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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

We theoretically propose a mechanism to realize the superconducting diode effect (SDE): The current can generate a magnetic field, affecting the magnetic moment of magnetic impurity. When the connection region of the Josephson junction is coupled with the magnetic impurity, the supercurrents in positive and negative directions have different influences on the magnetic moment. This results in a phenomenon that the critical supercurrents in these opposite directions are unequal, which is called SDE. We model the Josephson connection region by a quantum dot. Then the critical supercurrents are investigated by the non-equilibrium Green's function method, and we carry out a detailed symmetry analysis on the supercurrent relations. The calculation results confirm that the SDE does exist in this system. Besides, the SDE is significant in a wide parameter space and can be effectively adjusted in various ways. Our design only demands a magnetic impurity and conventional superconductors. The unconventional finite-momentum Cooper pair and spin-orbit coupling are not required, and there is also no need for the existence of chirality or an external magnetic field. Our work provides a universal device structure for the development of superconducting electronics., Comment: 10 pages, 6 figures

Quantum spin Hall effect is characterized by topologically protected helical edge states. Here we study the thermal dissipation of helical edge states by considering two types of dissipation sources. The results show that the helical edge states are dissipationless for normal dissipation sources with or without Rashba spin-orbit coupling in the system, but they are dissipative for spin dissipation sources. Further studies on the energy distribution show that electrons with spin-up and spin-down are both in their own equilibrium without dissipation sources. Spin dissipation sources can couple the two subsystems together to induce voltage drop and nonequilibrium distribution, leading to thermal dissipation, while normal dissipation sources cannot. With the increase of thermal dissipation, the subsystems of electrons with spin-up and spin-down evolve from non-equilibrium finally to mutual equilibrium. In addition, the effects of disorder on thermal dissipation are also discussed. Our work provides clues to reduce thermal dissipation in the quantum spin Hall systems, Comment: 18 pages, 7 figures

Nonuniform strain in graphene can induce a pseudo-magnetic field (PMF) preserving time-reversal symmetry, generating pseudo-Landau levels under zero real magnetic field (MF). The different natures between PMF and real MF lead to the counterpropagating valley-polarized edge states under the PMF and unidirectionally chiral edge states under the real MF. In this work, we find, due to the valley mixing on the armchair edges, the quantum valley Hall edge states only exist at the zigzag edges but not at armchair edges in a uniaxial strained graphene, very different from the case that chiral quantum Hall edge states exist at all edges in pristine graphene under a real MF. We theoretically demonstrate it through the wave function distributions, multi-terminal transport measurements and the electron local occupations, respectively. The interface state in a p-n junction under PMF is further proposed to transport electrons between the conductive zigzag boundaries, which could be used as a valley-polarized single pole double throw switch., Comment: 13 pages, 7 figures

The wavefront dislocation is an important and ubiquitous phenomenon in wave fields. It is closely related to the phase singularity in a wave function. Some recent studies have verified that the wavefront dislocations in the local density of states (LDOS) map can well manifest the intrinsic topological characteristics in graphene and some topological systems. Different from these previous schemes, we raise a transport method to measure such wavefront dislocations in monolayer and Bernal-stacked bilayer graphene. Combining analytical analysis and numerical calculation, we find phase singularities naturally appear in the transmission coefficients between different sublattices, due to the intervalley interference on the electron propagating paths. These phase singularities could contribute wavefront dislocations in the conductance map. Additionally, in bilayer graphene, the wavefront dislocations are found to remain robust even though the tip is coupled to multiple sublattices. Biased bilayer graphene is also explored. Our scheme provides a new transport routine to explore valley-related topological properties of materials., Comment: 15 pages, 9 figures

The photon-assisted tunneling of Majorana bound states in a Majorana nanowire driven by the periodic field is studied both theoretically and numerically. We find that Majorana bound states exhibit an anomalous photon-assisted tunneling signal which is different from an ordinary fermionic state : the height of photonic sidebands is related to the degree of Majorana nonlocality. Moreover, we show that the Bardeen-Cooper-Schrieffer (BCS) charge and spin components of subgap states can be well revealed by the local conductance. Our work illuminates the effect of driving field on Majorana bound states and provides a systematic scheme to directly measure BCS information of overlapping Majorana bound states, Comment: 14 pages, 8 figures

