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This paper addresses the problem of modeling and estimating dynamic multi-valued mappings. While most mathematical models provide a unique solution for a given input, real-world applications often lack deterministic solutions. In such scenarios, estimating dynamic multi-valued mappings is necessary to suggest different reasonable solutions for each input. This paper introduces a deep neural network framework incorporating a generative network and a classification component. The objective is to model the dynamic multi-valued mapping between the input and output by providing a reliable uncertainty measurement. Generating multiple solutions for a given input involves utilizing a discrete codebook comprising finite variables. These variables are fed into a generative network along with the input, producing various output possibilities. The discreteness of the codebook enables efficient estimation of the output's conditional probability distribution for any given input using a classifier. By jointly optimizing the discrete codebook and its uncertainty estimation during training using a specially designed loss function, a highly accurate approximation is achieved. The effectiveness of our proposed framework is demonstrated through its application to various imaging problems, using both synthetic and real imaging data. Experimental results show that our framework accurately estimates the dynamic multi-valued mapping with uncertainty estimation.

Moir\'e materials represent strongly interacting electron systems bridging topological and correlated physics. Despite significant advances, decoding wavefunction properties underlying the quantum geometry remains challenging. Here, we utilize polarization-resolved photocurrent measurements to probe magic-angle twisted bilayer graphene, leveraging its sensitivity to the Berry connection that encompasses quantum "textures" of electron wavefunctions. Using terahertz light resonant with optical transitions of its flat bands, we observe bulk photocurrents driven by broken symmetries and reveal the interplay between electron interactions and quantum geometry. We observe inversion-breaking gapped states undetectable through quantum transport, sharp changes in the polarization axes caused by interaction-induced band renormalization, and recurring photocurrent patterns at integer fillings of the moir\'e unit cell that track the evolution of quantum geometry through the cascade of phase transitions. The large and tunable terahertz response intrinsic to flat-band systems offers direct insights into the quantum geometry of interacting electrons and paves the way for innovative terahertz quantum technologies.

Space-based gravitational wave detection is extremely sensitive to disturbances. The Keplerian configuration cannot accurately reflect the variations in spacecraft configuration. Planetary gravitational disturbances are one of the main sources. Numerical simulation is an effective method to investigate the impact of perturbation on spacecraft orbits. This study shows that, in the context of the Taiji project, Earth's gravity is an essential factor in the change in heliocentric formation configuration, contributing to the relative acceleration between spacecrafts in the order of $\mathcal O(10^{-6})\,{\rm m\cdot s^{-2}}$. Considering 00:00:00 on 27 October 2032 as the initial orbiting moment, under the influence of Earth's gravitational perturbation, the maximum relative change in armlengths and variation rates of armlengths for Taiji is $1.6\times 10^{5}\,{\rm km}$, $32\,{\rm m\cdot s^{-1}}$, respectively, compared with the unperturbed Keplerian orbit. Additionally, by considering the gravitational perturbations of Venus and Jupiter, the armlength and relative velocity for Taiji are reduced by $16.01\%$ and $17.45\%$, respectively, compared with when only considering that of Earth. The maximum amplitude of the formation motion indicator changes with the orbit entry time. Results show that the relative velocity increase between the spacecrafts is minimal when the initial orbital moment occurs in July. Moreover, the numerical simulation results are inconsistent when using different ephemerides. The differences between ephemerides DE440 and DE430 are smaller than those between DE440 and DE421., Comment: 18 pages, 11 figures

Twisted bilayer graphene (TBG) represents a highly tunable, strongly correlated electron system owed to its unique flat electronic bands. However, understanding the single-particle band structure alone has been challenging due to complex lattice reconstruction effects and a lack of spectroscopic measurements over a broad energy range. Here, we probe the band structure of TBG around the magic angle using infrared spectroscopy. Our measurements reveal spectral features originating from interband transitions whose energies are uniquely defined by the twist angle. By combining with quantum transport, we connect spectral features over a broad energy range (10 to 700 meV) spanning several superlattice minibands and track their evolution with twist angle. We compare our data with calculations of the band structures obtained via the continuum model and find good agreement only when considering a variation of interlayer/intralayer tunnelling parameters with the twist angle. Our analysis suggests that the magic angle also shifts due to lattice relaxation, and is better defined for a wide angular range from 0.9{\deg} to 1.1{\deg}. Our work provides spectroscopic insights into TBG's band structure and offers an optical fingerprint of the magic angle for screening heterostructures before nanofabrication.

