predict that even in the amorphous state a quantized conductance might yet reemerge. Here we report that in strongly disordered thin films of the topological material Sb₂Te₃disorder-induced spin correlationsdominate transport of charge—they engender a spin memory phenomenon, generated by the nonequilibrium charge currents controlled by localized spins. We directly detect a glassy yet robust disorder-induced magnetic signal in filmsfree of extrinsic magnetic dopants, which becomes null in a lower-disorder crystalline state. This is where large isotropic negative magnetoresistance (MR)—a hallmark of spin memory—crosses over to positive MR, first with only one e²/hquantum conduction channel, in a weakly antilocalized diffusive transport regime with a 2D scaling characteristic of the topological state. A fresh perspective revealed by our findings is that spin memory effect sets a disorder threshold to the protected topological state. It also points to new possibilities of tuning spin-dependent charge transport by disorder engineering of topological materials.

    

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