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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

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

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

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.

Inducing and controlling electrostatic barriers in two-dimensional (2D) quantum materials has shown extraordinary promise to enable control of charge carriers, and is key for the realization of nanoscale electronic and optoelectronic devices1-10. Because of their atomically thin nature, the 2D materials have a congenital advantage to construct the thinnest possible p-n junctions1,3,7,9,10. To realize the ultimate functional unit for future nanoscale devices, creating atomically wide electrostatic barriers embedded in 2D materials is desired and remains an extremely challenge. Here we report the creation and manipulation of atomically wide electrostatic barriers embedded in graphene WSe2 heterostructures. By using a STM tip, we demonstrate the ability to generate a one-dimensional (1D) atomically wide boundary between 1T-WSe2 domains and continuously tune positions of the boundary because of ferroelasticity of the 1T-WSe2. Our experiment indicates that the 1D boundary introduces atomically wide electrostatic barriers in graphene above it. Then the 1D electrostatic barrier changes a single graphene WSe2 heterostructure quantum dot from a relativistic artificial atom to a relativistic artificial molecule.

We study the crossed Andreev reflection and the nonlocal transport in the proximitized graphene/supercondcutor/proximitized graphene junctions with the pseudospin staggered potential and the intrinsic spin-orbit coupling. The crossed Andreev reflection with the local Andreev reflection and the elastic cotunneling being completely eliminated can be realized for the electrons with the specific spin-valley index when the intrinsic spin-orbit couplings in the left graphene and the right graphene possess the opposite sign. The perfect crossed Andreev reflection with its probability equal to $100\%$ can be obtained in the space consisting of the incident angle and the energy of the electrons. The crossed conductance and its oscillation with the superconductor length are also investigated. The energy ranges for the crossed Andreev reflection without the local Andreev reflection and the elastic cotunneling are clarified for the different magnitudes of the pseudospin potential and the spin-orbit coupling. The spin-valley index of the electrons responsible for the perfect crossed Andreev reflection can be switched by changing the sign of the intrinsic spin-orbit coupling or exchanging the biases applied on the left graphene and the right graphene. Our results are helpful for designing the flexible and high-efficiency Cooper pair splitter based on the spin-valley degree of freedom., Comment: 9 pages,4 figures

In the last decade, chirality-induced spin selectivity (CISS) has been attracting extensive interest. However, there still exists a large gap between experiments and quantitative theoretical results, and the microscopic mechanism of CISS, especially transverse CISS where electrons are injected perpendicular to the helix axis of chiral molecules, remains elusive. Here, we address these issues by performing a combined experimental and theoretical study on conducting polyaniline helical nanofibers which are synthesized in the absence of any chiral species. Large spin polarization is measured in both left- and right-handed nanofibers for electrons injected perpendicular to their helix axis, which is comparable to the value of parallel electron injection in other chiral molecules, and it will be reversed by switching the handedness between two enantiomers. We develop a theoretical model with extremely weak spin-orbit coupling arising exclusively from electron propagation between neighboring polyanilines and the numerical results are quantitatively consistent with the experimental data. Our results demonstrate that the supramolecular handedness is sufficient for spin-selective electron transmission in chiral molecules assembled from achiral monomers and the mechanism of transverse CISS is revealed., Comment: 4 figures; comments are welcome

The quantum Hall effect (QHE), which was observed in 2D electron gas under an external magnetic field, stands out as one of the most remarkable transport phenomena in condensed matter. However, a long standing puzzle remains regarding the observation of the relativistic quantum Hall effect (RQHE). This effect, predicted for a single 2D Dirac cone immersed in a magnetic field, is distinguished by the intriguing feature of half-integer Hall conductivity (HIHC). In this work, we demonstrate that the condensed-matter realization of the RQHE and the direct measurement of the HIHC are feasible by investigating the underlying quantum transport mechanism. We reveal that the manifestation of HIHC is tied to the presence of dissipative half-integer quantized chiral channels circulating along the interface of the RQHE system and a Dirac metal. Importantly, we find that the Ohmic scaling of the longitudinal conductance of the system plays a key role in directly measuring the HIHC in experiments. Furthermore, we propose a feasible experimental scheme based on the 3D topological insulators to directly measure the HIHC. Our findings not only uncover the distinct transport mechanism of the HIHC for the RQHE, but also paves the way to the measurement of the HIHC in future experiments., Comment: 14 pages, 9 figures

