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Register a new userAnomalous nonreciprocal topological networks: stronger than Chern insulators
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Robustness against disorder and defects is a pivotal advantage of topological systems, manifested by absence of electronic backscattering in the quantum Hall and spin-Hall effects, and unidirectional waveguiding in their classical analogs. Two-dimensional (2D) topological insulators, in particular, provide unprecedented opportunities in a variety of fields due to their compact planar geometries compatible with the fabrication technologies used in modern electronics and photonics. Among all 2D topological phases, Chern insulators are to date the most reliable designs due to the genuine backscattering immunity of their non-reciprocal edge modes, brought via time-reversal symmetry breaking. Yet, such resistance to fabrication tolerances is limited to fluctuations of the same order of magnitude as their band gap, limiting their resilience to small perturbations only. Here, we tackle this vexing problem by introducing the concept of anomalous non-reciprocal topological networks, that survive disorder levels with strengths arbitrarily larger than their bandgap. We explore the general conditions to obtain such unusual effect in systems made of unitary three-port scattering matrices connected by phase links, and establish the superior robustness of the anomalous edge modes over the Chern ones to phase link disorder of arbitrarily large values. We confirm experimentally the exceptional resilience of the anomalous phase, and demonstrate its operation by building an ideal anomalous topological circulator despite its arbitrary shape and large number of ports. Our results pave the way to efficient, arbitrary planar energy transport on 2D substrates for wave devices with full protection against large fabrication flaws or imperfections.
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The quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has quantized Hall resistance of h/Ce2 and vanishing longitudinal resistance under zero magnetic field, where C is called the Chern number. The QAH effect has been realized in magnetic topological insulators (TIs) and magic-angle twisted bilayer graphene. Despite considerable experimental efforts, the zero magnetic field QAH effect has so far been realized only for C = 1. Here we used molecular beam epitaxy to fabricate magnetic TI multilayers and realized the QAH effect with tunable Chern number C up to 5. The Chern number of these QAH insulators is tuned by varying the magnetic doping concentration or the thickness of the interior magnetic TI layers in the multilayer samples. A theoretical model is developed to understand our experimental observations and establish phase diagrams for QAH insulators with tunable Chern numbers. The realization of QAH insulators with high tunable Chern numbers facilitates the potential applications of dissipationless chiral edge currents in energy-efficient electronic devices and opens opportunities for developing multi-channel quantum computing and higher-capacity chiral circuit interconnects.
Periodically driven systems can host so called anomalous topological phases, in which protected boundary states coexist with topologically trivial Floquet bulk bands. We introduce an anomalous version of reflection symmetry protected topological crystalline insulators, obtained as a stack of weakly-coupled two-dimensional layers. The system has tunable and robust surface Dirac cones even though the mirror Chern numbers of the Floquet bulk bands vanish. The number of surface Dirac cones is given by a new topological invariant determined from the scattering matrix of the system. Further, we find that due to particle-hole symmetry, the positions of Dirac cones in the surface Brillouin zone are controlled by an additional invariant, counting the parity of modes present at high symmetry points.
Within a relativistic quantum formalism we examine the role of second-order corrections caused by the application of magnetic fields in two-dimensional topological and Chern insulators. This allows to reach analytical expressions for the change of the Berry curvature, orbital magnetic moment, density of states and energy determining their canonical grand potential and transport properties. The present corrections, which become relevant at relatively low fields due to the small gap characterizing these systems, unveil a zero-field diamagnetic susceptibility which can be tuned by the external magnetic field.
We demonstrate, both theoretically and experimentally, the concept of non-linear second-order topological insulators, a class of bulk insulators with quantized Wannier centers and a bulk polarization directly controlled by the level of non-linearity. We show that one-dimensional edge states and zero-dimensional corner states can be induced in a trivial crystal insulator made of evanescently coupled resonators with linear and nonlinear coupling coefficients, simply by tuning the excitation intensity. This allows global external control over topological phase transitions and switching to a phase with non-zero bulk polarization, without requiring any structural or geometrical changes. We further show how these non-linear effects enable dynamic tuning of the spectral properties and localization of the topological edge and corner states. Such self-induced second-order topological insulators, which can be found and implemented in a wide variety of physical platforms ranging from electronics to microwaves, acoustics, and optics, hold exciting promises for reconfigurable topological energy confinement, power harvesting, data storage, and spatial management of high-intensity fields.
In Hermitian topological systems, the bulk-boundary correspondence strictly constraints boundary transport to values determined by the topological properties of the bulk. We demonstrate that this constraint can be lifted in non-Hermitian Floquet insulators. Provided that the insulator supports an anomalous topological phase, non-Hermiticity allows us to modify the boundary states independently of the bulk, without sacrificing their topological nature. We explore the ensuing possibilities for a Floquet topological insulator with non-Hermitian time-reversal symmetry, where the helical transport via counterpropagating boundary states can be tailored in ways that overcome the constraints imposed by Hermiticity. Non-Hermitian boundary state engineering specifically enables the enhancement of boundary transport relative to bulk motion, helical transport with a preferred direction, and chiral transport in the same direction on opposite boundaries. We explain the experimental relevance of our findings for the example of photonic waveguide lattices.
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