In recent years, counter-intuitive results have shown that the quantum Hall edge states with topological protection can be dissipative. In this paper, we point out that the non-equilibrium nature of edge states in quantum Hall interferometers leads to inevitable dissipation. We consider a graphene interferometer operating in the integer quantum Hall regime and simulate the inelastic scattering that causes both dissipation and dephasing in the interferometer using non-equilibrium Green's function and virtual leads. We describe the dissipation process with the numerical results of the spatial distribution of heat generation and the evolution of electron energy distribution. In addition, with the enhancement of dephasing, a competition between Aharonov-Bohm interference and topologically protected quantized Hall plateaus is observed in the oscillations and fluctuations of the Hall resistances. At a suitable dephasing strength, quantum Hall plateaus can be promoted by dephasing. Our results not only give clues for the design of dissipation-free devices but also provide a platform for studying the non-equilibrium relaxation and the dissipation mechanism of topological states., Comment: 14 pages, 7 figures

We propose a superconducting phase-controlled thermal switch based on a four-terminal graphene-superconductor system. By the coupling of two superconducting leads on a zigzag graphene nanoribbon, both the normal-transmission coefficient and the crossed-Andreev-reflection coefficient, which dominate the thermal conductivity of electrons in the graphene nanoribbon, can be well controlled simultaneously by the phase difference of the superconducting leads. As a result, the thermal conductivity of electrons in the graphene nanoribbon can be tuned and a thermal switching effect appears. Using the nonequilibrium Green's function method, we verify this thermal switching effect numerically. At ambient temperatures less than about one tenth of the superconducting transition temperature, the thermal switching ratio can exceed 2000. The performance of the thermal switch can be regulated by the ambient temperature, and doping or gating can slightly increase the thermal switching ratio. The use of narrower graphene nanoribbons and wider superconducting leads facilitates the obtaining of larger thermal switching ratios. This switching effect of electronic thermal conductance in graphene is expected to be experimentally realized and applied., Comment: 9 pages, 5 figures

We investigate the energy band structure and energy levels of a heterojunction composed of two antiferromagnetic graphene nanoflakes with opposite in-plane antiferromagnetic orderings, in which the modified Kane-Mele model is employed. Before forming an antiferromagnetic graphene heterojunction, the energy gap of helical edge states in each isolated graphene nanoflake are opened by the antiferromagnetic ordering and there is no the in-gap corner state. We find that when two opposite antiferromagnetic graphenes are coupled to form a heterojunction nanoflake, topologically protected zero-dimensional in-gap states can be induced. In addition, we demonstrate that the in-gap states locate at the end of the interface and are robust against magnetic disorder, Anderson disorder, and interfacial magnetic defects. The position and number of the in-gap interface end states in the heterojunction sample can be precise quantum controlled., Comment: 13 pages,12 figures

We study the energy spectrum and energy levels of the extended Kane-Mele model with magnetic atoms on their zigzag edges. It is demonstrated that the edges of ferromagnetism or antiferromagnetism are enough to break the time-reversal symmetry and host one-dimensional gapped edge states. Thus, a second-order topological phase transition could happen, which leads to the emergence of topological in-gap zero-dimensional corner states. We also prove that the in-gap corner states are robust against corner defects and magnetic disorder. Our proposal based on the edge antiferromagnetism shows that the high-order topological states can be realized, although the net magnetization of the material is zero. In addition, we discuss the influence of spin magnetization orientation on the degeneracy and energy of in-gap corner states., Comment: 9 pages, 8 figures

We study the energy spectrum and transport property of a one-dimensional Kitaev quantum ring in a threading magnetic field. It is demonstrated that the magnetic field can effectively induce topological phase transitions for the ring in the topologically nontrivial phase at the zero magnetic field. However, for the ring in the topologically trivial phase at the zero field, there is no topological phase transition, and the energy spectrum of the system is always gapped. The magnetic field can control the appearance and disappearance of Majorana zero-energy states in the Kitaev quantum ring, when one half of the ring is in the topologically nontrivial phase and the other half is in the topologically trivial phase. Furthermore, we calculate the transport properties of the ring connected by two semi-infinite leads. It is found that the resonant peaks of transmission coefficient TQT correspond to the critical points of topological phase transition. In addition, we extend our findings to a more realistic quantum ring adopting a semiconductor nanowire with high spin-orbit coupling, superconducting s-wave pairing, and Zeeman splitting, and prove that our findings are universal.