We study the Andreev reflections and the quantum transport in the proximitized graphene/superconductor junction. The proximitized graphene possesses the pseudospin staggered potential and the intrinsic spin-orbit coupling induced by substrate, which are responsible for the spin-valley dependent double Andreev reflections and the anomalous transport properties in the junction. The pure specular Andreev reflection can happen in the superconducting gap for the $K\uparrow$ and $K'\downarrow$ electrons while the pure retro-Andreev reflection happens for the $K\downarrow$ and $K'\uparrow$ electrons. The coexisting two types of Andreev reflections related to the fixed spin-valley indices strongly depend on the chemical potential of the proximitized graphene. The condition of the emergence of the specific type of Andreev reflection for the electrons with the fixed spin-valley index is clarified. The spin-valley dependent Andreev reflections bring about the peculiar conductance spectra of the junction, which can help determine the values of the pseudospin staggered potential and the intrinsic spin-orbit coupling induced in graphene. Hence, our research results not only provide an experimental method to detect the induced potential and coupling in graphene but also establish the foundation of the superconductor electronics based on the spin-valley indices., Comment: 7figures

We propose a universal spin superconducting diode effect (SDE) induced by spin-orbit coupling (SOC), where the critical spin supercurrents in opposite directions are unequal. By analysis from both the Ginzburg-Landau theory and energy band analysis, we show that the spin-$\uparrow \uparrow$ and spin-$\downarrow \downarrow$ Cooper pairs possess opposite phase gradients and opposite momenta from the SOC, which leads to the spin SDE. Two superconductors with SOC, a $p$-wave superconductor as a toy model and a practical superconducting nanowire, are numerically studied and they both exhibit spin SDE. In addition, our theory also provides a unified picture for both spin and charge SDEs. Besides, we propose spin-polarized detection and nonlocal spin transport, as mature experimental technologies, to confirm the spin SDE in superconducting nanowires., Comment: 6 pages, 4 figures (+ supplementary materials 4 pages, 1 figure)

Energy dissipation is of fundamental interest and crucial importance in quantum systems. However, whether energy dissipation can emerge inside topological systems remains a question, especially when charge transport is topologically protected and quantized. As a hallmark, we propose a microscopic picture that illustrates energy dissipation in the quantum Hall (QH) plateau regime of graphene. Despite the quantization of Hall, longitudinal, and two-probe resistances (dubbed as the quantum limit), we find that the energy dissipation emerges in the form of Joule heat. By analyzing the energy distribution of electrons, it is found that electrons can evolve between equilibrium and non-equilibrium without inducing extra two-probe resistance. The relaxation of non-equilibrium electrons results in the dissipation of energy along the QH edge states. Eventually, we suggest probing the phenomenon by measuring local temperature increases in experiments and reconsidering the dissipation typically ignored in realistic topological circuits., Comment: 7 pages, 4 figures;The computer programs associated with this paper are available via the GitHub website (https: //github.com/meplum-li/dissipation_calc.git)

We propose theoretically a Josephson diode consisting of the conventional superconductors with the plain s-wave pairing and a chiral quantum dot. When an external magnetic field is exerted on the quantum dot, the critical current of the Josephson structure is different for the opposite directions of current flow. The strong nonreciprocity can be obtained in a large area of the parameter space. The inversion and the on/off state of the nonreciprocity can be conveniently regulated by adjusting the direction of the external field. The dependences of the nonreciprocal behaviors on the the hopping amplitude, the magnitude of the magnetic field and the energy level of the quantum dot are investigated in details using the Keldysh nonequilibrium Green's function formalism under the self-consistent procedure. The symmetric and the antisymmetric properties of the nonreciprocity are analyzed from symmetries satisfied by the superconductors. The proposed diode effect also applies to other chiral conductors as interlayer. Its formation has no restriction on the type of the current-phase difference relations. The generality and flexibility of our proposed diode effect provides more possibilities for the design of the dissipationless diode devices., Comment: 4figures

Recently, electron transport along chiral molecules has been attracting extensive interest and several intriguing phenomena have been reported in recent experiments, such as the emergence of zero-bias conductance peaks upon the adsorption of single-helical protein on superconducting films. Here, we study theoretically the electron transport through a two-terminal single-helical protein sandwiched between a superconducting electrode and a normal-metal one in the presence of a perpendicular magnetic field. As the proximity-induced superconductivity attenuates with the distance from superconducting media, the pairing potential along the helix axis of the single-helical protein is expected to decrease exponentially, which is characterized by the decay exponent $\lambda$ and closely related to the experiments. Our results indicate that (i) a zero-bias conductance peak of $2e^2/h$ appears at zero temperature and the peak height (width) decreases (broadens) with increasing temperature, and (ii) this zero-bias peak can split into two peaks, which are in agreement with the experiments [see, e.g., Nano Lett. 19, 5167 (2019)]. Remarkably, Majorana zero modes are observed in this protein-superconductor setup in a wide range of model parameters, as manifested by the $Z_2$ topological invariant and the Majoroana oscillation. Interestingly, a specific region is demonstrated for decaying superconductivity, where topologically nontrivial and trivial zero modes coexist and the bandgap remains constant. With increasing the pairing potential, the topologically nontrivial zero modes will transform to the trivial ones without any bandgap closing-reopening, and the critical pairing potential of the phase transition attenuates exponentially with $\lambda$. Additionally, one of the two zero modes can be continuously shifted from one end of the protein toward the other end contacted by the normal-metal electrode., Comment: 11 pages, 6 figures

