We study the disorder-induced phase transition in two-dimensional non-Hermitian systems. First, the applicability of the noncommutative geometric method (NGM) in non-Hermitian systems is examined. By calculating the Chern number of two different systems (a square sample and a cylindrical one), the numerical results calculated by NGM are compared with the analytical one, and the phase boundary obtained by NGM is found to be in good agreement with the theoretical prediction. Then, we use NGM to investigate the evolution of the Chern number in non-Hermitian samples with the disorder effect. For the square sample, the stability of the non-Hermitian Chern insulator under disorder is confirmed. Significantly, we obtain a nontrivial topological phase induced by disorder. This phase is understood as the topological Anderson insulator in non-Hermitian systems. Finally, the disordered phase transition in the cylindrical sample is also investigated. The clean non-Hermitian cylindrical sample has three phases, and such samples show more phase transitions by varying the disorder strength: (1) the normal insulator phase to the gapless phase, (2) the normal insulator phase to the topological Anderson insulator phase, and (3) the gapless phase to the topological Anderson insulator phase.

The group-V monolayers (MLs) have been studied intensively after the experimental fabrication of two-dimensional (2D) graphene and black phosphorus. The observation of novel quantum phenomena, such as quantum spin Hall effect and ferroelectricity in group-V elemental layers, has attracted tremendous attention because of the novel physics and promising applications for nanoelectronics in the 2D limit. In this review, we comprehensively review recent research progress in engineering of topology and ferroelectricity, and several effective methods to control the quantum phase transition are discussed. We then introduce the coupling between topological orders and ferroelectric orders. The research directions and outlooks are discussed at the end of the perspective. It is expected that the comprehensive overview of topology and ferroelectricity in 2D group-V materials can provide guidelines for researchers in the area and inspire further explorations of interplay between multiple quantum phenomena in low-dimensional systems.

As a prototypical transition-metal dichalcogenide semiconductor, MoS₂ possesses strong spin-orbit coupling, which provides an ideal platform for the realization of interesting physical phenomena. Here, we report the magnetotransport properties in NbN-MoS₂-NbN sandwich junctions at low temperatures. Above the critical temperature around ～11 K, the junction resistance shows weak temperature dependence, indicating a tunneling behavior. While below ～11 K, nearly zero junction resistance is observed, indicating the superconducting state in the MoS₂ layer induced by the superconducting proximity effect. When a perpendicular magnetic field ～1 T is applied, such proximity effect is suppressed, accompanying with insulator-like temperature-dependence of the junction resistance. Intriguingly, when further increasing the magnetic field, the junction conductance is significantly enhanced, which is related to the enhanced single particle tunneling induced by the decrease of the superconducting energy gap with increasing magnetic fields. In addition, the possible Majorana zero mode on the surface of MoS₂ can further lead to the enhancement of the junction conductance.

The grain boundaries of graphene are disordered topological defects, which would strongly affect the physical and chemical properties of graphene. In this paper, the spectral characteristics and photoresponse of MoS₂/graphene heterostructures are studied. It is found that the blueshift of the G and 2D peaks of graphene in Raman spectrum is due to doping. The lattice mismatch at the graphene boundaries results in a blueshift of MoS₂ features in the photoluminescence spectra, comparing to the MoS₂ grown on SiO₂. In addition, the photocurrent signal in MoS₂/hexagonal single-crystal graphene heterostructures is successfully captured without bias, but not in MoS₂/polycrystalline graphene heterostructures. The electron scattering at graphene grain boundaries affects the optical response of MoS₂/graphene heterostructures. The photoresponse of the device is attributed to the optical absorption and response of MoS₂ and the high carrier mobility of graphene. These findings offer a new approach to develop optoelectronic devices based on two-dimensional material heterostructures.

The surface plasmon polaritons of the topological insulator Bi₂Se₃ can be excited by using etched grating or grave structures to compensate the wave vector mismatch of the incident photon and plasmon. Here, we demonstrate novel gold grating/Bi₂Se₃ thin film/sapphire hybrid structures, which allow the excitation of surface plasmon polaritons propagating through nondestructive Bi₂Se₃ thin film with the help of gold diffractive gratings. Utilizing periodic Au surface structures, the momentum can be matched and the normal-incidence infrared reflectance spectra exhibit pronounced dips. When the width of the gold grating W (with a periodicity 2W) increases from 400 nm to 1500 nm, the resonant frequencies are tuned from about 7000 cm^-1 to 2500 cm^-1. In contrast to the expected √q dispersion for both massive and massless fermions, where q～π/W is the wave vector, we observe a sound-like linear dispersion even at room temperature. This surface plasmon polaritons with linear dispersion are attributed to the unique noninvasive fabrication method and high mobility of topological surface electrons. This novel structure provides a promising application of Dirac plasmonics.

Two-dimensional topological insulators (2DTIs) have attracted increasing attention during the past few years. New 2DTIs with increasing larger spin-orbit coupling (SOC) gaps have been predicted by theoretical calculations and some of them have been synthesized experimentally. In this review, the 2DTIs, ranging from single element graphene-like materials to bi-elemental transition metal chalcogenides (TMDs) and to multi-elemental materials, with different thicknesses, structures, and phases, have been summarized and discussed. The topological properties (especially the quantum spin Hall effect and Dirac fermion feature) and potential applications have been summarized. This review also points out the challenge and opportunities for future 2DTI study, especially on the device applications based on the topological properties.

Majorana fermions have been predicted to exist at the edge states of a two-dimensional topological superconductor. We fabricated single quintuple layer (QL) Bi₂Te₃/FeTe heterostructure with the step-flow epitaxy method and studied the topological properties of this system by using angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy. We observed the coexistence of robust superconductivity and edge states on the single QL Bi₂Te₃ islands which can be potential evidence for topological superconductor.

The field of two-dimensional topological semimetals, which emerged at the intersection of two-dimensional materials and topological materials, has been rapidly developing in recent years. In this article, we briefly review the progress in this field. Our focus is on the basic concepts and notions, in order to convey a coherent overview of the field. Some material examples are discussed to illustrate the concepts. We discuss the outstanding problems in the field that need to be addressed in future research.