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The emergence of spinon quasiparticles, which carry spin but lack charge, is a hallmark of collective quantum phenomena in low-dimensional quantum spin systems. While the existence of spinons has been demonstrated through scattering spectroscopy in ensemble samples, real-space imaging of these quasiparticles within individual spin chains has remained elusive. In this study, we construct individual Heisenberg antiferromagnetic spin-$\frac{1}{2}$ chains using open-shell [2]triangulene molecules as building blocks. Each [2]triangulene unit, owing to its sublattice imbalance, hosts a net spin-$\frac{1}{2}$ in accordance with Lieb's theorem, and these spins are antiferromagnetically coupled within covalent chains with a coupling strength of $J = 45$ meV. Through scanning tunneling microscopy and spectroscopy, we probe the spin states, excitation gaps, and their spatial excitation weights within covalent spin chains of varying lengths with atomic precision. Our investigation reveals that the excitation gap decreases as the chain length increases, extrapolating to zero for long chains, consistent with Haldane's gapless prediction. Moreover, inelastic tunneling spectroscopy reveals an m-shaped energy dispersion characteristic of confined spinon quasiparticles in a one-dimensional quantum box. These findings establish a promising strategy for exploring the unique properties of excitation quasiparticles and their broad implications for quantum information.

Two-dimensional (2D) moir\'e materials have emerged as a highly tunable platform for investigating novel quantum states of matter arising from strong electronic correlations and nontrivial band topology. Recently, topological flat bands formed in 2D semiconducting moir\'e superlattices have attracted great interests. In particular, a series of topological quantum phases, including the long-sought fractional quantum anomalous Hall (FQAH) effect, have recently been experimentally observed in twisted bilayer MoTe2 (tMoTe2). However, the microscopic information of tMoTe2 moir\'e superlattice and its electronic structure is still lacking. Here, we present scanning tunneling microscopy and spectroscopy (STM/STS) studies of the tMoTe2 moir\'e superlattice, with twist angles ranging from about 2.3{\deg} to 2.8{\deg}. We developed a contact-STM mode to apply pressure on tMoTe2 and observed a phase transition from band insulator to metal of tMoTe2 under pressure at the charge neutrality point. STM imaging reveals a pronounced in-plane lattice reconstruction with periodic strain redistribution in the tMoTe2, which serves as gauge fields for generating topological moir\'e bands. Importantly, the electronic states of the low-energy moir\'e flat bands primarily concentrate at the XM and MX regions as revealed by STS imaging. Such spatial distributions are nicely reproduced by our first principal calculations with a large-scale basis, suggesting the low-energy moir\'e flat bands are formed through the hybridization of K valley bands of the top layer and K' valley bands of the bottom layer. Overall, our findings provide compelling real-space evidence of electronic structure under pressure and topological flat bands of tMoTe2, paving the way for further STM/STS investigations of correlated topological states within the topological flat band in gate-tunable tMoTe2 devices.

Topological materials hosting metallic edges characterized by integer quantized conductivity in an insulating bulk have revolutionized our understanding of transport in matter. The topological protection of these edge states is based on symmetries and dimensionality. However, only integer-dimensional models have been classified, and the interplay of topology and fractals, which may have a non-integer dimension, remained largely unexplored. Quantum fractals have recently been engineered in metamaterials, but up to present no topological states were unveiled in fractals realized in real materials. Here, we show theoretically and experimentally that topological edge and corner modes arise in fractals formed upon depositing thin layers of bismuth on an indium antimonide substrate. Scanning tunneling microscopy reveals the appearance of (nearly) zero-energy modes at the corners of Sierpi\'nski triangles, as well as the formation of outer and inner edge modes at higher energies. Unexpectedly, a robust and sharp depleted mode appears at the outer and inner edges of the samples at negative bias voltages. The experimental findings are corroborated by theoretical calculations in the framework of a continuum muffin-tin and a lattice tight-binding model. The stability of the topological features to the introduction of a Rashba spin-orbit coupling and disorder is discussed. This work opens the perspective to novel electronics in real materials at non-integer dimensions with robust and protected topological states., Comment: Main manuscript 14 pages, supplementary material 34 pages