The static topological fractional charge (TFC) in condensed matter systems is related to the band topology and thus has potential applications in topological quantum computation. However, the experimental measurement of these TFCs in electronic systems is quite challenging. We propose an electronic transport measurement scheme that both the charge amount and the spatial distribution of the TFC can be extracted from the differential conductance through a quantum dot coupled to the topological system being measured. For one-dimensional Su-Schrieffer-Heeger (SSH) model, both the $e/2$ charge of the TFC and its distribution can be verified. We also show that the Anderson disorder effect, which breaks certain symmetry related to the TFC, is significant in higher-dimensional systems while has little effect on the one-dimensional SSH chain. Nonetheless, our measurement scheme can still work well for specific higher-order topological insulator materials, for instance, the $2e/3$ TFC in the breathing kagome model could be confirmed even in the presence of disorder effect., Comment: 6 pages, 4 figures

In relativistic physics, both atomic collapse in heavy nucleus and Hawking radiation in black hole are predicted to occur through Klein tunneling process that couples particles and antiparticles. Recently, atomic collapse states (ACSs) were explicitly realized in graphene because of its relativistic Dirac excitation with large fine structure constant. However, essential role of the Klein tunneling on the ACSs remains elusive in experiment. Here we systematically study the quasibound states in elliptical graphene quantum dots (GQDs). Bonding and antibonding molecular collapse states formed by two coupled ACSs are observed in the elliptical GQDs. Our experiments, supported by theoretical calculations, indicate that the antibonding state of the ACSs will change into a Klein-tunneling-induced quasibound state, revealing deep connection between the ACSs and the Klein tunneling., Comment: 3 figures in main text

Introducing quantum confinement has uncovered a rich set of interesting quantum phenomena and allows one to directly probe the physics of confined (quasi-)particles. In most experiments, however, electrostatic potential is the only available method to generate the quantum confinement in a continuous system. Here, we demonstrated experimentally that inhomogeneous pseudomagnetic fields in strained graphene can introduce exotic quantum confinement of massless Dirac fermions. The pseudomagnetic fields have opposite directions in the two distinct valleys of graphene. By tuning real magnetic field, the total effective magnetic fields in the two valleys are imbalanced. Then, we realized valley-contrasting spatial confinement, which lifts the valley degeneracy and results in field-tunable valley-polarized confined states in graphene. Our results provide a new avenue to manipulate the valley degree of freedom.

Recently,a half-quantized Hall conductance (HQHC) plateau is experimentally observed in a semi-magnetic topological insulator heterostructure. However,the heterostructure is metallic with a nonzero longitudinal conductance, which contradicts the common belief that quantized Hall conductance is usually observed in insulators.In this work,we systematically study the surface transport of the semi-magnetic topological insulator with both gapped and gapless Dirac surfaces in the presence of dephasing process.In particular, we reveal that the HQHC is directly related to the half-quantized chiral current along the edge of a strongly dephasing metal. The Hall conductance keeps a half-quantized value for large dephasing strengths, while the longitudinal conductance varies with Fermi energies and dephasing strengths. Furthermore, we evaluate both the conductance and resistance as a function of the temperature, which is consistent with the experimental results.Our results not only provide the microscopic transport mechanism of the HQHC,but also are instructive for the probe of the HQHC in future experiments., Comment: 10 pages, 7 figures

Very recently, borophene has been attracting extensive and ongoing interest as the new wonder material with structural polymorphism and superior attributes, showing that the structural imperfection of line defects (LDs) occurs widely at the interface between $\nu_{1/5}$ ($\chi_3$) and $\nu_{1/6}$ ($\beta_{12}$) boron sheets. Motivated by these experiments, here we present a theoretical study of electron transport through two-terminal disordered borophene nanoribbons (BNRs) with random distribution of LDs. Our results indicate that LDs could strongly affect the electron transport properties of BNRs. In the absence of LDs, both $\nu_{1/5}$ and $\nu_{1/6}$ BNRs exhibit metallic behavior, in agreement with experiments. While in the presence of LDs, the overall electron transport ability is dramatically decreased, but some resonant peaks of conductance quantum can be found in the transmission spectrum of any disordered BNR with arbitrary arrangement of LDs. These disordered BNRs exhibit metal-insulator transition by varying nanoribbon width with tunable transmission gap in the insulating regime. Furthermore, the bond currents present fringe patterns and two evolution phenomena of resonant peaks are revealed for disordered BNRs with different widths. These results may help for understanding structure-property relationships and designing LD-based nanodevices., Comment: Comments are welcome; 6 pages; 4 figures

Fundamental symmetry breaking and relativistic spin-orbit coupling give rise to fascinating phenomena in quantum materials. Of particular interest are the interfaces between ferromagnets and common s-wave superconductors, where the emergent spin-orbit fields support elusive spin-triplet superconductivity, crucial for superconducting spintronics and topologically-protected Majorana bound states. Here, we report the observation of large magnetoresistances at the interface between a quasi-two-dimensional van der Waals ferromagnet Fe0.29TaS2 and a conventional s-wave superconductor NbN, which provides the possible experimental evidence for the spin triplet Andreev reflection and induced spin-triplet superconductivity at ferromagnet/superconductor interface arising from Rashba spin-orbit coupling. The temperature, voltage, and interfacial barrier dependences of the magnetoresistance further support the induced spin-triplet superconductivity and spin-triplet Andreev reflection. This discovery, together with the impressive advances in two-dimensional van der Waals ferromagnets, opens an important opportunity to design and probe superconducting interfaces with exotic properties.