Landauer's principle shows that the minimum energy cost to reset a classical bit in a bath with temperature $T$ is $k_{B}T\ln2$ in the infinite time. However, the task to reset the bit in finite time has posted a new challenge, especially for quantum bit (qubit) where both the operation time and controllability are limited. We design a shortcut-to-isothermal scheme to reset a qubit in finite time $\tau$ with limited controllability. The energy cost is minimized with the optimal control scheme with and without nonholonomic constraint. This optimal control scheme can provide a reference to realize qubit reset with minimum energy cost for the limited time., Comment: 8 pages, 7 figures

The knobs of modern database management systems have significant impact on the performance of the systems. With the development of cloud databases, an estimation service for knobs is urgently needed to improve the performance of database. Unfortunately, few attentions have been paid to estimate the performance of certain knob configurations. To fill this gap, we propose IWEK, an interpretable & transferable what-if estimator for database knobs. To achieve interpretable estimation, we propose linear estimator based on the random forest for database knobs for the explicit and trustable evaluation results. Due to its interpretability, our estimator capture the direct relationships between knob configuration and its performance, to guarantee the high availability of database. We design a two-stage transfer algorithm to leverage historical experiences to efficiently build the knob estimator for new scenarios. Due to its lightweight design, our method can largely reduce the overhead of collecting training data and could achieve cold start knob estimation for new scenarios. Extensive experiments on YCSB and TPCC show that our method performs well in interpretable and transferable knob estimation with limited training data. Further, our method could achieve efficient estimator transfer with only 10 samples in TPCC and YSCB.

Kagome lattices have an inherent two-dimensional nature. Despite previous realizations in the monolayer limit, their abilities to drive emergent electronic states such as correlated insulators have remained unobserved. Here, we report the experimental realization of a new structural phase of monolayer Mo33Te56, characterized by its virtually global uniformity as a mirror-twin boundary loop superlattice embedded in an H-MoTe2 monolayer. Through a combination of scanning tunnelling microscopy (STM) and theoretical calculations, we unveil a kagome geometry along with multiple associated sets of kagome flat bands. Crucially, the partial filling of these kagome bands induces ferromagnetism as revealed by spin-polarized STM, and leads to a correlated insulating state exhibiting a hard gap as large as 15 meV. Our findings represent a major advance in kagome materials, offering a framework with clearer band structures and more intrinsic two-dimensional properties for exploring flat-band physics., Comment: 22 pages, 4 figures

To achieve fast computation, it is crucial to reset the memory to a desired state within a limited time. However, the inherent delay in the system's response often prevents reaching the desired state once the control process is completed in finite time. To address this challenge, we propose a shortcut strategy that incorporates an auxiliary control to guide the system towards an equilibrium state that corresponds to the intended control, thus enabling accurate memory reset. Through the application of thermodynamic geometry, we derive an optimal shortcut protocol for erasure processes that minimizes the energy cost. This research provides an effective design principle for realizing the finite-time erasure process while simultaneously reducing the energy cost, thereby alleviating the burden of heat dissipation.