Breaking time reversal symmetry in a topological insulator may lead to quantum anomalous Hall effect and axion insulator phase. MnBi4Te7 is a recently discovered antiferromagnetic topological insulator with TN ~12.5 K, which is constituted of alternatively stacked magnetic layer (MnBi2Te4) and non-magnetic layer (Bi2Te3). By means of scanning tunneling spectroscopy, we clearly observe the electronic state present at a step edge of a magnetic MnBi2Te4 layer but absent at non-magnetic Bi2Te3 layers at 4.5 K. Furthermore, we find that as the temperature rises above TN, the edge state vanishes, while the point defect induced state persists upon temperature increasing. These results confirm the observation of magnetism induced edge states. Our analysis based on an axion insulator theory reveals that the nontrivial topological nature of the observed edge state.

Quantum spins, referred to the spin operator preserved by full SU(2) symmetry in the absence of the magnetic anistropy, have been proposed to host exotic interactions with superconductivity4. However, spin orbit coupling and crystal field splitting normally cause a significant magnetic anisotropy for d/f-shell spins on surfaces6,9, breaking SU(2) symmetry and fabricating the spins with Ising properties10. Recently, magnetic nanographenes have been proven to host intrinsic quantum magnetism due to their negligible spin orbital coupling and crystal field splitting. Here, we fabricate three atomically precise nanographenes with the same magnetic ground state of spin S=1/2 on Pb(111) through engineering sublattice imbalance in graphene honeycomb lattice. Scanning tunneling spectroscopy reveals the coexistence of magnetic bound states and Kondo screening in such hybridized system. Through engineering the magnetic exchange strength between the unpaired spin in nanographenes and cooper pairs, quantum phase transition from the singlet to the doublet state has been observed, in consistent with quantum models of spins on superconductors. Our work demonstrates delocalized graphene magnetism host highly tunable magnetic bound states with cooper pairs, which can be further developed to study the Majorana bound states and other rich quantum physics of low-dimensional quantum spins on superconductors., Comment: 13 pages, 4figures

Topological defects in graphene materials introduce exotic properties which are absent in their defect-free counterparts with both fundamental importance and technological implications. Although individual topological defects have been widely studied, collective magnetic behaviors originating from well-organized multiple topological defects remain a great challenge. Here, we studied the collective magnetic properties originating from three pentagon topological defects in truxene-based molecular graphenoids by using scanning tunneling microscopy and non-contact atomic force microscopy. Unpaired $\pi$ electrons are introduced into the aromatic topology of truxene molecular graphenoids one by one by dissociating hydrogen atoms at the pentagon defects via atom manipulation. Scanning tunneling spectroscopy measurements together with density functional theory calculations suggest that the unpaired electrons are ferromagnetically coupled, forming a collective high-spin quartet state of S=3/2. Our work demonstrates that the collective spin ordering can be realized through engineering regular patterned topological defects in molecular graphenoids, providing a new platform for designer one-dimensional ferromagnetic spin chains and two-dimensional ferromagnetic networks., Comment: 25 pages, 12 figures, include Supplementary Information

To realize the braiding operations of Majorana zero mode in the vortex cores of a topological superconductor (TSC), a novel approach is proposed in this letter to replace the common tip (or tip-like) method. Instead of on top of the TSC thin film, arrays of electrically controllable pining centers are built beneath the film, hence detecting can proceed along with braiding. It does not only increase the braiding rate, but also enables the braiding to be performed in an electrically controllable way and to be integrated into large scale. Our work paves the way towards large-scale topological quantum computation., Comment: 5 pages, 2 figures