We study the Josephson effect in spin-triplet superconductor$-$quantum anomalous Hall insulator$-$spin-triplet superconductor junctions using the nonequilibrium Green function method. The current-phase difference relations show strong dependence on the orientations of the $\bf{d}$-vectors in superconductors. We focus on two $\bf{d}$-vector configurations, the parallel one with the left and right ${\bf{d}}$-vectors being in the same direction, and the nonparallel one with the left ${\bf{d}}$-vector fixed at the $z$-axis. For the parallel configuration, the $0$-$\pi$ transition can be realized when one rotates the ${\bf{d}}$-vectors from the parallel to the junction plane to the perpendicular direction. The $\phi_{0}$ phase with nonzero Josephson current at zero phase difference can be obtained as long as ${d_{x}}{d_{z}}\ne0$. For the nonparallel configuration, the $0$-$\pi$ transition and the $\phi_{0}$ phase still exist. The condition for the formation of the $\phi_{0}$ phase becomes $d_{Rx}\ne0$. The switch effects of the Josephson current are found in both configurations when the ${\bf{d}}$-vectors are rotated in the $xy$ plane. Furthermore, the symmetries satisfied by the current-phase difference relations are analysed in details by the operations of the time-reversal, mirror-reflections, the spin-rotation and the gauge transformation, which can well explain the above selection rules for the $\phi_{0}$ phase. Our results reveal the peculiar Josephson effect between spin-triplet superconductors and the quantum anomalous Hall insulator, which provide helpful phases and effects for the device designs. The distinct current-phase difference relations for different orientations may be used to determine the direction of the ${\bf{d}}$-vector in the spin-triplet superconductor., Comment: 9 pages,4 figures

The relativistic massless charge carriers with a Fermi velocity of about c300 in graphene enable us to realize two distinct types of resonances (c, the speed of light in vacuum). One is electron whispering-gallery mode in graphene quantum dots arising from the Klein tunneling of the massless Dirac fermions. The other is atomic collapse state, which has never been observed in experiment with real atoms due to the difficulty of producing heavy nuclei with charge Z 170, however, can be realized near a Coulomb impurity in graphene with a charge Z 1 because of the small velocity of the Dirac excitations. Here, unexpectedly, we demonstrate that both the electron whispering-gallery modes and atomic collapse states coexist in grapheneWSe2 heterostructure quantum dots due to the Coulomb-like potential near their edges. By applying a perpendicular magnetic field, evolution from the atomic collapse states to unusual Landau levels in the collapse regime are explored for the first time.

Recently, a new class of second-order topological insulators (SOTIs) characterized by an electronic dipole has been theoretically introduced and proposed to host topological corner states. As a novel topological state, it has been attracting great interest and experimentally realized in artificial systems of various fields of physics based on multi-sublattice models, e.g., breathing kagome lattice. In order to realize such kind of SOTI in natural materials, we proposed a symmetry-faithful multi-orbital model. Then, we reveal several familiar transition metal dichalcogenide (TMD) monolayers as a material family of two-dimensional SOTI with large bulk gaps. The topologically protected corner state with fractional charge is pinned at Fermi level due to the charge neutrality and filling anomaly. Additionally, we propose that the zero-energy corner state preserves in the heterostructure composed of a topological nontrivial flake embedded in a trivial material. The novel second-order corner states in familiar TMD materials hold promise for revealing unexpected quantum properties and applications.

Berry phase plays an important role in determining many physical properties of quantum systems. However, a Berry phase altering energy spectrum of a quantum system is comparatively rare. Here, we report an unusual tunable valley polarized energy spectra induced by continuously tunable Berry phase in Bernal-stacked bilayer graphene quantum dots. In our experiment, the Berry phase of electron orbital states is continuously tuned from about pi to 2pi by perpendicular magnetic fields. When the Berry phase equals pi or 2pi, the electron states in the two inequivalent valleys are energetically degenerate. By altering the Berry phase to noninteger multiples of pi, large and continuously tunable valley polarized energy spectra are detected in our experiment. The observed Berry phase-induced valley splitting, on the order of 10 meV at a magnetic field of 1 T, is about 100 times larger than Zeeman splitting for spin, shedding light on graphene-based valleytronics., Comment: 4 figures in main text