The flavor-changing neutral current (FCNC) decays of charmed hadrons with missing energy $(\not\!\!E)$ can serve as potentially promising hunting grounds for hints of new physics, as the standard-model backgrounds are very suppressed. A few of such processes have been searched for in recent experiments, specifically $D^0\to\,\not\!\!E$ by Belle and $D^0\to\pi^0$$\not\!\!E$ and $\Lambda_c^+\to p\!\not\!\!E$ by BESIII, resulting in upper bounds on their branching fractions. We consider them to illuminate the possible contributions of the quark transition $c\to u\!\not\!\!E$ with a couple of invisible spinless bosons carrying away the missing energy, assuming that they are not charge conjugates of each other and hence can have unequal masses. We find that these data are complementary in that they constrain different sets of the underlying operators and do not cover the same ranges of the bosons' masses, but there are regions not yet accessible. From the allowed parameter space, we show that other $D$-meson decays, such as $D\to\rho$$\not\!\!E$, and the charmed-baryon ones $\Xi_c\to(\Sigma,\Lambda)$$\not\!\!E$ can have sizable branching fractions and therefore may offer further probes of the new-physics interactions. We point out the importance of $D^0\to\gamma\!\not\!\!E$ which are not yet searched for but could access parts of the parameter space beyond the reach of the other modes. In addition, we look at a scenario where the invisibles are instead fermionic, namely sterile neutrinos, and a scalar leptoquark mediates $c\to u\!\not\!\!E$. We discuss the implications of the aforesaid bounds for this model. The predictions we make for the various charmed-hadron decays in the different scenarios may be testable in the near future by BESIII and Belle II., Comment: 26 pages, 38 figures, Published version

We study the invisible scalar of $S$ in charmed meson and baryon decays with flavor-changing neutral currents (FCNCs) based on the model-independent effective Lagrangian between the quarks and invisible scalar. From the bounds of the coupling constants extracted from the recent BES III experiment on the decay of $D^{0}\to\pi^{0}\bar\nu\nu$, we predict that the decay branching ratios of $D^{+}\to\pi^{+}S$, $D_s^+\to K^+S$, $\Lambda_c\to pS$, $\Xi_c^{0(+)}\to \Sigma^{0(+)}S$, and $\Xi_c^0\to\Lambda S$ can be as large as $10.6,~2.53,~2.39,~0.963,~5.77$, and $2.92\times10^{-4}$ with $m_{_S}\approx 1.1~{\rm GeV}$, respectively. Some of these decay modes are accessible to the ongoing experiments, such as BES III, LHCb and Belle II, as well as the future ones, such as FCC-ee., Comment: 13 pages, 18 figures

Accelerating controlled thermodynamic processes requires an auxiliary Hamiltonian to steer the system into instantaneous equilibrium states. An extra energy cost is inevitably needed in such finite-time operation. We recently develop a geodesic approach to minimize such energy cost for the shortcut to isothermal process. The auxiliary control typically contains momentum-dependent terms, which are hard to be experimentally implemented due to the requirement of constantly monitoring the speed. In this work, we employ a variational auxiliary control without the momentum-dependent force to approximate the exact control. Following the geometric approach, we obtain the optimal control protocol with variational minimum energy cost. We demonstrate the construction of such protocol via an example of Brownian motion with a controllable harmonic potential.

It is predicted that a vortex in a topological superconductor contains a Majorana zero mode (MZM). The confirmative Majorana signature, i.e., the $2e^2/h$ quantized conductance, however is easily sabotaged by unavoidable interruptions, e.g. instrument broadening, non-Majorana signal, and extra particle channels. We propose to avoid the signal interruption by introducing disorder-induced dissipation that couples to the tip-sample tunneling. With dissipation involved, we highlight three features, each of which alone can provide a strong evidence to identify MZM. Firstly, dissipation suppresses a finite-energy Caroli-de Gennes-Matricon (CdGM) conductance peak into a valley, while it does not split MZM zero-bias conductance peak. Secondly, we predict a dissipation-dependent scaling feature of the zero-bias conductance peak. Thirdly, the introduced dissipation manifests the MZM signal by suppressing non-topological CdGM modes. Importantly, the observation of these features does not require a quantized conductance value $2e^2/h$., Comment: We express our gratitude to Dr. Odobesko for bringing to our attention an intriguing and pertinent experimental paper: Phys. Rev. B 102, 174502 (2020), which is Ref. [71] of the current arXiv version

