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Topologically protected corner states serve as a key indicator for two-dimensional higher-order topological insulators, yet they have not been experimentally identified in realistic materials. Here, by utilizing the effective tight-binding model and symmetry arguments, we establish a connection between higher-order topological insulators and twisted bilayer kagome lattices. We find that the topologically nontrivial bulk band gap arises in the twisted bilayer kagome lattice system due to twist-induced intervalley scattering, leading to the emergence of higher-order topological insulators with a range of commensurate twist angles, and the higher-order band topology is verified by the second Stiefel-Whitney number and fractionally quantized corner charges. Moreover, we investigate the influence of disorder and charge density wave order on the stability of higher-order topological insulator phases. The results show that the corner states of twisted bilayer kagome lattice systems are robust with respect to disorder and charge density wave. Our work not only provides a feasible approach to realize the readily controllable higher-order topological insulator phases by employing a simple twist technique, but also demonstrates that the twisted bilayer kagome lattice systems exhibit the robustness of higher-order band topology, making it feasible to check above prediction in experiments., Comment: 7 pages, 4 figures

Recent studies have attracted widespread attention on magnet-superconductor hybrid systems with emergent topological superconductivity. Here, we present the Floquet engineering of realistic two-dimensional topological nodal-point superconductors that are composed of antiferromagnetic monolayers in proximity to an s-wave superconductor. We show that Floquet chiral topological superconductivity arises naturally due to light-induced breaking of the effective time-reversal symmetry. More strikingly, we find that the Floquet chiral topological superconducting phases can be flexibly controlled by irradiating elliptically polarized light, with the photon-dressed quasi-energy spectrum carrying different Chern numbers. Such optically switchable topological transition is attributed to the simultaneous creations (or annihilations) of valley pairs. Our findings provide a feasible approach for achieving the Floquet chiral topological superconductivity with flexible tunability, which would draw extensive attention in experiments.

In two-dimensional topological nodal superconductors, Majorana edge states have been conventionally believed to exhibit only spin-triplet pairing correlations. However, we reveal a substantial spin-singlet pairing component in Majorana edge states of antiferromagnetic topological nodal-point superconductors. This unexpected phenomenon emerges from the interplay between antiferromagnetic order and symmetry, resulting in Majorana edge states with a nearly flat band dispersion, deviating from the strictly flat band. Crucially, this phenomenon is detectable through spin-selective Andreev reflection, where the zero-bias conductance peaks are maximized when the spin of incident electrons is nearly antiparallel to that of Majorana edge excitations. This discovery unveils a unique spin signature for Andreev reflection resonances, advancing our fundamental understanding of spin-dependent mechanisms in topological superconductivity and representing a significant step towards the experimental detection of Majorana fermions., Comment: 6 pages, 3 figures

In two-dimensional antiferromagnets, we identify the mixed Berry curvature as the geometrical origin of the nonreciprocal directional dichroism (NDD), which refers to the difference in light absorption with the propagation direction flipped. Such a Berry curvature is strongly tied to the uniaxial strain in accordance with the symmetry constraint, leading to a highly tunable NDD, whose sign and magnitude can be manipulated via the strain direction. As a concrete example, we demonstrate such a phenomenon in a lattice model of MnBi2Te4. The coupling between the mixed Berry curvature and strain also suggests the magnetic quadrupole of the Bloch wave packet as the macroscopic order parameter probed by the NDD in two dimensions, distinct from the multiferroic order P times M or the spin toroidal and quadrupole order within a unit cell in previous studies. Our work paves the way of the Berry-curvature engineering for optical nonreciprocity in two-dimensional antiferromagnets.

Recent studies have attracted intense attention on the quasi-2D kagome superconductors $ A\text{V}_3\text{Sb}_5 $ ($ A = $ K, Rb, and Cs) where the unexpected chiral flux phase (CFP) associates with the spontaneous time-reversal symmetry breaking in charge density wave (CDW) states. Here, commencing from the 2-by-2 CDW phases, we bridge the gap between topological superconductivity (TSC) and time-reversal asymmetric CFP in kagome systems. Several chiral TSC states featuring distinct Chern numbers emerge for an s-wave or a d-wave superconducting pairing symmetry. Importantly, these CFP-based TSC phases possess unique gapless edge modes with mixed chiralities (i.e., both positive and negative chiralities), but with the net chiralities consistent with the Bogoliubov-de Gennes Chern numbers. We further study the transport properties of a two-terminal junction, using Chern insulator or normal metal leads via atomic Green's function method with Landauer-B\"uttiker formalism. In both cases, the normal electron tunneling and the crossed Andreev reflection oscillate as the chemical potential changes, but together contribute to plateau transmissions (1 and 3/2, respectively). These behaviors can be regarded as the signature of a topological superconductor hosting edge states with mixed chiralities., Comment: 6 pages, 4 figures