As a secondary structure of DNA, DNA tetrahedra exhibit intriguing charge transport phenomena and provide a promising platform for wide applications like biosensors, as shown in recent electrochemical experiments. Here, we study charge transport in a multi-terminal DNA tetrahedron, finding that its charge transport properties strongly depend upon the interplay among contact position, on-site energy disorder, and base-pair mismatch. Our results indicate that the charge transport efficiency is nearly independent of contact position in the weak disorder regime, and is dramatically declined by the occurrence of a single base-pair mismatch between the source and the drain, in accordance with experimental results [J. Am. Chem. Soc. {\bf 134}, 13148 (2012); Chem. Sci. {\bf 9}, 979 (2018)]. By contrast, the charge transport efficiency could be enhanced monotonically by shifting the source toward the drain in the strong disorder regime, and be increased when the base-pair mismatch takes place exactly at the contact position. In particular, when the source moves successively from the top vertex to the drain, the charge transport through the tetrahedral DNA device can be separated into three regimes, ranging from disorder-induced linear decrement of charge transport to disorder-insensitive charge transport, and to disorder-enhanced charge transport. Finally, we predict that the DNA tetrahedron functions as a more efficient spin filter compared to double-stranded DNA and opposite spin polarization could be observed at different drains, which may be used to separate spin-unpolarized electrons into spin-up ones and spin-down ones. These results could be readily checked by electrochemical measurements and may help for designing novel DNA tetrahedron-based molecular nanodevices., Comment: Comments are welcome; 10 pages; 6 figures

We propose a universal method to detect the specular Andreev reflection taking the simple two dimensional Weyl nodal-line semimetal-superconductor double-junction structure as an example. The quasiclassical quantization conditions are established for the energy levels of bound states formed in the middle semimetal along a closed path. The establishment of the conditions is completely based on the intrinsic character of the specularly reflected hole which has the same sign relation of its wave vector and group velocity with the incident electron. This brings about the periodic oscillation of conductance with the length of the middle semimetal, which is lack for the retro-Andreev reflected hole having the opposite sign relation with the incident electron. The positions of the conductance peaks and the oscillation period can be precisely predicted by the quantization conditions. Our detection method is irrespective of the details of the materials, which may promote the experimental detection of and further researches on the specular Andreev reflection as well as its applications in superconducting electronics., Comment: 10 pages, 6 figures

The massless Dirac fermions and the ease to introduce spatial and magnetic confinement in graphene provide us unprecedented opportunity to explore confined relativistic matter in this condensed-matter system. Here we report the interplay between the confinement induced by external electric fields and magnetic fields of the massless Dirac fermions in graphene. When the magnetic length lB is larger than the characteristic length of the confined electric potential lV, the spatial confinement dominates and a relatively small critical magnetic field splits the spatial-confinement-induced atomic-like shell states by switching on a pi Berry phase of the quasiparticles. When the lB becomes smaller than the lV, the transition from spatial confinement to magnetic confinement occurs and the atomic-like shell states condense into Landau levels (LLs) of the Fock-Darwin states in graphene. Our experiment demonstrates that the spatial confinement dramatically changes the energy spacing between the LLs and generates large electron-hole asymmetry of the energy spacing between the LLs. These results shed light on puzzling observations in previous experiments, which hitherto remained unaddressed., Comment: 4 Figures in main text

The chirality-induced spin selectivity (CISS), demonstrated in diverse chiral molecules by numerous experimental and theoretical groups, has been attracting extensive and ongoing interest in recent years. As the secondary structure of DNA, the charge transfer along DNA hairpins has been widely studied for more than two decades, finding that DNA hairpins exhibit spin-related effects as reported in recent experiments. Here, we propose a setup to demonstrate directly the CISS effect in DNA hairpins contacted by two nonmagnetic leads at both ends of the stem. Our results indicate that DNA hairpins present pronounced CISS effect and the spin polarization could be enhanced by using conducting molecules as the loop. In particular, DNA hairpins show several intriguing features, which are different from other chiral molecules. First, the local spin currents can flow circularly and assemble into a number of vortex clusters when the electron energy locates in the left/right electronic band of the stem. The chirality of vortex clusters in each band is the same and will be reversed by switching the electron energy from the left band to the right one, inducing the sign reversal of the spin polarization. Interestingly, the local spin currents can be greater than the corresponding spin component of the source-drain current. Second, both the conductance and the spin polarization can increase with molecular length as well as dephasing strength, contrary to the physical intuition that the transmission ability of molecular wires should be poorer when suffering from stronger scattering. Third, we unveil the optimal contact configuration of efficient electron transport and that of the CISS effect, which are distinct from each other and can be controlled by dephasing strength. The underlying physical mechanism is illustrated., Comment: 12 pages, 9 figures; comments are welcome