The magnetic properties of carbon materials are at present the focus of an intense research effort in physics, chemistry and materials science due to their potential applications in spintronics and quantum computations. Although the presence of spins in open-shell nanographenes has been recently confirmed, the ability to control magnetic coupling sign has remained elusive, but the most desirable. Here, we demonstrate an effective approach of engineering magnetic ground states in atomically precise open-shell bipartite/nonbipartite nanographenes using combined scanning probe techniques and mean-field Hubbard model calculations. The magnetic coupling sign between two spins has been controlled via breaking bipartite lattice symmetry of nanographenes. In addition, the exchange-interaction strength between two spins has been widely tuned by finely tailoring their spin density overlap, realizing a large exchange-interaction strength of 42 meV. Our demonstrated method provides ample opportunities for designer above-room-temperature magnetic phases and functionalities in graphene nanomaterials., Comment: 18 pages, 4 figures

Since the early days of Bardeen-Cooper-Schrieffer theory, it has been predicted that a sufficiently large supercurrent can close the energy gap in a superconductor and creates gapless Bogoliubov quasiparticles through the Doppler shift of quasiparticle energy due to the Cooper pair momentum. In this gapless superconducting state, zero-energy quasiparticles reside on a segment of the normal state Fermi surface, while its remaining part is still gapped. The finite density of states of field-induced quasiparticles, known as the Volovik effect, has been observed in tunneling and specific heat measurements on d- and s-wave superconductors. However, the segmented Fermi surface of a finite-momentum state carrying a supercurrent has never been detected directly. Here we use quasiparticle interference (QPI) technique to image field-controlled Fermi surface of Bi$_2$Te$_3$ thin films proximitized by the superconductor NbSe$_2$. By applying a small in-plane magnetic field, a screening supercurrent is induced which leads to finite-momentum pairing on topological surface states of Bi$_2$Te$_3$. Our measurements and analysis reveal the strong impact of finite Cooper pair momentum on the quasiparticle spectrum, and thus pave the way for STM study of pair density wave and FFLO states in unconventional superconductors., Comment: 25 pages, 14 figures

A quantum spin hall insulator(QSHI) is manifested by its conducting edge channels that originate from the nontrivial topology of the insulating bulk states. Monolayer 1T'-WTe2 exhibits this quantized edge conductance in transport measurements, but because of its semimetallic nature, the coherence length is restricted to around 100 nm. To overcome this restriction, we propose a strain engineering technique to tune the electronic structure, where either a compressive strain along a axis or a tensile strain along b axis can drive 1T'-WTe2 into an full gap insulating phase. A combined study of molecular beam epitaxy and in-situ scanning tunneling microscopy/spectroscopy then confirmed such a phase transition. Meanwhile, the topological edge states were found to be very robust in the presence of strain., Comment: 15 pages, 5 figure and 21 pages of supplementary material

Stanene was proposed to be a quantum spin hall insulator containing topological edges states and a time reversal invariant topological superconductor hosting helical Majorana edge mode. Recently, experimental evidences of existence of topological edge states have been found in monolayer stanene films and superconductivity has been observed in few-layer stanene films excluding single layer. An integrated system with both topological edge states and superconductivity are higly pursued as a possible platform to realize topological superconductivity. Few-layer stanene show great potential to meet this requirement and is highly desired in experiment. Here we successfully grow few-layer stanene on bismuth (111) substrate. Both topological edge states and superconducting gaps are observed by in-situ scanning tunneling microscopy/spectroscopy (STM/STS). Our results take a further step towards topological superconductivity by stanene films., Comment: 14 pages,4 figures

Topological materials and topological phases have recently become a hot topic in condensed matter physics. In this work, we report a topological nodal-line semimetal InxTaSe2, in the presence of both charge density wave (CDW) and superconductivity. In the x = 0.58 samples, the 2 * /3 commensurate CDW (CCDW) and the 2 * 2 CCDW are observed below 116 K and 77 K, respectively. Consistent with theoretical calculations, the spin-orbital coupling gives rise to two two-fold-degenerate nodal rings (Weyl rings) connected by drumhead surface states, confirmed by angle-resolved photoemission spectroscopy. Our results suggest that the 2 * 2 CCDW ordering gaps out one Weyl ring in accordance with the CDW band folding, while the other Weyl ring remains gapless with intact surface states. In addition, superconductivity emerges at 0.91 K, with the upper critical field deviating from the s-wave behavior at low temperature, implying possibly unconventional superconductivity. Therefore, InxTaSe2 represents an interesting material system to study the interplay between CDW, nontrivial band topology and superconductivity.

