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The interplay between novel topological states and superconductivity has garnered substantial interest due to its potential for topological quantum computing. The Josephson effect serves as a useful probe for edge superconductivity in these hybrid topological materials. In Josephson junctions based on topological materials, supercurrents exhibit unique quantum interference patterns, including the conventional Fraunhofer oscillations, the $\Phi_0$-periodic oscillation, and the $2\Phi_0$-periodic oscillation in response to the external magnetic field ($\Phi_0 = h/2e$ is the flux quantum, $h$ the Planck constant, and $e$ the electron charge). These interference patterns stem from varied Andreev reflection mechanisms and the associated current density profiles. This review seeks to comprehensively examine the theoretical and experimental advancements in understanding the quantum interference patterns of edge supercurrents in Josephson junctions based on quantum spin Hall, quantum Hall, and quantum anomalous Hall systems., Comment: 14 pages, 7 figures

Anderson localization is anticipated to play a pivotal role in the manifestation of the quantum anomalous Hall effect, akin to its role in conventional quantum Hall effects. The significance of Anderson localization is particularly pronounced in elucidating the reasons behind the fragility of the observed quantum anomalous Hall state in the intrinsic magnetic topological insulator MnBi2Te4 with a large predicted magnetic gap. Here, employing varying sized MnBi2Te4 micro/nano-structures fabricated from a single molecular-beam-epitaxy-grown thin film, we have carried out a systematic size- and temperature-dependent study on the transport properties of the films regarding the quantum anomalous Hall states. The low-temperature transport properties of the finite-sized MnBi2Te4 samples can be quantitatively understood through Anderson localization, which plays an indispensable role in stabilizing the ground states. At higher temperatures, the failure of electron localization induced by an excessively short electronic dephasing length is identified as the cause of deviation from quantization. The work reveals that electronic dephasing and localization are non-negligible factors in designing high-temperature quantum anomalous Hall systems., Comment: 20 pages, 4 figures

The intriguing interplay between topology and superconductivity has attracted significant attention, given its potential for realizing topological superconductivity. In the quantum anomalous Hall insulators (QAHIs)-based junction, the supercurrents are carried by the chiral edge states, characterized by a $2\Phi_0$ magnetic flux periodicity ($\Phi_0 = h/2e$ is the flux quantum, $h$ the Planck constant, and $e$ the electron charge). However, experimental observations indicate the presence of bulk carriers in QAHI samples due to magnetic dopants. In this study, we reveal a systematic transition from edge-state to bulk-state dominant supercurrents as the chemical potential varies from the bulk gap to the conduction band. This results in an evolution from a $2\Phi_0$-periodic oscillation pattern to an asymmetric Fraunhofer pattern. Furthermore, a novel Fraunhoher-like pattern emerges due to the coexistence of chiral edge states and bulk states caused by magnetic {\color{black}domains}, even when the chemical potential resides within the gap. These findings not only advance the theoretical understanding but also pave the way for the experimental discovery of the chiral Josephson effect based on QAHI doped with magnetic impurities., Comment: 8 pages, 8 figures

The real magnetic fields (MFs) acting on the graphene can induce flat real Landau levels (LLs). As an analogy, strains in graphene can produce significant pseudo MFs, triggering the appearance of dispersive pseudo LLs. By analyzing the low-energy effective Hamiltonian, we introduce the concept of the effective orbital MFs to integrate the real MFs and pseudo MFs. Accordingly, we obtain the complex LLs which incorporate the real LLs and pseudo LLs, and calculate the related transport properties. These concepts enable us to uncover the mechanisms driving the fragility of pseudo LLs against disorders and dephasing, proving that tuning the real MFs and Fermi energy can effectively improve the robust performances. Furthermore, the tunability of the valley-polarized currents is also studied, opening up new possibilities for the design of valleytronics devices., Comment: 9 figures

Strain can tailor the band structures and properties of graphene nanoribbons (GNRs) with the well-known emergent pseudo-magnetic fields and the corresponding pseudo-Landau levels (pLLs). We design one type of the zigzag GNR (ZGNR) with reverse strains, producing pseudo-magnetic fields with opposite signs in the lower and upper half planes. Therefore, electrons propagate along the interface as "snake states", experiencing opposite Lorentz forces as they cross the zero field border line. By using the Landauer-Buttiker formalism combined with the nonequilibrium Green's function method, the existence and robustness of the reverse strain-induced snake states are further studied. Furthermore, the realization of long-thought pure valley currents in monolayer graphene systems is also proposed in our device., Comment: 6 figures