Numerous attempts have been made so far to explore the quantum anomalous Hall effect (QAHE), but the ultralow observed temperature strongly hinders its practical applications. Hence, it is of great interest to go beyond the existing paradigm of QAHE. Here, we propose that Floquet engineering offers a strategy to realize the QAHE via hybridization of Floquet-Bloch bands. Based on first-principles calculations and Floquet theorem, we unveil that nonequilibrium valley-polarized QAHE (VP-QAHE), independent of magnetic orders, is widely present in ferromagnetic and nonmagnetic members of two-dimensional family materials $M$Si$_2$$Z_4$ ($M$ = Mo, W, V; $Z$ = N, P, As) by irradiating circularly polarized light (CPL). Remarkably, by tuning the frequency, intensity, and handedness of incident CPL, the Chern number of VP-QAHE is highly tunable and up to $\mathcal{C}=\pm 4$. We reveal that such Chern number tunable VP-QAHE attributes to light-induced trigonal warping and multiple band inversion at different valleys. The valley-resolved chiral edge states and quantized plateau of Hall conductance, which facilitates the experimental measurement, are visible inside the global band gap. Our work not only establishes Floquet Engineering of nonequilibrium VP-QAHE with tunable Chern number in realistic materials, but also provides a promising avenue to explore emergent topological phases under light irradiation., Comment: 6 pages, 4 figures

Recently, the magnetic domain walls have been experimentally observed in antiferromagnetic topological insulators MnBi$_2$Te$_4$, where we find that the topological zero-line modes (ZLMs) appear along the domain walls. Here, we theoretically demonstrate that these ZLMs are layer-dependent in MnBi$_2$Te$_4$ multilayers. For domain walls with out-of-plane ferromagnetism, we find that ZLMs are equally distributed in the odd-number layers. When domain walls possess in-plane magnetization, the ZLMs can also exist in even-number layers due to in-plane mirror-symmetry breaking. Moreover, the conductive channels are mainly distributed in the outermost layers with increasing layer thickness. Our findings lay out a strategy in manipulating ZLMs and also can be utilized to distinguish the corresponding magnetic structures.

Two-dimensional higher-order topology is usually studied in (nearly) particle-hole symmetric models, so that an edge gap can be opened within the bulk one. But more often deviates the edge anticrossing even into the bulk, where corner states are difficult to pinpoint. We address this problem in a graphene-based $\mathbb{Z}_2$ topological insulator with spin-orbit coupling and in-plane magnetization both originating from substrates through a Slater-Koster multi-orbital model. The gapless helical edge modes cross inside the bulk, where is also located the magnetization-induced edge gap. After demonstrating its second-order nontriviality in bulk topology by a series of evidence, we show that a difference in bulk-edge onsite energy can adiabatically tune the position of the crossing/anticrossing of the edge modes to be inside the bulk gap. This can help unambiguously identify two pairs of topological corner states with nonvanishing energy degeneracy for a rhombic flake. We further find that the obtuse-angle pair is more stable than the acute-angle one. These results not only suggest an accessible way to "find" topological corner states, but also provide a higher-order topological version of "bulk-boundary correspondence".