Electronic structure of single crystalline Ba(Zn$_{0.875}$Mn$_{0.125}$)$_{2}$As$_{2}$, parent compound of the recently founded high-temperature ferromagnetic semiconductor, was studied by high-resolution photoemission spectroscopy (ARPES). Through systematically photon energy and polarization dependent measurements, the energy bands along the out-of-plane and in-plane directions were experimentally determined. Except the localized states of Mn, the measured band dispersions agree very well with the first-principle calculations of undoped BaZn$_{2}$As$_{2}$. A new feature related to Mn 3d states was identified at the binding energies of about -1.6 eV besides the previously observed feature at about -3.3 eV. We suggest that the hybridization between Mn and As orbitals strongly enhanced the density of states around -1.6 eV. Although our resolution is much better compared with previous soft X-ray photoemission experiments, no clear hybridization gap between Mn 3d states and the valence bands proposed by previous model calculations was detected.

Majorana fermion (MF) whose antiparticle is itself has been predicted in condensed matter systems. Signatures of the MFs have been reported as zero energy modes in various systems. More definitive evidences are highly desired to verify the existence of the MF. Very recently, theory has predicted MFs to induce spin selective Andreev reflection (SSAR), a novel magnetic property which can be used to detect the MFs. Here we report the first observation of the SSAR from MFs inside vortices in Bi2Te3/NbSe2 hetero-structure, in which topological superconductivity was previously established. By using spin-polarized scanning tunneling microscopy/spectroscopy (STM/STS), we show that the zero-bias peak of the tunneling differential conductance at the vortex center is substantially higher when the tip polarization and the external magnetic field are parallel than anti-parallel to each other. Such strong spin dependence of the tunneling is absent away from the vortex center, or in a conventional superconductor. The observed spin dependent tunneling effect is a direct evidence for the SSAR from MFs, fully consistent with theoretical analyses. Our work provides definitive evidences of MFs and will stimulate the MFs research on their novel physical properties, hence a step towards their statistics and application in quantum computing., Comment: 4 figures 15 pages

Using high-resolution angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy, the atomic and low energy electronic structure of the Sr-doped superconducting topological insulators (SrxBi2Se3) was studied. Scanning tunneling microscopy shows that most of the Sr atoms are not in the van der Waals gap. After Sr doping, the Fermi level was found to move further upwards when compared with the parent compound Bi2Se3, which is consistent with the low carrier density in this system. The topological surface state was clearly observed, and the position of the Dirac point was determined in all doped samples. The surface state is well separated from the bulk conduction bands in the momentum space. The persistence of separated topological surface state combined with small Fermi energy makes this superconducting material a very promising candidate for the time reversal invariant topological superconductor

Using high-resolution angle-resolved photoemission spectroscopy, the electronic structure near the Fermi level and the topological property of the Bi(111) films grown on the Bi$_2$Te$_3$(111) substrate were studied. Very different from the bulk Bi, we found another surface band near the $\bar{M}$ point besides the two well-known surface bands on the Bi(111) surface. With this new surface band, the bulk valence band and the bulk conduction band of Bi can be connected by the surface states. Our band mapping revealed odd number of Fermi crossings of the surface bands, which provided a direct experimental signature that Bi(111) thin films of a certain thickness on the Bi$_2$Te$_3$(111) substrate can be topologically nontrivial in three dimension.