The quantum Hall (QH) effect, the quantum spin Hall (QSH) effect and the quantum valley Hall (QVH) effect are three peculiar topological insulating phases in graphene. They are characterized by three different types of edge states. These three effects are caused by the external magnetic field, the intrinsic spin-orbit coupling (SOC) and the strain-induced pseudomagnetic field, respectively. Here we theoretically study phase diagrams when these effects coexist and analyze how the edge states evolve between the three. We find the real magnetic field and the pseudomagnetic field will compete above the SOC energy gap while the QSH effect is almost unaffected within the SOC energy gap. The edge states transition from the QH effect or the QVH effect to the QSH effect directly relies on the arrangement of the zeroth Landau levels. Using edge states transitions, we raise a device similar to a spin field effect transistor (spin-FET) and also design a spintronics multiple-way switch., Comment: 16 pages, 10 figures

Without applied bias voltage, a superconducting phase difference can drive a charge Josephson supercurrent in a superconductor junction. In analogy, we here theoretically propose a spin phase that intrinsically generates spin Josephson supercurrent, and this spin Josephson effect is studied in a junction of superconducting nanowire (SNW). We show that spin-orbit coupling and magnetic field give rise to spin-triplet superconductivity in the SNW, thus allow the superfluid of both charge and spin. Next we introduce the concept of spin phase that can be generated by controls of spin current, magnetic field or electric field. By the analysis of pairing correlations and Ginzburg-Landau-type theory, it is shown that the spin phase makes spin-up and spin-down $S=1$ Cooper pairs get opposite phases and move oppositely in a Josephson junction, so that a dissipationless pure spin current is induced. We also derive the formula that the spin current is equal to the derivative of Andreev bound state to the spin phase, which is analogous to that of charge Josephson effect. At last, our calculation verifies the existence of spin supercurrent inside the superconducting gap in the topologically nontrivial phase. Our study provides a view on spin Josephson effect and indicates the potential combination of topological superconductivity and spintronics., Comment: 9 pages, 3 figures

Zero-bias charge conductance peak (ZBCCP) is a significant symbol of Majorana zero modes (MZMs). The proximity effect of s-wave superconductor is usually demanded in the fabrication of MZMs. So in transport experiments, the system is inevitably coupled to the s-wave superconductor. Here we study how the ZBCCP is affected by coupling of the s-wave superconductor. The results show that the ZBCCP could be changed into a zero-bias valley due to the coupling of s-wave superconductor, although the conductance at the zero bias still keeps a quantized value $2e^2/h$. So it does not mean no MZM exists when no ZBCCP is experimentally observed. In addition, the spin transport is investigated. Four reflection processes (the normal reflection, spin-flip reflection, normal Andreev reflection, and equal-spin Andreev reflection) usually occur. The reflection coefficients are strongly dependent on the spin direction of the incident electron, and they may be symmetrical or Fano resonance shapes. But the spin conductance always shows a zero-bias peak with the height $e/2\pi$ regardless of the direction of the spin bias and the coupling strength of the s-wave superconductor. So measuring spin transport properties could be a more reliable method to judge the existence of MZMs., Comment: 8 pages, 5 figures

We investigate the Andreev reflection in a normal metal/charge-4e superconductor junction.Compare with the electron-hole conversion in normal charge-2e superconductors, here four electrons participate simultaneously, enriching the possibility of conversion ways.Using nonequilibrium Green's function method, we obtain a four-particle-type Laudauer-B\"uttiker formula with generalized charge-4e anomalous Green's function to describe it.We then calculate and clarify the behavior of the Andreev coefficient with various incident energy and show the conductance contributed by it.Our research makes up the blank of research for transport property of charge-4e superconductors and can be served as hallmarks for future experimental verifications., Comment: 15 pages, 5 figures

From the low-energy model, the topological field theory indicates that the surface magnetization can open a surface gap in 3D topological insulators (TIs), resulting in a half-quantized Hall conductance. Here by employing the realistic lattice model, we show the occurrence of { the surface phase transitions}, accompanied with the sharp changes of the surface Chern number from $\frac{1}{2}$ to $-\frac{3}{2}$ finally to $-\frac{1}{2}$, in 3D TIs induced by surface magnetization. These surface phase transitions lead to the sudden jumps in the magneto-electric coefficient and the quantum Hall conductance, which are experimentally observable. Furthermore, we present the phase diagram that elucidates the behavior of the 3D TI surface Chern numbers under surface magnetization for different $Z_{4}$ topological numbers. Our study highlights the presence of the new phases with broken bulk-boundary correspondence and enriches understandings of the properties of TIs.

