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1. Quantized topological phases beyond square lattices in Floquet synthetic dimensions [Invited]

   https://doi.org/10.1364/OME.546801  

   Sriram, Samarth; Sridhar, Sashank_Kaushik; Dutt, Avik (January 2025, Optical Materials Express)

   Topological effects manifest in a variety of lattice geometries. While square lattices, due to their simplicity, have been used for models supporting nontrivial topology, several exotic topological phenomena such as Dirac points, Weyl points, and Haldane phases are most commonly supported by non-square lattices. Examples of prototypical non-square lattices include the honeycomb lattice of graphene and 2D materials, and the Kagome lattice, both of which break fundamental symmetries and can exhibit quantized transport, especially when long-range hoppings and gauge fields are incorporated. The challenge of controllably realizing such long-range hoppings and gauge fields has motivated a large body of research focused on harnessing lattices encoded in synthetic dimensions. Photons in particular have many internal degrees of freedom and hence show promise for implementing these synthetic dimensions; however, most photonic synthetic dimensions have hitherto created 1D or 2D square lattices. Here we show that non-square lattice Hamiltonians such as the Haldane model and its variations can be implemented using Floquet synthetic dimensions. Our construction uses dynamically modulated ring resonators and provides the capacity for directk-space engineering of lattice Hamiltonians. Thisk-space construction lifts constraints on the orthogonality of lattice vectors that make square geometries simpler to implement in lattice-space constructions and instead transfers the complexity to the engineering of tailored, complex Floquet drive signals. We simulate topological signatures of the Haldane and the brick-wall Haldane model and observe them to be robust in the presence of external optical drive and photon loss, and discuss unique characteristics of their topological transport when implemented on these Floquet lattices. Our proposal demonstrates the potential of driven-dissipative Floquet synthetic dimensions as a new architecture fork-space Hamiltonian simulation of high-dimensional lattice geometries, supported by scalable photonic integration, that lifts the constraints of several existing platforms for topological photonics and synthetic dimensions. 

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2. Topological frequency conversion in Weyl semimetals

   https://doi.org/10.48550/arXiv.2201.07804  

   Frederik Nathan, Ivar Martin (October 2022, Physical review research)

   We theoretically predict a new working principle for optical amplification, based on Weyl semimetals: when a Weyl semimetal is suitably irradiated at two frequencies, electrons close to the Weyl points convert energy between the frequencies through the mechanism of topological frequency conversion from [Martin et al, PRX 7 041008 (2017)]. Each electron converts energy at a quantized rate given by an integer multiple of Planck's constant multiplied by the product of the two frequencies. In simulations, we show that optimal, but feasible band structures can support topological frequency conversion in the "THz gap" at intensities down to 2W/mm2; the gain from the effect can exceed the dissipative loss when the frequencies are larger than the relaxation time of the system. Topological frequency conversion provides a new paradigm for optical amplification, and further extends Weyl semimetals' promise for technological applications. 

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3. Control of electronic topology in a strongly correlated electron system

   https://doi.org/10.1038/s41467-022-33369-8  

   Dzsaber, Sami; Zocco, Diego A; McCollam, Alix; Weickert, Franziska; McDonald, Ross; Taupin, Mathieu; Eguchi, Gaku; Yan, Xinlin; Prokofiev, Andrey; Tang, Lucas_M K; et al (December 2022, Nature Communications)

   Abstract It is becoming increasingly clear that breakthrough in quantum applications necessitates materials innovation. In high demand are conductors with robust topological states that can be manipulated at will. This is what we demonstrate in the present work. We discover that the pronounced topological response of a strongly correlated “Weyl-Kondo” semimetal can be genuinely manipulated—and ultimately fully suppressed—by magnetic fields. We understand this behavior as a Zeeman-driven motion of Weyl nodes in momentum space, up to the point where the nodes meet and annihilate in a topological quantum phase transition. The topologically trivial but correlated background remains unaffected across this transition, as is shown by our investigations up to much larger fields. Our work lays the ground for systematic explorations of electronic topology, and boosts the prospect for topological quantum devices. 

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4. Topology stabilized fluctuations in a magnetic nodal semimetal

   https://doi.org/10.1038/s41467-023-40765-1  

   Drucker, Nathan C.; Nguyen, Thanh; Han, Fei; Siriviboon, Phum; Luo, Xi; Andrejevic, Nina; Zhu, Ziming; Bednik, Grigory; Nguyen, Quynh T.; Chen, Zhantao; et al (August 2023, Nature Communications)

   Abstract The interplay between magnetism and electronic band topology enriches topological phases and has promising applications. However, the role of topology in magnetic fluctuations has been elusive. Here, we report evidence for topology stabilized magnetism above the magnetic transition temperature in magnetic Weyl semimetal candidate CeAlGe. Electrical transport, thermal transport, resonant elastic X-ray scattering, and dilatometry consistently indicate the presence of locally correlated magnetism within a narrow temperature window well above the thermodynamic magnetic transition temperature. The wavevector of this short-range order is consistent with the nesting condition of topological Weyl nodes, suggesting that it arises from the interaction between magnetic fluctuations and the emergent Weyl fermions. Effective field theory shows that this topology stabilized order is wavevector dependent and can be stabilized when the interband Weyl fermion scattering is dominant. Our work highlights the role of electronic band topology in stabilizing magnetic order even in the classically disordered regime. 

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5. Strong and fragile topological Dirac semimetals with higher-order Fermi arcs

   https://doi.org/10.1038/s41467-020-14443-5  

   Wieder, Benjamin J.; Wang, Zhijun; Cano, Jennifer; Dai, Xi; Schoop, Leslie M.; Bradlyn, Barry; Bernevig, B. Andrei (January 2020, Nature Communications)

   Abstract Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of ans–d-hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- (α) and intermediate-temperature (α″) phases of Cd₃As₂, KMgBi, and rutile-structure ($$ \beta ^{\prime} $$ ${\beta }^{\prime }$-) PtO₂. 

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