Photoelectromagnetic Effect Induced by Terahertz Laser Radiation in Topological Crystalline Insulators Pb1−xSnxTe

Topological crystalline insulators form a class of semiconductors for which surface electron states with the Dirac dispersion relation are formed on surfaces with a certain crystallographic orientation. Pb1−xSnxTe alloys belong to the topological crystalline phase when the SnTe content x exceeds 0.35, while they are in the trivial phase at x < 0.35. For the surface crystallographic orientation (111), the appearance of topologically nontrivial surface states is expected. We studied the photoelectromagnetic (PEM) effect induced by laser terahertz radiation in Pb1−xSnxTe films in the composition range x = (0.11–0.44), with the (111) surface crystallographic orientation. It was found that in the trivial phase, the amplitude of the PEM effect is determined by the power of the incident radiation, while in the topological phase, the amplitude is proportional to the flux of laser radiation quanta. A possible mechanism responsible for the effect observed presumes damping of the thermalization rate of photoexcited electrons in the topological phase and, consequently, prevailing of electron diffusion, compared with energy relaxation.

Multi-class, multi-functional design of photonic topological insulators by rational symmetry-indicators engineering

An explicit topology optimization-based design paradigm is proposed for the design of photonic topological crystalline insulators (TCIs). To strictly guarantee the topological property, rational engineering of symmetry-indicators is carried out by mathematical programming, which simultaneously maximizes the width of nontrivial topological band gaps and achieves the desired quantized bulk polarization. Our approach is successfully applied to design photonic TCIs with time-reversal symmetry in two-dimensional point groups, higher-order magnetic TCIs, and higher-order photonic TCIs. This methodology paves the way for inverse design of optimized photonic/phononic, multiphysics, and multifunctional three-dimensional TCIs.

Structural buckling induced higher-order topology

ABSTRACT The higher-order topological insulator (HOTI) states, such as two-dimension (2D) HOTI featured with topologically protected corner modes at the intersection of two gapped crystalline boundaries, have attracted much recent interest. However, physical mechanism underlying the formation of HOTI states is not fully understood, which has hindered our fundamental understanding and discovery of HOTI materials. Here we propose a mechanistic approach to induce higher-order topological phases via structural buckling of 2D topological crystalline insulators (TCIs). While in-plane mirror symmetry is broken by structural buckling, which destroys the TCI state, the combination of mirror and rotation symmetry preserves in the buckled system, which gives rise to the HOTI state. We demonstrate that this approach is generally applicable to various 2D lattices with different symmetries and buckling patterns, opening a horizon of possible materials to realize 2D HOTIs. The HOTIs so generated are also shown to be robust against buckling height fluctuation and in-plane displacement. A concrete example is given for the buckled $\beta $-Sb monolayer from first-principles calculations. Our finding not only enriches our fundamental understanding of higher-order topology, but also opens a new route to discovering HOTI materials.

Acoustic Möbius insulators from projective symmetry

Symmetry plays a critical role in classifying phases of matter. This is exemplified by how crystalline symmetries enrich the topological classification of materials and enable unconventional phenomena in topologically nontrivial ones. After an extensive study over the past decade, the list of topological crystalline insulators and semimetals seems to be exhaustive and concluded. However, in the presence of gauge symmetry, common but not limited to artificial crystals, the algebraic structure of crystalline symmetries needs to be projectively represented, giving rise to unprecedented topological physics. Here we demonstrate this novel idea by exploiting a projective translation symmetry and constructing a variety of Möbius-twisted topological phases. Experimentally, we realize two Möbius insulators in acoustic crystals for the first time: a two-dimensional one of first-order band topology and a three-dimensional one of higher-order band topology. We observe unambiguously the peculiar Möbius edge and hinge states via real-space visualization of their localiztions, momentum-space spectroscopy of their 4π periodicity, and phase-space winding of their projective translation eigenvalues. Not only does our work open a new avenue for artificial systems under the interplay between gauge and crystalline symmetries, but it also initializes a new framework for topological physics from projective symmetry.

Acoustic Möbius insulators from projective symmetry

Symmetry plays a critical role in classifying phases of matter. This is exemplified by how crystalline symmetries enrich the topological classification of materials and enable unconventional phenomena in topologically nontrivial ones. After an extensive study over the past decade, the list of topological crystalline insulators and semimetals seems to be exhaustive and concluded. However, in the presence of gauge symmetry, common but not limited to artificial crystals, the algebraic structure of crystalline symmetries needs to be projectively represented, giving rise to unprecedented topological physics. Here we demonstrate this novel idea by exploiting a projective translation symmetry and constructing a variety of Möbius-twisted topological phases. Experimentally, we realize two Möbius insulators in acoustic crystals for the first time: a two-dimensional one of first-order band topology and a three-dimensional one of higher-order band topology. We observe unambiguously the peculiar Möbius edge and hinge states via real-space visualization of their localiztions, momentum-space spectroscopy of their 4π periodicity, and phase-space winding of their projective translation eigenvalues. Not only does our work open a new avenue for artificial systems under the interplay between gauge and crystalline symmetries, but it also initializes a new framework for topological physics from projective symmetry.