We show that in the proximity of s-wave superconductors, the magnetic topological surface states can transform into Majorana surface state, featuring a single gapless Majorana cone with parity anomaly when the superconducting pairing gap matches the surface magnetization gap. The emergence of $N=1/2$ Majorana chiral edge current is observed at the boundaries between the gap region and the gapless region. Additionally, in systems with a single gapless Majorana cone, a quarter-quantized thermal Hall conductance appears under the dephasing. By mapping the system to a conductor-network model, we identify the appearance of 1/4 chiral heat channels as the cause of the quarter-quantized Hall thermal conductance. We observe the stability of this quarter-quantized thermal conductance under temperature variations, serving as a distinctive feature indicating the presence of a single gapless Majorana cone in the system. Our models can be experimentally realized using magnetic topological insulators or iron-based superconductors.

The combination of spin-orbit coupling and superconductivity induces unconventional spin-triplet correlation in Ising superconductors. We theoretically investigate the spin transport through a normal metal-Ising superconductor junction, showing that Ising superconductors also have the characteristic of spin superconductivity.Due to the existence of spin-triplet Cooper pairs, not only charge supercurrent but also spin supercurrent can transport in Ising superconductors.We analyze the transport process in the junction which is mainly contributed by the equal-spin Andreev reflection and spin-flip reflection, and calculate the spin conductance and the spin injection efficiency under different conditions.Our findings broaden the boundary of spin superconductivity and reveal the potential applications of Ising superconductors in spintronics, especially in controlled long-distance dissipationless spin transport., Comment: 8 pages,6 figures

Fill-in-the-Middle (FIM) has become integral to code language models, enabling generation of missing code given both left and right contexts. However, the current FIM training paradigm, which reorders original training sequences and then performs regular next-token prediction (NTP), often leads to models struggling to generate content that aligns smoothly with the surrounding context. Crucially, while existing works rely on rule-based post-processing to circumvent this weakness, such methods are not practically usable in open-domain code completion tasks as they depend on restrictive, dataset-specific assumptions (e.g., generating the same number of lines as in the ground truth). Moreover, model performance on FIM tasks deteriorates significantly without these unrealistic assumptions. We hypothesize that NTP alone is insufficient for models to learn effective planning conditioned on the distant right context, a critical factor for successful code infilling. To overcome this, we propose Horizon-Length Prediction (HLP), a novel training objective that teaches models to predict the number of remaining middle tokens (i.e., horizon length) at each step. HLP advances FIM with lookahead planning, enabling models to inherently learn infilling boundaries for arbitrary left and right contexts without relying on dataset-specific post-processing. Our evaluation across different models and sizes shows that HLP significantly improves FIM performance by up to 24% relatively on diverse benchmarks, across file-level and repository-level, and without resorting to unrealistic post-processing methods. Furthermore, the enhanced planning capability gained through HLP boosts model performance on code reasoning. Importantly, HLP only incurs negligible training overhead and no additional inference cost, ensuring its practicality for real-world scenarios.

The Chern number is a crucial topological invariant for distinguishing the phases of Chern insulators. Here we find that for Chern insulators with inversion symmetry, the Chern number alone is insufficient to fully characterize their topology. Specifically, distinct topological phases can be differentiated based on skyrmions at different high-symmetry points. Interfaces between these topological phases exhibit gapless helical states, which provide counter-propagating transport channels and robust quantized transport. Additionally, we identify topological transitions that do not involve changes in the Chern number but can be characterized by transitions of skyrmions between high-symmetry points. These transitions arise due to the toroidal structure of the two-dimensional Brillouin zone, which is generally applicable to two-dimensional periodic lattice system. Our research introduces new degrees of freedom for controlling topological optical transport and deepens the understanding of Chern insulators with inversion symmetry.

We propose a universal theory for tunable second-order topological corner states induced by interlayer coupling in bilayer Chern insulators with opposite Chern numbers. We demonstrate that the existence of the topological corner state is determined by the relationship between the twist angle of the bilayer Chern insulators and the normal angles of the two sides of the corner. In addition, the position of these corner states can be sensitively controlled by the twist angle, as confirmed by a rigorous analysis of edge state theory. Our findings serve as a universal theory, opening avenues for the design and realization of higher-order topological materials.