To accelerate learning process with few samples, meta-learning resorts to prior knowledge from previous tasks. However, the inconsistent task distribution and heterogeneity is hard to be handled through a global sharing model initialization. In this paper, based on gradient-based meta-learning, we propose an ensemble embedded meta-learning algorithm (EEML) that explicitly utilizes multi-model-ensemble to organize prior knowledge into diverse specific experts. We rely on a task embedding cluster mechanism to deliver diverse tasks to matching experts in training process and instruct how experts collaborate in test phase. As a result, the multi experts can focus on their own area of expertise and cooperate in upcoming task to solve the task heterogeneity. The experimental results show that the proposed method outperforms recent state-of-the-arts easily in few-shot learning problem, which validates the importance of differentiation and cooperation.

Majorana zero modes (MZMs) obey non-Abelian statistics and are considered building blocks for constructing topological qubits. Iron-based superconductors with topological band structures have emerged as promising hosting materials, since isolated candidate MZMs in the quantum limit have been observed inside the topological vortex cores. However, these materials suffer from issues related to alloying-induced disorder, uncontrolled vortex lattices and a low yield of topological vortices. Here, we report the formation of an ordered and tunable MZM lattice in naturally-strained stoichiometric LiFeAs by scanning tunneling microscopy/spectroscopy (STM/S). We observe biaxial charge density wave (CDW) stripes along the Fe-Fe and As-As directions in the strained regions. The vortices are pinned on the CDW stripes in the As-As direction and form an ordered lattice. We detect more than 90 percent of the vortices to be topological and possess the characteristics of isolated MZMs at the vortex center, forming an ordered MZM lattice with the density and the geometry tunable by an external magnetic field. Remarkably, with decreasing the spacing of neighboring vortices, the MZMs start to couple with each other. Our findings provide a new pathway towards tunable and ordered MZM lattices as a platform for future topological quantum computation.

We study the invisible Majorana fermions of $\chi$ in bottomed baryon decays with flavor-changing neutral currents (FCNCs) based on the model-independent effective Lagrangian between the quarks and invisible particles. From the bounds of the coupling constants extracted from the experiments, we examine the decay branching ratios of $\Lambda_b\to\Lambda\chi\chi$, $\Xi_b^{0(-)}\to\Xi^{0(-)}\chi\chi$, $\Lambda_b\to n \chi\chi$, $\Xi_b^{-}\to \Sigma^{-} \chi\chi$, $\Xi_b^{0}\to \Sigma^{0} \chi\chi$, and $\Xi_b^{0}\to \Lambda \chi\chi$, which can be as large as $6.3,~9.2,~5.7,~5.8,~2.7$, and $1.0\times10^{-5}$ for $m_\chi=2$ GeV, respectively. Some of these decays are accessible to the future experimental searches, such as Belle II., Comment: 18 pages, 29 figures

Dual-species single-atom array in optical tweezers has several advantages over the single-species atom array as a platform for quantum computing and quantum simulation. Thus, creating the defect-free dual-species single-atom array with atom numbers over hundreds is essential. As recent experiments demonstrated, one of the main difficulties lies in designing an efficient algorithm to rearrange the stochastically loaded dual-species atoms arrays into arbitrary demanded configurations. We propose a heuristic connectivity optimization algorithm (HCOA) to provide the near-fewest number of atom moves. Our algorithm introduces the concept of using articulation points in an undirected graph to optimize connectivity as a critical consideration for arranging the atom moving paths. Tested in array size of hundreds atoms and various configurations, our algorithm shows a high success rate (> 97%), low extra atom moves ratio, good scalability, and flexibility. Furthermore, we proposed a complementary step to solve the problem of atom loss during the rearrangement.

The iron-based superconductors (FeSCs) have recently emerged as a promising single-material Majorana platform by hosting isolated Majorana zero modes (MZMs) at relatively high temperatures. To further verify its Majorana nature and move forward to build topological quantum qubit, it is highly desirable to achieve tunability for MZMs on homogeneous FeSCs. Here, with an in-situ strain device, we can controllably create MZMs on the homogeneous surface of stoichiometric superconductor LiFeAs by inducing a topological phase transition. The evolution of discrete energy modes inside a strained vortex is found to mimics exactly as the predicted topological vortex case, proving the Majorana nature of emerging zero modes of vortex. Such tunability of MZMs in a homogeneous superconductor is an important step toward their application in topological quantum computation.