We theoretically investigate the localization mechanism of quantum anomalous Hall Effect (QAHE) with large Chern numbers $\mathcal{C}$ in bilayer graphene and magnetic topological insulator thin films, by applying either nonmagnetic or spin-flip (magnetic) disorders. We show that, in the presence of nonmagnetic disorders, the QAHEs in both two systems become Anderson insulating as expected when the disorder strength is large enough. However, in the presence of spin-flip disorders, the localization mechanisms in these two host materials are completely distinct. For the ferromagnetic bilayer graphene with Rashba spin-orbit coupling, the QAHE with $\mathcal{C}=4$ firstly enters a Berry-curvature mediated metallic phase, and then becomes localized to be Anderson insulator along with the increasing of disorder strength. While in magnetic topological insulator thin films, the QAHE with $\mathcal{C=N}$ firstly enters a Berry-curvature mediated metallic phase, then transitions to another QAHE with ${\mathcal{C}}={\mathcal{N}}-1$ along with the increasing of disorder strength, and is finally localized to the Anderson insulator after ${\mathcal{N}}-1$ cycling between the QAHE and metallic phases. For the unusual findings in the latter system, by analyzing the Berry curvature evolution, it is known that the phase transitions originate from the exchange of Berry curvature carried by conduction (valence) bands. At the end, we provide a phenomenological picture related to the topological charges to help understand the underlying physical origins of the two different phase transition mechanisms.

We numerically investigate the electronic transport properties between two mesoscopic graphene disks with a twist by employing the density functional theory coupled with non-equilibrium Green's function technique. By attaching two graphene leads to upper and lower graphene layers separately, we explore systematically the dependence of electronic transport on the twist angle, Fermi energy, system size, layer stacking order and twist axis. When choose different twist axes for either AA- or AB-stacked bilayer graphene, we find that the dependence of conductance on twist angle displays qualitatively distinction, i.e., the systems with "top" axis exhibit finite conductance oscillating as a function of the twist angle, while the ones with "hollow" axis exhibit nearly vanishing conductance for different twist angles or Fermi energies near the charge neutrality point. These findings suggest that the choice of twist axis can effectively tune the interlayer conductance, making it a crucial factor in designing of nanodevices with the twisted van der Waals multilayers.

We theoretically study the finite-size effects in the dynamical response of a quantum anomalous Hall insulator in the disk geometry. Semi-analytic and numerical results are obtained for the wavefunctions and energies of the disk within a continuum Dirac Hamiltonian description subject to a topological infinite mass boundary condition. Using the Kubo formula, we obtain the frequency-dependent longitudinal and Hall conductivities and find that optical transitions between edge states contribute dominantly to the real part of the dynamic Hall conductivity for frequency values both within and beyond the bulk band gap. We also find that the topological infinite mass boundary condition changes the low-frequency Hall conductivity to $ e^2/h $ in a finite-size system from the well-known value $ e^2/2h $ in an extended system. The magneto-optical Faraday rotation is then studied as a function of frequency for the setup of a quantum anomalous Hall insulator mounted on a dielectric substrate, showing both finite-size effects of the disk and Fabry-P\'erot resonances due to the substrate. Our work demonstrates the important role played by the boundary condition in the topological properties of finite-size systems through its effects on the electronic wavefunctions., Comment: 11 pages, 8 figures

Femtosecond micromachining offers a contact-free and mask-less technique for material patterning. With ultrafast laser irradiation, permanent modifications to the properties of single layer graphene through material ablation or defect introduction can be induced. Multiple femtosecond pulse interactions with a single layer graphene are studied and a low laser ablation threshold ~9.2 mJ/cm2 is reported for a 15 second illumination time. Clean ablated structures are generated in such a multi pulse irradiation configuration at low pulse energies as an attractive alternative to ablation with single femtosecond, high energy pulses. For a fully ablated graphene hole, a radially symmetric region extending around 2 um from the ablated edge is characterized by strong defect generation. Average distances between point-defects down to ~58 nm are derived and Raman spectroscopy implies that overall there is a strong resemblance to amorphous structures. For fluence values around 75% of the ablation threshold, modification with defect generation down to ~48 nm average defects lengths is reported, while the underlying graphene structure is maintained. Thus, depending on the laser parameter choice, the same laser configuration can be used to ablate graphene or to primarily introduce defect states. The presented findings offer interesting insights into femtosecond induced structural modifications of graphene that can lead to improved precision ablation and patterning of single-layer materials at the micro- and nano-scale. Further, this can be attractive for graphene or carbon-based device fabrication as well as sensor and transistor applications, where regions of varying carrier concentrations and different electrical, optical or physical properties are desired.