Recently, the magnetic topological insulator MnBi$_2$Te$_4$ emerged as a competitive platform to realize quantum anomalous Hall (QAH) states. We report a Berry-curvature splitting mechanism to realize the QAH effect in the disordered magnetic TI multilayers when switching from an antiferromagnetic order to a ferromagnetic order. We reveal that the splitting of spin-resolved Berry curvature, originating from the separation of the mobility edge during the magnetic switching, can give rise to a QAH insulator even \emph{without} closing the band gap. We present a global phase diagram, and also provide a phenomenological picture to elucidate the Berry curvature splitting mechanism by the evolution of topological charges. At last, we predict that the Berry curvature splitting mechanism will lead to a reentrant QAH effect, which can be detected by tuning gate voltage. Our theory will be instructive for the studies of the QAH effect in MnBi$_2$Te$_4$ in future experiments., Comment: 6 pages, 5 figures

Quantum Griffiths singularity (QGS) reveals the profound influence of quenched disorder on the quantum phase transitions, characterized by the divergence of the dynamical critical exponent at the boundary of the vortex glass-like phase, named as quantum Griffiths phase. However, in the absence of vortices, whether the QGS can exist under parallel magnetic field remains a puzzle. Here we study the magnetic field induced superconductor-metal transition in ultrathin crystalline PdTe2 films grown by molecular beam epitaxy. Remarkably, the QGS emerges under both perpendicular and parallel magnetic field in 4-monolayer PdTe2 films. The direct activated scaling analysis with a new irrelevant correction has been proposed, providing important evidence of QGS. With increasing film thickness to 6 monolayers, the QGS disappears under perpendicular field but persists under parallel field, and this discordance may originate from the differences in microscopic processes. Our work demonstrates the universality of parallel field induced QGS and can stimulate further investigations on novel quantum phase transitions under parallel magnetic field.

The interplay between quenched disorder and critical behavior in quantum phase transitions is conceptually fascinating and of fundamental importance for understanding phase transitions. However, it is still unclear whether or not the quenched disorder influences the universality class of quantum phase transitions. More crucially, the absence of superconducting-metal transitions under in-plane magnetic fields in 2D superconductors imposes constraints on the universality of quantum criticality. Here, we discover the tunable universality class of superconductor-metal transition by changing the disorder strength in $\beta$-W films with varying thickness. The finite-size scaling uncovers the switch of universality class: quantum Griffiths singularity to multiple quantum criticality at a critical thickness of $t_{c \perp 1}\sim 8 nm$ and then from multiple quantum criticality to single criticality at $t_{c\perp 2}\sim 16 nm$. Moreover, the superconducting-metal transition is observed for the first time under in-plane magnetic fields and the universality class is changed at $t_{c \parallel }\sim 8 nm$. The discovery of tunable universality class under both out-of-plane and in-plane magnetic fields provides broad information for the disorder effect on superconducting-metal transitions and quantum criticality.

Twisted light carries a well-defined orbital angular momentum (OAM) per photon. The quantum number l of its OAM can be arbitrarily set, making it an excellent light source to realize high-dimensional quantum entanglement and ultra-wide bandwidth optical communication structures. To develop solid-state optoelectronic systems compatible with such promising light sources, a timely challenging task is to efficiently and coherently transfer the optical OAM of light to certain solid-state optoelectronic materials. Among the state-of-the-art emergent materials, atomically thin monolayer transition metal dichalcogenide (ML-TMD), featured by ultra-strong light-matter interaction due to its reduced dimensionality, renders itself a potential material suitable for novel applications. In this study, we carried out photoluminescence (PL) spectroscopy studies of ML-MoS2 under photoexcitation of twisted light with well-defined quantized OAM. We mainly observed pronounced increases in the spectral peak energy for every increment of l of the incident twisted light. The observed non-linear l-dependence of the spectral blue shifts evidences the OAM transfer from the exciting twisted light to the valley excitons in ML-TMDs, which is well accounted for by our analysis and computational simulation. Even more excitingly, the twisted light excitation is shown to make excitonic transitions relative to the transferred OAM, enabling us to infer the exciton band dispersion from the measured spectral shifts. Consequently, the measured non-linear l-dependent spectral shifts revealed an unusual lightlike exciton band dispersion of valley excitons in ML-TMDs that is predicted by previous theoretical studies and evidenced for the first time via our experimental setup that utilizes the unique twisted light source., Comment: 29 pages, 12 figures

Scaling theory predicts complete localization in $d=2$ in quantum systems belonging to orthogonal class (i.e. with time-reversal symmetry and spin-rotation symmetry). The conductance $g$ behaves as $g \sim exp(-L/l)$ with system size $L$ and localization length $l$ in the strong disorder limit. However, classical systems can always have metallic states in which Ohm's law shows a constant $g$ in $d=2$. We study a two-dimensional quantum percolation model by controlling dephasing effects. The numerical investigation of $g$ aims at simulating a quantum-to-classical percolation evolution. An unexpected metallic phase, where $g$ increases with $L$, generates immense interest before the system becomes completely classical. Furthermore, the analysis of the scaling plot of $g$ indicates a metal-insulator crossover., Comment: 5 pages, 5 figures