Topology is an important branch of mathematics, focusing on the invariants of a system under continuous variations of other parameters [1]. The discovery of the quantum Hall effect opens a new chapter in the study of condensed matter physics concerning the topological properties of a system [2]. Unidirectional propagation of topological edge state (TES) without backscattering can exist along the interface between structures with different topological properties. This kind of unidirectional transmission of energies is robust to imperfections along interface in the system due to the topological protection, which has potential applications in the future spintronics and quantum computing [3], [4].

In 2005, Haldane et al. first introduced the concept of topology to the field of photonics [5]. They predicted that a kind of chiral edge state similar to that of the quantum Hall effect in electronics can be realized by breaking the time reversal symmetry (TRS) of electromagnetic (EM) wave when an external field is added along gyroelectric cylinders. However, this kind of photonic topological states (PTSs) is not observed in experiment due to the weak magneto-optical effect of gyroelectric materials. In 2008, Wang et al. proposed an alternative solution by using gyromagnetic cylinders instead of gyroelectric cylinders [6]. The next year, they experimentally observed such topologically protected PTSs for the first time [7]. Since then, constructing PTSs by breaking the TRS in magneto-optic materials has been a hot topic in field of photonics [8], [9], [10], [11], [12]. However, due to the requirement of the external magnetic field and the limitation of magnetic response speed in magneto-optic material, the PTSs in magnetic material can only be realized in the microwave frequency range, and cannot be extended to the visible and infrared light area, which impedes them to integrate with current widely used optical communication and optical computing techniques. To this end, researchers have made attempts to seek and design other PTSs, such as the topological states with pseudospin protection in coupled ring waveguides [13], the Floquet PTSs in helical waveguide arrays [14], [15], [16], and pseudospin PTSs in bianisotropic metamaterials [17].

Among these PTSs, the pseudospin topological states proposed by Hu et al. in 2015 has attracted more attentions due to the full dielectric material design, simple structure, easy realization in visible and infrared frequencies, and friendly integration with current photonics technologies [18]. Their design was based on a two-dimensional (2D) triangular lattice photonic crystal containing six identical dielectric rods in each primitive cell. And each rod has the same distance from the center of the primitive cell. By shrinking or expanding the six rods structure in primitive cell through adjusting the distance between the rods and center of the primitive cell, frequency band structures of the photonic crystal can be engineered. By combining the TRS of EM wave with the C6v symmetry of the lattice itself, they constructed the pseudo-TRS operation of the system. And by analogy with the p and d orbitals structure in electronic system, they designed the photonic pseudospin states p+, p−, d+ and d− of the transverse magnetic (TM) modes in the photonic crystal. Along the interface between two photonic crystals with different pseudospins, the helical edge states (HESs) with pseudospin-locked unidirectional propagation of EM wave can be constructed.

Recently, many pseudospin PTSs based on structures with C6v symmetry have been proposed theoretically [19], [20], [21] and the unidirectional transmission of such pseudospin-locked HESs have also been observed experimentally, and some other photonic crystal structures [22], [23], [24], [25], [26], [27], [28], [29], [30], [31] have also been proposed to construct the pseudospin PTSs through moving the scattering elements in the primitive cell. However, in these systems, accurately controlling the movement of rod elements is hard, and the moving is also constrained by the size of the primitive cell. So, in this paper, we design a kind of 2D triangular lattice photonic crystal with its primitive cell containing six identical rods composed of two half cylinders with different dielectric materials. Only by rotating each rod in the system, the p and d orbitals can be exchanged, and the pseudospin topological phase transitions (TPTs) are realized and the HESs are constructed. Our design is simple to operate and easy to implement, and our scheme also avoids the geometric constraints of moving of the rods in the system during the regulation of the PTSs.