More Like this

1. Non-Abelian effects in dissipative photonic topological lattices

   https://doi.org/10.1038/s41467-023-37065-z  

   Parto, Midya; Leefmans, Christian; Williams, James; Nori, Franco; Marandi, Alireza (March 2023, Nature Communications)

   Abstract Topology is central to phenomena that arise in a variety of fields, ranging from quantum field theory to quantum information science to condensed matter physics. Recently, the study of topology has been extended to open systems, leading to a plethora of intriguing effects such as topological lasing, exceptional surfaces, as well as non-Hermitian bulk-boundary correspondence. Here, we show that Bloch eigenstates associated with lattices with dissipatively coupled elements exhibit geometric properties that cannot be described via scalar Berry phases, in sharp contrast to conservative Hamiltonians with non-degenerate energy levels. This unusual behavior can be attributed to the significant population exchanges among the corresponding dissipation bands of such lattices. Using a one-dimensional example, we show both theoretically and experimentally that such population exchanges can manifest themselves via matrix-valued operators in the corresponding Bloch dynamics. In two-dimensional lattices, such matrix-valued operators can form non-commuting pairs and lead to non-Abelian dynamics, as confirmed by our numerical simulations. Our results point to new ways in which the combined effect of topology and engineered dissipation can lead to non-Abelian topological phenomena. 

   more » « less
2. An operator-based approach to topological photonics

   https://doi.org/10.1515/nanoph-2022-0547  

   Cerjan, Alexander; Loring, Terry A. (October 2022, Nanophotonics)

   Abstract Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, nonreciprocal chiral edge states and cavity-like confined states that have applications in both linear and nonlinear devices. However, current band theoretic approaches to understanding topology in photonic systems yield fundamental limitations on the classes of structures that can be studied. Here, we develop a theoretical framework for assessing a photonic structure’s topology directly from its effective Hamiltonian and position operators, as expressed in real space, and without the need to calculate the system’s Bloch eigenstates or band structure. Using this framework, we show that nontrivial topology, and associated boundary-localized chiral resonances, can manifest in photonic crystals with broken time-reversal symmetry that lack a complete band gap, a result that may have implications for new topological laser designs. Finally, we use our operator-based framework to develop a novel class of invariants for topology stemming from a system’s crystalline symmetries, which allows for the prediction of robust localized states for creating waveguides and cavities. 

   more » « less
3. Digging for topological property in disordered alloys: the emergence of Weyl semimetal phase and sequential band inversions in PbSe–SnSe alloys

   https://doi.org/10.1039/C9MH00574A  

   Wang, Zhi; Liu, Qihang; Luo, Jun-Wei; Zunger, Alex (November 2019, Materials Horizons)

   The search for topological systems has recently broadened to include random substitutional alloys, which lack the specific crystalline symmetries that protect topological phases, raising the question of whether topological properties can be preserved, or are modified by disorder. To address this question, we avoid methods that assumed at the outset high (averaged) symmetry, using instead a fully-atomistic, topological description of an alloy. Application to the (PbSe) 1−x (SnSe) x alloy reveals that topology survives in an interesting fashion: (a) spatial randomness removes the valley degeneracy (splitting ≥150 meV), leading to a sequential inversion of the split valley components over a range of compositions; (b) the absence of inversion lifts spin degenerates, leading to a Weyl semimetal phase without the need of an external magnetic field, an unexpected result, given that the alloy constituent compounds are inversion-symmetric. (a) and (b) underpin the topological physics at low symmetry and complete the missing understanding of possible topological phases within the normal-topological insulator transition. 

   more » « less
4. Topological Nanomaterials

   https://doi.org/doi.org/10.1038/s41578-019-0113-4  

   Liu, Pengzi; Williams, James; Cha, Judy (January 2019, Nature reviews. Materials)

   The past decade has witnessed the emergence of a new frontier in condensed matter physics: topological materials with an electronic band structure belonging to a different topological class from that of ordinary insulators and metals. This non-trivial band topology gives rise to robust, spin-polarized electronic states with linear energy–momentum dispersion at the edge or surface of the materials. For topological materials to be useful in electronic devices, precise control and accurate detection of the topological states must be achieved in nanostructures, which can enhance the topological states because of their large surface-to-volume ratios. In this Review, we discuss notable synthesis and electron transport results of topological nanomaterials, from topological insulator nanoribbons and plates to topological crystalline insulator nanowires and Weyl and Dirac semimetal nanobelts. We also survey superconductivity in topological nanowires, a nanostructure platform that might enable the controlled creation of Majorana bound states for robust quantum computations. Two material systems that can host Majorana bound states are compared: spin–orbit coupled semiconducting nanowires and topological insulating nanowires, a focus of this Review. Finally, we consider the materials and measurement challenges that must be overcome before topological nanomaterials can be used in next-generation electronic devices. 

   more » « less
5. Flat bands, strange metals and the Kondo effect

   https://doi.org/10.1038/s41578-023-00644-z  

   Checkelsky, Joseph G; Bernevig, B Andrei; Coleman, Piers; Si, Qimiao; Paschen, Silke (February 2024, Nature Reviews Materials)

   Flat-band materials such as the kagome metals or moiré superlattices are of intense current interest. Flat bands can result from the electron motion on numerous (special) lattices and usually exhibit topological properties. Their reduced bandwidth proportionally enhances the effect of Coulomb interaction, even when the absolute magnitude of the latter is relatively small. Seemingly unrelated to these materials is the large family of strongly correlated electron systems, which include the heavy-fermion compounds, and cuprate and pnictide superconductors. In addition to itinerant electrons from large, strongly overlapping orbitals, they frequently contain electrons from more localized orbitals, which are subject to a large Coulomb interaction. The question then arises as to what commonality in the physical properties and microscopic physics, if any, exists between these two broad categories of materials. A rapidly increasing body of strikingly similar phenomena across the different platforms — from electronic localization–delocalization transitions to strange-metal behaviour and unconventional superconductivity — suggests that similar underlying principles could be at play. Indeed, it has recently been suggested that flat-band physics can be understood in terms of Kondo physics. Inversely, the concept of electronic topology from lattice symmetry, which is fundamental in flat-band systems, is enriching the field of strongly correlated electron systems, in which correlation-driven topological phases are increasingly being investigated. In this Perspective article, we elucidate this connection, survey the new opportunities for cross-fertilization across platforms and assess the prospect for new insights that may be gained into correlation physics and its intersection with electronic topology. 

   more » « less