In this Letter, we study an Anderson-localization-induced quantized transport in disordered Chern insulators (CIs). By investigating the disordered CIs with a step potential, we find that the chiral interface states emerge along the interfaces of the step potential, and the energy range for such quantized transport can be manipulated through the potential strength. Furthermore, numerical simulations on cases with a multi-step potential demonstrate that such chiral state can be spatially shifted by varying the Fermi energy, and the energy window for quantized transport is greatly enlarged. Experimentally, such chiral interface states can be realized by imposing transverse electric field, in which the energy window for quantized transport is much broader than the intrinsic band gap of the corresponding CI. These phenomena are quite universal for disordered CIs due to the direct phase transition between the CI and the normal insulator., Comment: 20 pages, 20 figures

We investigate the many-body effects of a magnetic adatom in ferromagnetic graphene by using the numerical renormalization group method. The nontrivial band dispersion of ferromagnetic graphene gives rise to interesting Kondo physics different from that in conventional ferromagnetic materials. For a half-filled impurity in undoped graphene, the presence of ferromagnetism can bring forth Kondo correlations, yielding two kink structures in the local spectral function near the Fermi energy. When the spin splitting of local occupations is compensated by an external magnetic field, the two Kondo kinks merge into a full Kondo resonance characterizing the fully screened ground state. Strikingly, we find the resulting Kondo temperature monotonically increases with the spin polarization of Dirac electrons, which violates the common sense that ferromagnetic bands are usually detrimental to Kondo correlations. Doped ferromagnetic graphene can behave as half metals, where its density of states at the Fermi energy linearly vanishes for one spin direction but keeps finite for the opposite direction. In this regime, we demonstrate an abnormal Kondo resonance that occurs in the first spin direction, while completely absent in the other one., Comment: 9 pages, 7 figures

Recent studies indicated that helical organic molecules, such as DNA and $\alpha$-helical protein, can behave as Thouless quantum pumps when a rotating electric field is applied perpendicularly to their helical axes. Here we investigate the influence of long-range hoppings on this topological pumping of electrons in single-helical organic molecules. Under variation of the long-range hoppings governed by a decay exponent $\mu$, we find an energy gap in the molecular band structure closes at a critical value $\mu_c$ of the decay exponent and reopens for $\mu$ deviating from $\mu_c$. The relevant bulk bands in a pumping cycle acquire different Chern numbers in the strong ($\mu<\mu_c$) and weak ($\mu>\mu_c$) long-range hopping regimes, with a sudden jump at criticality. This topological phase transition is also shown to separate two distinct behaviors of the midgap end states in the pumping process. The end states carry quantized current pumped by the rotating electric field and the current forms a plateau by sweeping the Fermi energy over the gap. In the strong hopping phase, the quantized current plateau is positive, which is reversed to a negative one with smaller amplitude in the weak hopping phase. However, the reversal is a smooth crossover, not a sharp transition, due to the finite sizes of the molecules. We show that these transport characteristics of the topological phase transition could also be observed at finite temperatures., Comment: 8 pages, 6 figures

Inside a three-dimensional strong topological insulator, a tube with $h/2e$ magnetic flux carries a pair of protected one-dimensional linear fermionic modes. This phenomenon is known as the "wormhole effect". In this work, we find that the "wormhole effect", as a unique degree of freedom, introduces exotic transport phenomena and thus manipulates the transport properties of topological insulators. Our numerical results demonstrate that the transport properties of a double-wormhole system can be manipulated by the wormhole interference. Specifically, the conductance and local density of states both oscillate with the Fermi energy due to the interference between the wormholes. Furthermore, by studying the multi-wormhole systems, we find that the number of wormholes can also modulate the differential conductance through a $\mathbb{Z}$$_{2}$ mechanism. Finally, we propose two types of topological devices in real applications, the "wormhole switch" device and the "traversable wormhole" device, which can be finely tuned by controlling the wormhole degree of freedom., Comment: 12 pages, 10 fiugres

We study systematically the scattering processes and the conductance spectra in nodal-line semimetalsuperconductor junctions using the extended Blonder-Tinkham-Klapwijk theory. The coexistence of peculiar quadruple reflections are found, which are the specular normal reflection, the retro-normal reflection, the specular Andreev reflection and the retro-Andreev reflection. The incident angle dependence and the quasiparticle energy dependence of the double normal reflections and the double Andreev reflections are investigated under various values of parameters such as the interfacial barrier height, the chemical potentials, and the orbital coupling strength. It is found that the appearance and the disappearance of the reflections and their magnitudes can be controlled through tuning these parameters. The scattering mechanism for the reflections are analyzed in details from the viewpoint of the band structure. We also investigate the conductance spectra for the junctions, which show distinctive features and strong anisotropy about the orientation relationships of the nodal line and interface. The unique scattering processes and conductance spectra found in the junctions are helpful in designing superconducting electronic devices and searching for the nodal line in materials experimentally.