Shortcut to isothermality is a driving strategy to steer the system to its equilibrium states within finite time, and enables evaluating the impact of a control promptly. Finding optimal scheme to minimize the energy cost is of critical importance in applications of this strategy in pharmaceutical drug test, biological selection, and quantum computation. We prove the equivalence between designing the optimal scheme and finding the geodesic path in the space of control parameters. Such equivalence allows a systematic and universal approach to find the optimal control to reduce the energy cost. We demonstrate the current method with examples of a Brownian particle trapped in controllable harmonic potentials.

In Weyl semimetals, charge density wave (CDW) order can spontaneously break the chiral symmetry, gap out the Weyl nodes, and drive the material into the axion insulating phase. Investigations have however been limited since CDWs are rarely seen in Weyl semimetals. Here, using scanning tunneling microscopy/spectroscopy, we report the discovery of a novel unidirectional CDW order on the (001) surface of chiral crystal CoSi - a unique Weyl semimetal with unconventional chiral fermions. The CDW is incommensurate with both lattice momentum and crystalline symmetry directions, and exhibits an intra unit cell {\pi} phase shift in the layer stacking direction. The tunneling spectrum shows a particle-hole asymmetric V-shaped energy gap around the Fermi level that modulates spatially with the CDW wave vector. Combined with first-principle calculations, we identify that the CDW is locked to the crystal chirality and is related by a mirror reflection between the two enantiomers of the chiral crystal. Our findings reveal a novel correlated topological quantum state in chiral CoSi crystals and raise the potential for realizing an axion insulator and exploring the unprecedented physical behaviors of unconventional chiral fermions.

The modulation of topological electronic states by an external magnetic field is highly desired for condensed matter physics. Schemes to achieve this have been proposed theoretically, but few can be realized experimentally. Here, combining transverse transport, theoretical calculations, and scanning tunneling microscopy/spectroscopy (STM/S) investigations, we provide an observation that the topological electronic states, accompanied by an emergent magneto-transport phenomenon, were modulated by applying magnetic fields through induced non-collinear magnetism in the magnetic Weyl semimetal EuB6. A giant unconventional anomalous Hall effect (UAHE) is found during the magnetisation re-orientation from easy axis to hard ones in magnetic fields, with a UAHE peak around the low field of 5 kOe. Under the reasonable spin-canting effect, the folding of the topological anti-crossing bands occurs, generating a strong Berry curvature that accounts for the observed UAHE. Field-dependent STM/S reveals a highly synchronous evolution of electronic density of states, with a dI/dV peak around the same field of 5 kOe, which provides evidence to the folded bands and excited UAHE by external magnetic fields. This finding elucidates the connection between the real-space non-collinear magnetism and the k-space topological electronic states and establishes a novel manner to engineer the magneto-transport behaviours of correlated electrons for future topological spintronics., Comment: 13 pages, 4 figures

Recently, some Neural Architecture Search (NAS) techniques are proposed for the automatic design of Graph Convolutional Network (GCN) architectures. They bring great convenience to the use of GCN, but could hardly apply to the Federated Learning (FL) scenarios with distributed and private datasets, which limit their applications. Moreover, they need to train many candidate GCN models from scratch, which is inefficient for FL. To address these challenges, we propose FL-AGCNS, an efficient GCN NAS algorithm suitable for FL scenarios. FL-AGCNS designs a federated evolutionary optimization strategy to enable distributed agents to cooperatively design powerful GCN models while keeping personal information on local devices. Besides, it applies the GCN SuperNet and a weight sharing strategy to speed up the evaluation of GCN models. Experimental results show that FL-AGCNS can find better GCN models in short time under the FL framework, surpassing the state-of-the-arts NAS methods and GCN models., Comment: 10 pages