Ultrathin semiconductors present various novel electronic properties. The first experimental realized two-dimensional (2D) material is graphene. Searching 2D materials with heavy elements bring the attention to Si, Ge and Sn. 2D buckled Si-based silicene was realized by molecular beam epitaxy (MBE) growth1,2. Ge-based germanene was realized by mechanical exfoliation3. Sn-based stanene has its unique properties. Stanene and its derivatives can be 2D topological insulators (TI) with a very large band gap as proposed by first-principles calculations4, or can support enhanced thermoelectric performance5, topological superconductivity6 and the near-room-temperature quantum anomalous Hall (QAH) effect7. For the first time, in this work, we report a successful fabrication of 2D stanene by MBE. The atomic and electronic structures were determined by scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES) in combination with first-principles calculations. This work will stimulate the experimental study and exploring the future application of stanene., Comment: 20 pages, 4 figures

Recently, interface has been employed to enhance superconductivity in the single-layer FeSe films grown on SrTiO3(001)(STO) with a possible Tc of ~ 80 K, which is nearly ten times of the Tc of bulk FeSe and is above the Tc record of 56 K for the bulk Fe-based superconductors. This work together with those on superconducting oxides interfaces revives the long-standing idea that electron pairing at a two-dimensional (2D) interface between two different materials is a potential path to high transition temperature (Tc) superconductivity. Subsequent angle-resolved photoemission spectroscopy (ARPES) measurements revealed different electronic structure from those of bulk FeSe with a superconducting-like energy gap closing at around 65K. However, previous ex situ electrical transport measurements could only detect the zero-resistance below ~30 K. Here we report the observation of high Tc superconductivity in the FeSe/STO system. By in situ 4-point probe (4PP) electrical transport measurement that can be conducted at an arbitrary position of the FeSe film on STO, we detected superconductivity above 100 K. Our finding makes FeSe/STO the exciting and ideal research platform for higher Tc superconductivity., Comment: 10 pages, 3 figures, 7 pages supplementary materials

Electronic structures of single crystalline black phosphorus were studied by state-of-art angleresolved photoemission spectroscopy. Through high resolution photon energy dependence measurements, the band dispersions along out-of-plane and in-plane directions are experimentally determined. The electrons were found to be more localized in the ab-plane than that is predicted in calculations. Beside the kz-dispersive bulk bands, resonant surface state is also observed in the momentum space. Our finds strongly suggest that more details need to be considered to fully understand the electronic properties of black phosphorus theoretically.

Combining first-principles calculations and spin- and angle-resolved photoemission spectroscopy measurements, we identify the helical spin textures for three different Dirac cone states in the interfaced systems of a 2D topological insulator (TI) of Bi(111) bilayer and a 3D TI Bi2Se3 or Bi2Te3. The spin texture is found to be the same for the intrinsic Dirac cone of Bi2Se3 or Bi2Te3 surface state, the extrinsic Dirac cone of Bi bilayer state induced by Rashba effect, and the hybridized Dirac cone between the former two states. Further orbit- and atom-resolved analysis shows that s and pz orbits have a clockwise (counterclockwise) spin rotation tangent to the iso-energy contour of upper (lower) Dirac cone, while px and py orbits have an additional radial spin component. The Dirac cone states may reside on different atomic layers, but have the same spin texture. Our results suggest that the unique spin texture of Dirac cone states is a signature property of spin-orbit coupling, independent of topology.

Due to the large spin-orbital coupling in the layered 5d-transition metal chalcogenides compound, the occurrence of superconductivity in Ir2-xPdxTe2 offers a good chance to search for possible topological superconducting states in this system. We did comprehensive studies on the superconducting properties and electronic structures of single crystalline Ir0.95Pd0.05Te2 samples. The superconducting gap size, critical fields and coherence length along different directions were experimentally determined. Macroscopic bulk measurements and microscopic low temperature scanning tunneling spectroscopy results suggest that Ir0.95Pd0.05Te2 possesses a BCS-like s-wave state. No sign of zero bias conductance peak were found in the vortex core at 0.4K.