The field-free and highly efficient diodes with the nonreciprocity of supercurrent are believed to be the core block of the superconducting computing devices without dissipation. In this paper, we propose a Josephson diode based upon altermagnets with the vanishing net macroscopic magnetization. The nonreciprocity of supercurrent can be realized without applying any external magnetic field or ferromagnetic exchange field, which can avoid the magnetic cross-talk between the basic elements of the devices. The high efficiency exceeding $40\%$ can be obtained and the efficiency shows the high stability when the structure parameters are changed. The diode efficiency is antisymmetric about the relative orientation angle of the superconducting leads, so that its sign can easily be inverted by adjusting the relative orientation angle. The symmetries satisfied by the current-phase difference relations and the diode efficiency are analyzed by considering the transformations of the junctions under the time-reversal, the spin-rotation and the mirror reflection operations. The high efficiency and the high stability of the Josephson diode effect in our junctions provide the possibility for the design of the field-free dissipationless diode devices., Comment: 13pages,6figures

Full waveform inversion (FWI) is a powerful tool for reconstructing material fields based on sparsely measured data obtained by wave propagation. For specific problems, discretizing the material field with a neural network (NN) improves the robustness and reconstruction quality of the corresponding optimization problem. We call this method NN-based FWI. Starting from an initial guess, the weights of the NN are iteratively updated to fit the simulated wave signals to the sparsely measured data set. For gradient-based optimization, a suitable choice of the initial guess, i.e., a suitable NN weight initialization, is crucial for fast and robust convergence. In this paper, we introduce a novel transfer learning approach to further improve NN-based FWI. This approach leverages supervised pretraining to provide a better NN weight initialization, leading to faster convergence of the subsequent optimization problem. Moreover, the inversions yield physically more meaningful local minima. The network is pretrained to predict the unknown material field using the gradient information from the first iteration of conventional FWI. In our computational experiments on two-dimensional domains, the training data set consists of reference simulations with arbitrarily positioned elliptical voids of different shapes and orientations. We compare the performance of the proposed transfer learning NN-based FWI with three other methods: conventional FWI, NN-based FWI without pretraining and conventional FWI with an initial guess predicted from the pretrained NN. Our results show that transfer learning NN-based FWI outperforms the other methods in terms of convergence speed and reconstruction quality.

Approximation of solutions to partial differential equations (PDE) is an important problem in computational science and engineering. Using neural networks as an ansatz for the solution has proven a challenge in terms of training time and approximation accuracy. In this contribution, we discuss how sampling the hidden weights and biases of the ansatz network from data-agnostic and data-dependent probability distributions allows us to progress on both challenges. In most examples, the random sampling schemes outperform iterative, gradient-based optimization of physics-informed neural networks regarding training time and accuracy by several orders of magnitude. For time-dependent PDE, we construct neural basis functions only in the spatial domain and then solve the associated ordinary differential equation with classical methods from scientific computing over a long time horizon. This alleviates one of the greatest challenges for neural PDE solvers because it does not require us to parameterize the solution in time. For second-order elliptic PDE in Barron spaces, we prove the existence of sampled networks with $L^2$ convergence to the solution. We demonstrate our approach on several time-dependent and static PDEs. We also illustrate how sampled networks can effectively solve inverse problems in this setting. Benefits compared to common numerical schemes include spectral convergence and mesh-free construction of basis functions., Comment: 16 pages, 15 figures

Impurities exist inevitably in two-dimensional materials as they spontaneously adsorb onto the surface during fabrication, usually exerting detrimental effects on electronic transport. Here, we focus on a special type of impurities that preferentially adsorb onto the hollow regions of graphene nanoribbons (GNRs), and study how they affect the quantum transport in GNRs. Contrary to previous knowledge that random adatoms should localize electrons, the so-called Anderson localization, noteworthy quantized conductance peaks (QCPs) are observed at specific electron energies. These QCPs are remarkably robust against variations in system size, GNR edge, and adatom properties, and they can reappear at identical energies following an arithmetic sequence of device width. Further investigation of wavefunction reveals a unique transport mode at each QCP energy which transmits through disordered GNRs reflectionlessly, while all the others become fully Anderson localized, indicating the survival of quantum ballistic transport in the localized regime. Our findings highlight the potential utility of hollow adatoms as a powerful tool to manipulate the conductivity of GNRs, and deepen the understanding of the interplay between impurities and graphene., Comment: 8 pages, 4 figures, and 1 table; comments are welcome