In this paper, we present a hierarchical path planning framework called SG-RL (subgoal graphs-reinforcement learning), to plan rational paths for agents maneuvering in continuous and uncertain environments. By "rational", we mean (1) efficient path planning to eliminate first-move lags; (2) collision-free and smooth for agents with kinematic constraints satisfied. SG-RL works in a two-level manner. At the first level, SG-RL uses a geometric path-planning method, i.e., Simple Subgoal Graphs (SSG), to efficiently find optimal abstract paths, also called subgoal sequences. At the second level, SG-RL uses an RL method, i.e., Least-Squares Policy Iteration (LSPI), to learn near-optimal motion-planning policies which can generate kinematically feasible and collision-free trajectories between adjacent subgoals. The first advantage of the proposed method is that SSG can solve the limitations of sparse reward and local minima trap for RL agents; thus, LSPI can be used to generate paths in complex environments. The second advantage is that, when the environment changes slightly (i.e., unexpected obstacles appearing), SG-RL does not need to reconstruct subgoal graphs and replan subgoal sequences using SSG, since LSPI can deal with uncertainties by exploiting its generalization ability to handle changes in environments. Simulation experiments in representative scenarios demonstrate that, compared with existing methods, SG-RL can work well on large-scale maps with relatively low action-switching frequencies and shorter path lengths, and SG-RL can deal with small changes in environments. We further demonstrate that the design of reward functions and the types of training environments are important factors for learning feasible policies., Comment: 20 pages

Due to their nonlocality, Majorana bound states have been proposed to induce current-current correlations (CCCs) that are completely different from those induced by low-energy fermionic Andreev bound states. Such characteristics can be used as a signature to detect Majorana bound states. Herein, we studied the Majorana and fermionic Andreev bound states in a two-dimensional topological insulator system. We found that nonlocality occurs for both types of bound states and that their coupling strengths depend on system parameters in the same pattern. Majorana and fermionic Andreev bound states show the same differential CCCs characteristics, thereby indicating a universal behavior for both types of bound states. The maximal cross differential CCCs are robust to the structural asymmetry of the system.

At the interface between two-dimensional materials with different topologies, topologically protected one-dimensional states (also named as zero-line modes) arise. Here, we focus on the quantum anomalous Hall effect based zero-line modes formed at the interface between regimes with different Chern numbers. We find that, these zero-line modes are chiral and unilaterally conductive due to the breaking of time-reversal invariance. For a beam splitter consisting of two intersecting zero lines, the chirality ensures that current can only be injected from two of the four terminals. Our numerical results further show that, in the absence of contact resistance, the (anti-)clockwise partitions of currents from these two terminals are the same owing to the current conservation, which effectively simplifies the partition laws. We find that the partition is robust against relative shift of Fermi energy, but can be effectively adjusted by tuning the relative magnetization strengths at different regimes or relative angles between zero lines., Comment: 6 pages, 4 figures

We demonstrate that zero-energy Majorana bound state, in the ferromagnetic insulator (FI)-superconductor (SC) junction formed on the edge of two-dimensional topological insulator, exhibits three types of spin-triplet pairing correlations and its spin polarization direction is position independent in ferromagnetic insulator. When an electron is injected with a spin (anti-)parallel to this direction, equal-spin Andreev reflection exhibits the widest (narrowest) resonance peak. Similar behaviour is found when the coupling between two Majorana bound states in a FI-SC-FI junction is invoked, though an additional weak spin-singlet pairing correlation is generated. These signatures can readily facilitate the experimental detection of spin-triplet correlations and spin polarization of Majorana bound states., Comment: 5 pages, 5 figures

In van der Waals multilayers of triangular lattice, trigonal warping occurs universally due to the interlayer hopping. We theoretically investigate the effect of trigonal warping upon distinctive topological phases, like the quantum anomalous Hall effect (QAHE) and the quantum valley Hall effect (QVHE). Taking Bernal-stacked bilayer graphene as an example, we find that the trigonal warping plays a crucial role in the formation of QAHE in large exchange field and/or interlayer potential difference by inducing extra band inversion points at momentum further away from high symmetric point. The presence of trigonal warping shrinks the phase space of QAHE and QVHE, leading to the emergence of valley-polarized QAHE with high Chern numbers ranging from $ \mathcal{C}=-7 $ to $ 7 $. These results suggest that the universal trigonal warping may play important role when the Bloch states at momentum away from high-symmetric points are involved., Comment: 4+1 pages, 3 figures