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Register a new userThe emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
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Non-Hermitian systems distinguish themselves from Hermitian systems by exhibiting a phase transition point called an exceptional point (EP), which is the point at which two eigenstates coalesce under a system parameter variation. Many interesting EP phenomena such as level crossings/repulsions in nuclear/molecular and condensed matter physics, and unusual phenomena in optics such as loss-induced lasing and unidirectional transmission can be understood by considering a simple 2x2 non-Hermitian matrix. At a higher dimension, more complex EP physics not found in two-state systems arises. We consider the emergence and interaction of multiple EPs in a four-state system theoretically and realize the system experimentally using four coupled acoustic cavities with asymmetric losses. We find that multiple EPs can emerge and as the system parameters vary, these EPs can collide and merge, leading to higher order singularities and topological characteristics much richer than those seen in two-state systems.
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We theoretically investigate the emergence of non-hermitian physics at the heterojunction of a type-II Dirac semi-metal (DSM) and a dirty superconductor (DSC). The non-hermiticity is introduced in the DSM through the self-energy term incorporated via the dirtiness of the superconducting material. This causes the spectra of the effective Hamiltonian to become complex, which gives rise to the appearance of the exceptional points (EPs). This complex self energy, apart from having a frequency dependence, also acquires spatial dependence as well, which is unique and can provide interesting effects related to non-hermitian physics in spectral function analysis. At an appropriate distance from the normal metal-superconductor junction of the DSC, non-hermitian degeneracies appear and a single Dirac point splits into two EPs. In the spectral function analysis, apart from the EPs, a Fermi-arc like structure also emerges, which connects the two degeneracies (EPs). The results discussed here are distinctive and possibly can be realized in spectroscopy measurements.
Weyl points emerge as topological monopoles of Berry flux in the three-dimensional (3D) momentum space and have been extensively studied in topological semimetals. As the underlying topological principles apply to any type of waves under periodic boundary conditions, Weyl points can also be realized in classical wave systems, which are easier to engineer compared to condensed matter materials. Here, we made an acoustic Weyl phononic crystal by breaking space inversion (P) symmetry using a combination of slanted acoustic waveguides. We conducted angle-resolved transmission measurements to characterize the acoustic Weyl points. We also experimentally confirmed the existence of acoustic Fermi arcs and demonstrated robust one-way acoustic transport, where the surface waves can overcome a step barrier without reflection. This work lays a solid foundation for the basic research in 3D topological acoustic effects.
Very recently, increasing attention has been focused on non-Abelian topological charges, e.g. the quaternion group Q8. Different from Abelian topological band insulators, these systems involve multiple tangled bulk bandgaps and support non-trivial edge states that manifest the non-Abelian topological features. Furthermore, a system with even or odd number of bands will exhibit significant difference in non-Abelian topological classifications. Up to now, there is scant research investigating the even-band non-Abelian topological insulators. Here, we both theoretically explored and experimentally realized a four-band PT (inversion and time-reversal) symmetric system, where two new classes of topological charges as well as edge states are comprehensively studied. We illustrate their difference from four-dimensional rotation senses on the stereographically projected Clifford tori. We show the evolution of bulk topology by extending the 1D Hamiltonian onto a 2D plane and provide the accompanying edge state distributions following an analytical method. Our work presents an exhaustive study of four-band non-Abelian topological insulators and paves the way to other even band systems.
Topological insulators materialize a topological quantum state of matter where unusual gapless metallic state protected by time-reversal symmetry appears at the edge or surface. Their discovery stimulated the search for new topological states protected by other symmetries, and a recent theory predicted the existence of topological crystalline insulators (TCIs) in which the metallic surface states are protected by mirror symmetry of the crystal. However, its experimental verification has not yet been reported. Here we show the first and definitive experimental evidence for the TCI phase in tin telluride (SnTe) which was recently predicted to be a TCI. Our angle-resolved photoemission spectroscopy shows clear signature of a metallic Dirac-cone surface band with its Dirac point slightly away from the edge of the surface Brillouin zone in SnTe. On the other hand, such a gapless surface state is absent in a cousin material lead telluride (PbTe), in line with the theoretical prediction. Our result establishes the presence of a TCI phase, and opens new avenues for exotic topological phenomena.
Low-energy electrons near Dirac/Weyl nodal points mimic massless relativistic fermions. However, as they are not constrained by Lorentz invariance, they can exhibit tipped-over type-II Dirac/Weyl cones which provide highly anisotropic physical properties and responses, creating unique possibilities. Recently, they have been observed in several quantum and classical systems. Yet, there is still no simple and deterministic strategy to realize them since their nodal points are accidental degeneracies, unlike symmetry-guaranteed type-I counterparts. Here, we propose a band-folding scheme for constructing type-II Dirac points, and we use a tight-binding analysis to unveil its generality and deterministic nature. Through realizations in acoustics, type-II Dirac points are experimentally visualized and investigated using near-field mappings. As a direct effect of tipped-over Dirac cones, strongly tilted kink states originating from their valley-Hall properties are also observed. This deterministic scheme could serve as platform for further investigations of intriguing physics associated with various strongly Lorentz-violating nodal points.
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