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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.
2. Band structure and polarization effects in photothermoelectric spectroscopy of a Bi ₂ Se ₃ device

   https://doi.org/10.1063/5.0075924  

   Pournia, Seyyedesadaf ; Jnawali, Giriraj ; Need, Ryan F. ; Jackson, Howard E. ; Wilson, Stephen D. ; Smith, Leigh M. ( March 2022 , Applied Physics Letters)

   Bi₂Se₃is a prototypical topological insulator, which has a small bandgap (∼0.3 eV) and topologically protected conducting surface states. This material exhibits quite strong thermoelectric effects. Here, we show in a mechanically exfoliated thick (∼100 nm) nanoflake device that we can measure the energy dependent optical absorption through the photothermoelectric effect. Spectral signatures are seen for a number of optical transitions between the valence and conduction bands, including a broad peak at 1.5 eV, which is likely dominated by bulk band-to-band optical transitions but is at the same energy as the well-known optical transition between the two topologically protected conducting surface states. We also observe a surprising linear polarization dependence in the response of the device that reflects the influence of the metal contacts.
3. Unidirectional Maxwellian spin waves

   https://doi.org/10.1515/nanoph-2019-0092  

   Van Mechelen, Todd ; Jacob, Zubin ( June 2019 , Nanophotonics)

   Abstract In this article, we develop a unified perspective of unidirectional topological edge waves in nonreciprocal media. We focus on the inherent role of photonic spin in nonreciprocal gyroelectric media, i.e. magnetized metals or magnetized insulators. Due to the large body of contradicting literature, we point out at the outset that these Maxwellian spin waves are fundamentally different from well-known topologically trivial surface plasmon polaritons. We first review the concept of a Maxwell Hamiltonian in nonreciprocal media, which immediately reveals that the gyrotropic coefficient behaves as a photon mass in two dimensions. Similar to the Dirac mass, this photonic mass opens bandgaps in the energy dispersion of bulk propagating waves. Within these bulk photonic bandgaps, three distinct classes of Maxwellian edge waves exist – each arising from subtle differences in boundary conditions. On one hand, the edge wave solutions are rigorous photonic analogs of Jackiw-Rebbi electronic edge states. On the other hand, for the exact same system, they can be high frequency photonic counterparts of the integer quantum Hall effect, familiar at zero frequency. Our Hamiltonian approach also predicts the existence of a third distinct class of Maxwellian edge wave exhibiting topological protection. This occurs in an intriguing topological bosonicmore »phase of matter, fundamentally different from any known electronic or photonic medium. The Maxwellian edge state in this unique quantum gyroelectric phase of matter necessarily requires a sign change in gyrotropy arising from nonlocality (spatial dispersion). In a Drude system, this behavior emerges from a spatially dispersive cyclotron frequency that switches sign with momentum. A signature property of these topological electromagnetic edge states is that they are oblivious to the contacting medium, i.e. they occur at the interface of the quantum gyroelectric phase and any medium (even vacuum). This is because the edge state satisfies open boundary conditions – all components of the electromagnetic field vanish at the interface. Furthermore, the Maxwellian spin waves exhibit photonic spin-1 quantization in exact analogy with their supersymmetric spin-1/2 counterparts. The goal of this paper is to discuss these three foundational classes of edge waves in a unified perspective while providing in-depth derivations, taking into account nonlocality and various boundary conditions. Our work sheds light on the important role of photonic spin in condensed matter systems, where this definition of spin is also translatable to topological photonic crystals and metamaterials.« less
4. Emergent helical edge states in a hybridized three-dimensional topological insulator

   https://doi.org/10.1038/s41467-022-33643-9  

   Chong, Su Kong ; Liu, Lizhe ; Watanabe, Kenji ; Taniguchi, Takashi ; Sparks, Taylor D. ; Liu, Feng ; Deshpande, Vikram V. ( October 2022 , Nature Communications)

   As the thickness of a three-dimensional (3D) topological insulator (TI) becomes comparable to the penetration depth of surface states, quantum tunneling between surfaces turns their gapless Dirac electronic structure into a gapped spectrum. Whether the surface hybridization gap can host topological edge states is still an open question. Herein, we provide transport evidence of 2D topological states in the quantum tunneling regime of a bulk insulating 3D TI BiSbTeSe₂. Different from its trivial insulating phase, this 2D topological state exhibits a finite longitudinal conductance at ~2e²/h when the Fermi level is aligned within the surface gap, indicating an emergent quantum spin Hall (QSH) state. The transition from the QSH to quantum Hall (QH) state in a transverse magnetic field further supports the existence of this distinguished 2D topological phase. In addition, we demonstrate a second route to realize the 2D topological state via surface gap-closing and topological phase transition mechanism mediated by a transverse electric field. The experimental realization of the 2D topological phase in a 3D TI enriches its phase diagram and marks an important step toward functionalized topological quantum devices.
5. Correlated oxide Dirac semimetal in the extreme quantum limit

   https://doi.org/10.1126/sciadv.abf9631  

   Ok, Jong Mok ; Mohanta, Narayan ; Zhang, Jie ; Yoon, Sangmoon ; Okamoto, Satoshi ; Choi, Eun Sang ; Zhou, Hua ; Briggeman, Megan ; Irvin, Patrick ; Lupini, Andrew R. ; et al ( September 2021 , Science Advances)

   Quantum materials (QMs) with strong correlation and nontrivial topology are indispensable to next-generation information and computing technologies. Exploitation of topological band structure is an ideal starting point to realize correlated topological QMs. Here, we report that strain-induced symmetry modification in correlated oxide SrNbO 3 thin films creates an emerging topological band structure. Dirac electrons in strained SrNbO 3 films reveal ultrahigh mobility (μ max ≈ 100,000 cm 2 /Vs), exceptionally small effective mass ( m * ~ 0.04 m e ), and nonzero Berry phase. Strained SrNbO 3 films reach the extreme quantum limit, exhibiting a sign of fractional occupation of Landau levels and giant mass enhancement. Our results suggest that symmetry-modified SrNbO 3 is a rare example of correlated oxide Dirac semimetals, in which strong correlation of Dirac electrons leads to the realization of a novel correlated topological QM.