Advances in pseudo-magnetic field in artificial structures

Abstract

<p indent=0mm>Pseudo-magnetic fields (PMFs) are firstly proposed in stretched graphene systems, in which the electrons behave as they do in a real magnetic field. Physically, the mechanical strain results in a lattice deformation and changes the hopping strength between carbon atoms, and thus induces an effective vector potential by shifting the Dirac points at the Brillouin zone. The PMF opens the door to control quantum transport by mechanical means and to explore unprecedented physics in a high-field regime, thus has drawn widespread attention recently. Inspired by the realization of strain-induced PMF in graphene, the concept of PMF is introduced into classical wave (e.g., optical and acoustic) systems using similar ways, because the strain tensor can also be written in the form of the vector potential within the tight binding approximation in classical wave systems. For classical wave systems that do not (or weakly) respond to external magnetic fields, the introduction of PMFs provides a new mechanism for controlling waves, and brings many physical properties analogous to those in real magnetic fields, such as Landau level quantization and quantum-Hall-like effect. Meanwhile, the macroscopic controllability enables the (optical or acoustic) artificial structure to provide an excellent macroscopic platform to explore PMFs and associated phenomena. In this review article, we introduce the recent progress of PMFs in artificial structures, especially on the construction routes of PMFs and related physical properties. The first classical PMF is realized in a triaxially deformed honeycomb photonic lattice, which consists of long dielectric waveguide arrays. Similarly, the PMF can be achieved in the other classical wave systems like microwave and acoustic systems by applying a triaxial strain field on the artificial structures or using the simulated strain effect by displacing the lattice sites. To simplify the experimental realization, a uniaxial strain field or deformation is proposed to realize the PMF in classical wave systems. Particularly, the microscopic controllability of artificial structures provides us a more simple approach to experimentally generate the PMF by engineering the individual unit-cell structure. By patterning the gradually varied unit-cell structures, the linearly varying vector potential can be realized in the gradient artificial structure, which results in a large uniform PMF. In such a system, the frequency-resolved spectrum is measured to demonstrate the Landau Levels induced by the PMF, and the quantum-Hall-like edge states are also observed. Benefiting from the macroscopic controllability of artificial structures, the PMF can be extended to 3D classical systems by engineering gradient artificial structures, in which the shifting of Weyl points effectively induces a gauge field. Particularly, in contrast to the zero-order Landau plateau in a 2D system with PMF, the zero-order chiral Landau level with linear dispersion is observed in 3D artificial structures with PMF. The zero-order chiral Landau level is characterized by one-way propagation, and the direction of group velocity is determined by the chirality of the Weyl point and the direction of PMF. The introduction of PMFs in 2D and 3D classical systems not only provides us a possibility to explore novel physics associated to the magnetic field without real magnetic field, but also opens the door to a wide range of potential applications, such as enhancing light or sound emission and nonlinear wave mixing due to the high density of states of Landau levels, optical or sound laser, and topological transports of the edge states under PMFs.