Phase singularities are phase-indeterminate points where wave amplitudes are zero, which manifest as phase vertices or wavefront dislocations. In the realm of optical and electron beams, the phase singularity has been extensively explored, demonstrating a profound connection to orbital angular momentum. Direct local imaging of the impact of orbital angular momentum on phase singularities at the nanoscale, however, remains a challenge and has yet to be achieved. Here, we study the role of orbital angular momentum in phase singularities in graphene, particularly at the atomic level, through scanning tunneling microscopy and spectroscopy. Our experiments demonstrate that the scatterings between different orbital angular momentum states, which are induced by local rotational symmetry-breaking potentials, can generate additional phase singularity, and result in robust single wavefront dislocation in real space. Our results pave the way for exploring the effects of orbital degree of freedom on quantum phases in quasiparticle interference processes., Comment: 28 pages, 3 figures, 10 extended figures

This study introduces bifurcated attention, a method designed to enhance language model inference in shared-context batch decoding scenarios. Our approach addresses the challenge of redundant memory IO costs, a critical factor contributing to latency in high batch sizes and extended context lengths. Bifurcated attention achieves this by strategically dividing the attention mechanism during incremental decoding into two separate GEMM operations: one focusing on the KV cache from prefill, and another on the decoding process itself. While maintaining the computational load (FLOPs) of standard attention mechanisms, bifurcated attention ensures precise computation with significantly reduced memory IO. Our empirical results show over 2.1$\times$ speedup when sampling 16 output sequences and more than 6.2$\times$ speedup when sampling 32 sequences at context lengths exceeding 8k tokens on a 7B model that uses multi-head attention. The efficiency gains from bifurcated attention translate into lower latency, making it particularly suitable for real-time applications. For instance, it enables massively parallel answer generation without substantially increasing latency, thus enhancing performance when integrated with post-processing techniques such as re-ranking.

We study the energy levels and transport properties of an extended Kitaev chain with a phase gradient. It is demonstrated that the hopping phase difference can effectively induce the generation of Majorana bound states, which are located at the non-endpoint sites of the chain. The number and positions of the non-endpoint Majorana bound states can be modulated by the hopping phase difference and initial hopping phase, respectively. In addition, we propose a protocol to realize topological braiding operation by exchanging the positions of two Majorana bound states in the extended Kitaev ring. Furthermore, we also implement the braiding of any two of the multiple Majorana bound states in the extended Kitaev double rings.

We propose a general principle for realizing second-order topological corner states in the modified Kane-Mele model with magnetization. It is demonstrated that the sign of the edge Dirac mass depends on the magnetization of the edge sublattice termination. By adjusting the directions of magnetization according to the type of sublattice at the termination of two edges, a mass domain wall can be induced in the presence of topological corner states at an arbitrary position. All previous work on introducing magnetization in the Kane-Mele model to realize second-order topological corner states can be explained by the presence of the Dirac mass domain wall with opposite signs. Applying this principle, we design square-shaped and armchair-type hexagon-shaped graphene nanoflakes with edge magnetization, allowing for the emergence of second-order topological corner states. Our findings serve as a general theory, demonstrating that the realization of second-order topological corner states is not limited by boundary type or nanoflake shape.

We study the Josephson effect in the spin-singlet superconductor/altermagnet/spin-triplet superconductor junctions using the Green's function method. The current-phase difference relationships in the junctions strongly depend on the orientation of altermagnet and the types of the Cooper pairs. For the orientation angle equal to odd multiples of $\pi/4$, the current-phase difference relationships are of the $\sin{2\phi}$ type, which are irrespective of the pairing wave functions in superconductors. For the other orientation angles, the emergence of the lowest order current becomes possible and its form, $\sin\phi$ or $\cos\phi$, depends on the pairing wave functions in superconductors. The $\phi_{0}$ phase and the $0$-$\pi$ transition can be realized in our junctions due to the appearance of the lowest order current. The selection rules for the lowest order current are presented. The symmetric relations satisfied by the current-phase difference relationships are analyzed through considering the transformations of the junctions under the mirror reflection, the time-reversal and the spin rotation operations. Our results not only provide a method to detect the intrinsic spin-triplet superconductivity but also possess application values in the design of the field-free quantum devices., Comment: 10pages,3figures