In the vicinity of the magic angle in twisted bilayer graphene (TBG), the two low-energy van Hove singularities (VHSs) become exceedingly narrow1-10 and many exotic correlated states, such as superconductivity, ferromagnetism, and topological phases, are observed11-16. Heterostrain, which is almost unavoidable in the TBG, can modify its single-particle band structure and lead to novel properties of the TBG that have never been considered so far. Here, we show that heterostrain in a TBG near the magic angle generates a new zero-energy flat band between the two VHSs. Doping the TBG to partially fill the zero-energy flat band, we observe a correlation-induced gap of about 10 meV that splits the flat band. By applying perpendicular magnetic fields, a large and linear response of the gap to magnetic fields is observed, attributing to the emergence of large orbital magnetic moments in the TBG when valley degeneracy of the flat band is lifted by electron-electron interactions. The orbital magnetic moment per moire supercell is measured as about 15 uB in the TBG.

Nonlocality is an interesting topic in quantum physics and is usually mediated by some unique quantum states. Here we investigate a Weyl semimetal slab and find an exotic nonlocal correlation effect when placing two potential wells merely on the top and bottom surfaces. This correlation arises from the peculiar Weyl orbit in Weyl semimetals and is a consequence of the bulk-boundary correspondence in topological band theory. A giant nonlocal transport signal and a body breakdown by Weyl fermions are further uncovered, which can serve as signatures for verifying this nonlocal correlation effect experimentally. Our results extend a new member in the nonlocality family and have potential applications for designing new electric devices with fancy functions., Comment: 5 pages, 3 figures, and one Supplementary Material

We theoretically study the Josephson current in Ising superconductor-half-metal-Ising superconductor junctions. By solving the Bogoliubov-de Gennes equations, the Josephson currents contributed by the discrete Andreev levels and the continuous spectrum are obtained. For very short junctions, because the direct tunneling of the Cooper pair dominates the Josephson current, the current-phase difference relation is independent of the magnetization direction, which is the same as the conventional superconductor-ferromagnet-superconductor junctions. On the other hand, when the length of the half-metal is similar to or greater than the superconducting coherence length, the spin-triplet Josephson effect occurs and dominates the Josephson current. In this case, the current-phase difference relations show the strong magnetoanisotropic behaviors with the period \pi. When the magnetization direction points to the $\pm$ z directions, the current is zero regardless of the phase difference. However, the current has a large value when the magnetization direction is parallel to the junction plane, which leads to a perfect switch effect of the Josephson current. Furthermore, we find that the long junctions can host both the 0 state and \pi state, and the $0$-$\pi$ transitions can be achieved with the change of the magnetization direction. The physical origins of the switch effect and $0$-$\pi$ transitions are interpreted from the perspectives of the spin-triplet Andreev reflection, the Ising pairing order parameter and the Ginzburg-Landau type of free energy. In addition, the influences of the chemical potential, the magnetization magnitude, and the strength of the Ising spin-orbit coupling on the switch effect and $0$-$\pi$ transitions are also investigated. Furthermore, the two-dimensional Josephson junctions are also investigated and we show that the spin-triplet Josephson effect can exist always.

Impurities are unavoidable during the preparation of graphene samples and play an important role in graphene's electronic properties when they are adsorbed on graphene surface. In this work, we study the electronic structures and transport properties of a two-terminal zigzag graphene nanoribbon (ZGNR) device whose scattering region is covered by various adsorbates within the framework of the tight-binding approximation, by taking into account the coupling strength $\gamma$ between adsorbates and carbon atoms, the adsorbate concentration $n_i$, and the on-site energy disorder of adsorbates. Our results indicate that when the scattering region is fully covered by homogeneous adsorbates, i.e., $n_i=1$, a transmission gap opens around the Dirac point and its width is almost proportional to $\gamma^2$. In particular, two conductance plateaus of $G=2e^2/h$ appear in the vicinity of the electron energy $E=\pm \gamma$. When the scattering region is partially covered by homogeneous adsorbates ($0

Chiral Majorana edge modes are theoretically proposed to perform braiding operations for the potential quantum computation. Here, we suggest a scheme to regulate trajectories of the chiral Majorana fermion based on a quantum anomalous Hall insulator (QAHI)-topological superconductor heterostructure. An applied external gate voltage to the QAHI region introduces a dynamical phase so that the outgoing Majorana fermions can be prominently tuned to different leads. The trajectory is mechanically analyzed and the electrical manipulation is represented by the oscillating transmission coefficients versus the gate voltage. Through the optimization of devices, the conductance is likewise detectable to be periodically oscillating, which means an experimental control of chiral Majorana edge modes. Besides, this oscillating period which is robust against disorder also provides an attainable method of observing the energy dispersion relation of the edge mode of the QAHI. Furthermore, the oscillating behavior of conductance serves as smoking-gun evidence of the existence of the chiral Majorana fermion, which could be experimentally confirmed., Comment: 14 pages, 11 figures

Since its discovery, Berry phase has been demonstrated to play an important role in many quantum systems. In gapped Bernal bilayer graphene, the Berry phase can be continuously tuned from zero to 2pi, which offers a unique opportunity to explore the tunable Berry phase on the physical phenomena. Here, we report experimental observation of Berry phases-induced valley splitting and crossing in moveable bilayer graphene p-n junction resonators. In our experiment, the bilayer graphene resonators are generated by combining the electric field of scanning tunneling microscope tip with the gap of bilayer graphene. A perpendicular magnetic field changes the Berry phase of the confined bound states in the resonators from zero to 2pi continuously and leads to the Berry phase difference for the two inequivalent valleys in the bilayer graphene. As a consequence, we observe giant valley splitting and unusual valley crossing of the lowest bound states. Our results indicate that the bilayer graphene resonators can be used to manipulate the valley degree of freedom in valleytronics.

