The studies of topological phases of matter have been extended from condensed matter physics to photonic systems, resulting in fascinating designs of robust photonic devices. Recently, higher-order topological insulators (HOTIs) have been investigated as a novel topological phase of matter beyond the conventional bulk-boundary correspondence. Previous studies of HOTIs have been mainly focused on the topological multipole systems with negative coupling between lattice sites. Here we experimentally demonstrate that second-order topological insulating phases without negative coupling can be realized in two-dimensional dielectric photonic crystals (PCs). We visualize both one-dimensional topological edge states and zero-dimensional topological corner states by using nearfield scanning technique. To characterize the topological properties of PCs, we define a topological invariant based on the bulk polarizations. Our findings open new research frontiers for searching HOTIs in dielectric PCs and provide a new mechanism for light-manipulating in a hierarchical way.Introduction.-One of the most enchanting developments of condensed matter physics over the past few decades has been the discovery of topological phases of matter primarily found in electronic systems [1,2] and recently extended to bosonic systems such as photonics [3][4][5][6][7][8][9][10][11][12][13][14] and phononics [16][17][18][19][20][21]. A key feature of the topological insulators is the backscattering-immune edge states which are robust against perturbations and provide potential designs of various topological devices [3-6, 18, 20]. Typically, n-dimensional (nD) topological insulators (TIs) have (n − 1)D edge states which is defined as the bulk-boundary correspondence (BBC) [15]. However, a new kind of TIs defined as the higher-order topological insulators (HOTIs), have been recently proposed in tight-binding models in electronic systems which go beyond the traditional BBC description [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Concretely, the mth-order TIs have nD gapped bulk states and (n − 1)D, (n − 2)D, ..., (n − m − 1)D gapped edge states while having (n − m)D gapless edge states. The arising of these lower-dimensional topological edge states can either stem from the quantization of quadrupole moments such as the topological quadrupole insulators [22] which have been realized in mechanics [23], microwave systems [24] and topolectrical circuits [25], or stem from the quantization of the dipole moments [22] such as the HOTIs in 2D breathing kagome lattice [29] which have been realized in sonic crystals [33-35] and a waveguide array [32].

Metallic transition metal dichalcogenides (TMDs) have exhibited various exotic physical properties and hold the promise of novel optoelectronic and topological devices applications. However, the synthesis of metallic TMDs is based on gas-phase methods and requires high-temperature condition. As an alternative to the gas-phase synthetic approach, lower temperature eutectic liquid-phase synthesis presents a very promising approach with the potential for larger-scale and controllable growth of high-quality thin metallic TMD single crystals. Here, the first realization of low-temperature eutectic liquid-phase synthesis of type-II Dirac semimetal PtTe 2 single crystals with thickness ranging from 2 to 200 nm is presented. The electrical measurement of synthesized PtTe 2 reveals a record-high conductivity of as high as 3.3 × 10 6 S m −1 at room temperature. Besides, the weak antilocalization behavior is identified experimentally in the type-II Dirac semimetal PtTe 2 for the first time. Furthermore, a simple and general strategy is developed to obtain atomically thin PtTe 2 crystal by thinning as-synthesized bulk samples, which can still retain highly crystalline and exhibits excellent electrical conductivity. The results of controllable and scalable low-temperature eutectic liquid-phase synthesis and layer-by-layer thinning of high-quality thin PtTe 2 single crystals offer a simple and general approach for obtaining different thickness metallic TMDs with high meltingpoint transition metal.

The quantum spin Hall effect lays the foundation for the topologically protected manipulation of waves, but is restricted to one-dimensional-lower boundaries of systems and hence limits the diversity and integration of topological photonic devices. Recently, the conventional bulkboundary correspondence of band topology has been extended to higher-order cases that enable explorations of topological states with codimensions larger than one such as hinge and corner states. Here, we demonstrate a higher-order quantum spin Hall effect in a twodimensional photonic crystal. Owing to the non-trivial higher-order topology and the pseudospin-pseudospin coupling, we observe a directional localization of photons at corners with opposite pseudospin polarizations through pseudospin-momentum-locked edge waves, resembling the quantum spin Hall effect in a higher-order manner. Our work inspires an unprecedented route to transport and trap spinful waves, supporting potential applications in topological photonic devices such as spinful topological lasers and chiral quantum emitters.

Nano-structuring is an extremely promising path to high performance thermoelectrics. Favorable improvements in thermal conductivity are attainable in many material systems, and theoretical work points to large improvements in electronic properties. However, realization of the electronic benefits in practical materials has been elusive experimentally. A key challenge is that experimental identification of the quantum confinement length, below which the thermoelectric power factor is significantly enhanced, remains elusive due to lack of simultaneous control of size and carrier density. Here we investigate gate-tunable and temperature-dependent thermoelectric transport in γ-phase indium selenide (γ-InSe, n-type semiconductor) samples with thickness varying from 7 to 29 nm. This allows us to properly map out dimension and doping space. Combining theoretical and experimental studies, we reveal that the sharper pre-edge of the conduction-band density of states arising from quantum confinement gives rise to an enhancement of the Seebeck coefficient and the power factor in the thinner InSe samples. Most importantly, we experimentally identify the role of the competition between quantum confinement length and thermal de Broglie wavelength in the enhancement of power factor. Our results provide an important and general experimental guideline for optimizing the power factor and improving the thermoelectric performance of two-dimensional layered semiconductors.