The goal of Continual Learning (CL) is to continuously learn from new data streams and accomplish the corresponding tasks. Previously studied CL assumes that data are given in sequence nose-to-tail for different tasks, thus indeed belonging to Serial Continual Learning (SCL). This paper studies the novel paradigm of Parallel Continual Learning (PCL) in dynamic multi-task scenarios, where a diverse set of tasks is encountered at different time points. PCL presents challenges due to the training of an unspecified number of tasks with varying learning progress, leading to the difficulty of guaranteeing effective model updates for all encountered tasks. In our previous conference work, we focused on measuring and reducing the discrepancy among gradients in a multi-objective optimization problem, which, however, may still contain negative transfers in every model update. To address this issue, in the dynamic multi-objective optimization problem, we introduce task-specific elastic factors to adjust the descent direction towards the Pareto front. The proposed method, called Elastic Multi-Gradient Descent (EMGD), ensures that each update follows an appropriate Pareto descent direction, minimizing any negative impact on previously learned tasks. To balance the training between old and new tasks, we also propose a memory editing mechanism guided by the gradient computed using EMGD. This editing process updates the stored data points, reducing interference in the Pareto descent direction from previous tasks. Experiments on public datasets validate the effectiveness of our EMGD in the PCL setting., Comment: Submited to IEEE TPAMI

In a molecule formed by two atoms, energy difference between bonding and antibonding orbitals should depend on distance of the two atoms. However, exploring molecular orbitals of two natural atoms with tunable distance has remained an outstanding experimental challenge. Graphene quantum dots (GQDs) can be viewed as relativistic artificial atoms, therefore, offering a unique platform to study molecular physics. Here, through scanning tunneling microscope (STM), we create and directly visualize the formation process of relativistic artificial molecules based on two coupled GQDs with tunable distance. Our study indicates that energy difference between the bonding and antibonding orbitals of the lowest quasibound state increases linearly with inverse distance of the two GQDs due to the relativistic nature of the artificial molecule. For quasibound states with higher orbital momenta, the coupling between these states leads to half-energy spacing of the confined states because the length of the molecular-like orbit is about twice that of the atomic-like orbit. Evolution from ring-like whispering-gallery modes in the artificial atoms to figure-eight orbitals in the artificial molecules is directly imaged. The ability to resolve the coupling and orbitals of the relativistic artificial molecule at the nanoscale level yields insights into the behavior of quantum-relativistic matter.

Non-Hermitian systems have garnered significant attention due to the emergence of novel topology of complex spectra and skin modes. However, investigating transport phenomena in such systems faces obstacles stemming from the non-unitary nature of time evolution. Here, we establish the continuity equation for a general non-Hermitian Hamiltonian in the Schr\"odinger picture. It attributes the universal non-conservativity to the anti-commutation relationship between particle number and non-Hermitian terms. Our work derives a comprehensive current formula for non-Hermitian systems using Green's function, applicable to both time-dependent and steady-state responses. To demonstrate the validity of our approach, we calculate the local current in models with one-dimensional and two-dimensional settings, incorporating scattering potentials. The spatial distribution of local current highlights the widespread non-Hermitian phenomena, including skin modes, non-reciprocal quantum dots, and corner states. Our findings offer valuable insights for advancing theoretical and experimental research in the transport of non-Hermitian systems.

In this work, an innovative data-driven moving horizon state estimation is proposed for model dynamic-unknown systems based on Bayesian optimization. As long as the measurement data is received, a locally linear dynamics model can be obtained from one Bayesian optimization-based offline learning framework. Herein, the learned model is continuously updated iteratively based on the actual observed data to approximate the actual system dynamic with the intent of minimizing the cost function of the moving horizon estimator until the desired performance is achieved. Meanwhile, the characteristics of Bayesian optimization can guarantee the closest approximation of the learned model to the actual system dynamic. Thus, one effective data-driven moving horizon estimator can be designed further on the basis of this learned model. Finally, the efficiency of the proposed state estimation algorithm is demonstrated by several numerical simulations., Comment: 12 pages,3 figures