Majorana fermions have been intensively studied in recent years for their importance to both fundamental science and potential applications in topological quantum computing1,2. Majorana fermions are predicted to exist in a vortex core of superconducting topological insulators3. However, they are extremely difficult to be distinguished experimentally from other quasiparticle states for the tiny energy difference between Majorana fermions and these states, which is beyond the energy resolution of most available techniques. Here, we overcome the problem by systematically investigating the spatial profile of the Majorana mode and the bound quasiparticle states within a vortex in Bi2Te3/NbSe2. While the zero bias peak in local conductance splits right off the vortex center in conventional superconductors, it splits off at a finite distance ~20nm away from the vortex center in Bi2Te3/NbSe2, primarily due to the Majorana fermion zero mode. While the Majorana mode is destroyed by reducing the distance between vortices, the zero bias peak splits as a conventional superconductor again. This work provides strong evidences of Majorana fermions and also suggests a possible route to manipulating them., Comment: 16 pages, 4 figures

Topological superconductors (TSCs) have a full gap in the bulk and gapless surface states consisting of Majorana fermions, which have potential applications in fault-tolerant topological quantum computation. Because TSCs are very rare in nature, an alternative way to study the TSC is to artificially introduce superconductivity into the surface states of a topological insulator (TI) through proximity effect (PE)1-4. Here we report the first experimental realization of the PE induced TSC in Bi2Te3/NbSe2 thin films as demonstrated by the density of states probed using scanning tunneling microscope. We observe Abrikosov vortices and lower energy bound states on the surface of topological insulator and the dependence of superconducting coherence length on the film thickness and magnetic field, which are attributed to the superconductivity in the topological surface states. This work demonstrates the practical feasibility of fabricating a TSC with individual Majorana fermions inside superconducting vortex as predicted in theory and accomplishes the pre-requisite step towards searching for Majorana fermions in the PE induced TSCs., Comment: 15 pages, 4 figures

Topological insulators (TIs) and graphene present two unique classes of materials which are characterized by spin polarized (helical) and non-polarized Dirac-cone band structures, respectively. The importance of many-body interactions that renormalize the linear bands near Dirac point in graphene has been well recognized and attracted much recent attention. However, renormalization of the helical Dirac point has not been observed in TIs. Here, we report the experimental observation of the renormalized quasi-particle spectrum with a skewed Dirac cone in a single Bi bilayer grown on Bi2Te3 substrate, from angle-resolved photoemission spectroscopy. First-principles band calculations indicate that the quasi-particle spectra are likely associated with the hybridization between the extrinsic substrate-induced Dirac states of Bi bilayer and the intrinsic surface Dirac states of Bi2Te3 film at close energy proximity. Without such hybridization, only single-particle Dirac spectra are observed in a single Bi bilayer grown on Bi2Se3, where the extrinsic Dirac states Bi bilayer and the intrinsic Dirac states of Bi2Se3 are well separated in energy. The possible origins of many-body interactions are discussed. Our findings provide a means to manipulate topological surface states.

The electronic and magnetic properties of iron-doped topological insulator Bi1.84-xFe0.16CaxSe3 single crystals were studied. By co-doping Fe and Ca atoms, ferromagnetic bulk states with different carrier density (from n-type to p-type) were obtained. Effective magnetic moments for each Fe atom was estimated as small as about 0.07$\mu$B. Magnetic and non-magnetic phases separation was observed in all samples. Our results suggest that the bulk ferromagnetism in Fe-doped Bi2Se3 is not intrinsic and regardless of carrier density.

Topological insulators (TIs) are a unique class of materials characterized by a surface (edge) Dirac cone state of helical Dirac fermions in the middle of bulk (surface) gap. When the thickness (width) of TIs is reduced, however, interaction between the surface (edge) states will open a gap removing the Dirac cone. Using density function theory calculation, we demonstrate the creation of helical Dirac fermions from interfacing two gapped TI films, a single bilayer Bi grown on a single quintuple layer Bi2Se3 or Bi2Te3. The theoretical prediction is directly confirmed by experiment. We further show that the extrinsic helical Dirac fermions consists of predominantly Bi bilayer states, which are created by a giant Rashba effect due to interfacial charge transfer. Our findings provide a promising new method to create novel TI materials by interface engineering., Comment: 18 pages and 4 figures

This paper has been withdrawn by the author due to journal requirement., Comment: This paper has been withdrawn by the author due to journal requirement