Majorana zero modes (MZMs)--bearing potential applications for topological quantum computing--are verified in quasi-one-dimensional (1D) Fermion systems, including semiconductor nanowires, magnetic atomic chains, planar Josephson junctions. However, the existence of multi-bands in these systems makes the MZMs fragile to the influence of disorder. Moreover, in practical perspective, the proximity induced superconductivity may be difficult and restricted for 1D systems. Here, we propose a flexible route to realize MZMs through 1D topological kink states by engineering a 2D electron gas with antidot lattices, in which both the aforementioned issues can be avoided owing to the robustness of kink states and the intrinsically attainable superconductivity in high-dimensional systems. The MZMs are verified to be quite robust against disorders and the bending of kink states, and can be conveniently tuned by varying the Rashba spin-orbit coupling strength. Our proposal provides an experimental feasible platform for MZMs with systematic manipulability and assembleability based on the present techniques in 2D electron gas system., Comment: 6 page, 4 figures, Supplementary include

A planar Josephson junction with a normal metal attached on its top surface will form a hollow nanowire structure due to its three dimensional nature. In such hollow nanowire structure, the magnetic flux induced by a small magnetic field (about 0.01T) will tune the system into topologically non-trivial phase and therefore two Majorana zero-modes will form at the ends of the nanowire. Through tuning the chemical potential of the normal metal, the topologically non-trivial phase can be obtained for almost all energy within the band. Furthermore, the system can be conveniently tuned between the topologically trivial and non-trivial phases via the phase difference between the superconductors. Such device, manipulable through flux, can be conveniently fabricated into desired 2D networks. Finally, we also propose a cross-shaped junction realizing the braiding of Majorana zero-modes through manipulating the phase differences., Comment: 5 pages, 4 figures

The spin Nernst effect describes a transverse spin current induced by the longitudinal thermal gradient in a system with the spin-orbit coupling. Here we study the spin Nernst effect in a mesoscopic four-terminal cross-bar Weyl semimetal device under a perpendicular magnetic field. By using the tight-binding Hamiltonian combining with the nonequilibrium Green's function method, the three elements of the spin current in the transverse leads and then spin Nernst coefficients are obtained. The results show that the spin Nernst effect in the Weyl semimetal has the essential difference with the traditional one: The z direction spin currents is zero without the magnetic field while it appears under the magnetic field, and the x and y direction spin currents in the two transverse leads flows out or flows in together, in contrary to the traditional spin Nernst effect, in which the spin current is induced by the spin-orbit coupling and flows out from one lead and flows in on the other. So we call it the anomalous spin Nernst effect. In addition, we show that the Weyl semimetals have the center-reversal-type symmetry, the mirror-reversal-type symmetry and the electron-hole-type symmetry, which lead to the spin Nernst coefficients being odd function or even function of the Fermi energy, the magnetic field and the transverse terminals. Moreover, the spin Nernst effect in the Weyl semimetals are strongly anisotropic and its coefficients are strongly dependent on both the direction of thermal gradient and the direction of the transverse lead connection. Three non-equivalent connection modes (x-z, z-x and x-y modes) are studied in detail, and the spin Nernst coefficients for three different modes exhibit very different behaviors. These strongly anisotropic behaviors of the spin Nernst effect can be used as the characterization of magnetic Weyl semimetals., Comment: 12 pages, 11 figures

The non-Abelian braiding of Majorana fermions is one of the most promising operations providing a key building block for the realization of topological quantum computation. Recently, the chiral Majorana fermions were observed in a hybrid junction btween a quantum anomalous Hall insulator and an s-wave superconductor. Here we show that if a quantum dot or Majorana zero mode couples to the chiral Majorana fermions, the resulting resonant exchange of chiral Majorana fermions can lead to the non-Abelian braiding. Remarkably, any operation in the braid group can be achieved by this scheme. We further propose electrical transport experiments to observe the braiding of four chiral Majorana fermions and demonstrate the non-Abelian braiding statistics in four-terminal devices of the hybrid junctions. Both a conductance peak due to the braiding and the braiding-order dependent conductance are predicted. These findings pave a way to perform any braiding operation of chiral Majorana fermions by electrically controllable quantum dots., Comment: 11 pages, 9 figures