In this paper, we study the FCNC decay processes of $B$ and $B_c$ meson, in which one invisible particle is emitted. Both the spin-0 and spin-1 cases are considered. The model-independent effective Lagrangian is introduced to describe the coupling between the light invisible boson and quarks. The constraints of the coupling coefficients are extracted by experimental upper limits of the missing energy in $B$ meson decays. The bounds are used to predict the upper limits of branching fractions of corresponding $B_c$ decays, which are of the order of $10^{-6}$ or $10^{-5}$ when final meson is pseudoscalar or vector, respectively. The maximum branch ratios are achieved when $m_\chi\approx3.5- 4$~GeV, where $m_\chi$ is the mass of the invisible particle., Comment: 17 pages, 27 figures

The transition-metal kagome lattice materials host frustrated, correlated, and topological quantum states of matter. Recently, a new family of vanadium-based kagome metals AV3Sb5 (A=K, Rb, and Cs) with topological band structures has been discovered. These layered compounds are nonmagnetic and undergo charge density wave transitions before developing superconductivity at low temperatures. Here we report the observation of unconventional superconductivity and pair density wave (PDW) in CsV3Sb5 using scanning tunneling microscope/spectroscopy (STM/STS) and Josephson STS. We find that CsV3Sb5 exhibits a V-shaped pairing gap {\Delta}~0.5 meV and is a strong-coupling superconductor (2{\Delta}/kBTc~5) that coexists with 4a0 unidirectional and 2a0X2a0 charge order. Remarkably, we discover a 3Q PDW accompanied by bidirectional 4a0/3 spatial modulations of the superconducting gap, coherence peak and gap-depth in the tunneling conductance. We term this novel quantum state a roton-PDW associated with an underlying vortex-antivortex lattice that can account for the observed conductance modulations. Probing the electronic states in the vortex halo in an applied magnetic field, in strong-field that suppresses superconductivity, and in zero-field above Tc reveals that the PDW is a primary state responsible for an emergent pseudogap and intertwined electronic order. Our findings show striking analogies and distinctions to the phenomenology of high-Tc cuprate superconductors, and provide groundwork for understanding the microscopic origin of correlated electronic states and superconductivity in vanadium-based kagome metals., Comment: Nature (2021)

Silicene is a promising 2D Dirac material as a building block for van der Waals heterostructures (vdWHs). Here we investigate the electronic properties of hexagonal boron nitride/silicene (BN/Si) vdWHs using first-principles calculations. We calculate the energy band structures of BN/Si/BN heterostructures with different rotation angles and find that the electronic properties of silicene are retained and protected robustly by the BN layers. In BN/Si/BN/Si/BN heterostructure, we find that the band structure near the Fermi energy is sensitive to the stacking configurations of the silicene layers due to interlayer coupling. The coupling is reduced by increasing the number of BN layers between the silicene layers and becomes negligible in BN/Si/(BN)3/Si/BN. In (BN)n/Si superlattices, the band structure undergoes a conversion from Dirac lines to Dirac points by increasing the number of BN layers between the silicene layers. Calculations of silicene sandwiched by other 2D materials reveal that silicene sandwiched by low-carbon-doped boron nitride or HfO2 is semiconducting.

A low-temperature ultra-high vacuum scanning probe microscopy (SPM) system with molecular beam epitaxy capability and optical access was conceived, built, and tested in our lab. The design of the whole system is discussed here, with special emphasis on some critical parts. We made an SPM scanner head with a modified Pan-type design, enclosed by a double-layer cold room under a bath type cryostat. The scanner head is very rigid, compatible with optical access paths, and can accommodate both scanning tunneling microscope (STM) tips and atomic force sensors. Two piezo-actuated focus-lens stages are mounted on the two sides of the cold room to couple light in and out. To demonstrate the system performance, we performed STM and scanning tunneling spectroscopy studies. The herringbone reconstruction and atomic structure of Au(111) surface were clearly resolved. The dI/dV spectra of an Au(111) surface were obtained at 5 K. In addition, a periodic 2D tellurium (Te) structure was grown on Au(111) surface using MBE.