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<jats:p>Ultra-thin topological insulators provide a platform for realizing many exotic phenomena such as the quantum spin Hall effect, and quantum anomalous Hall effect. These effects or states are characterized by quantized transport behavior of edge states. Experimentally, although these states have been realized in various systems, the temperature for the edge states to be the dominating channel in transport is extremely low, contrary to the fact that the bulk gap is usually in the order of a few tens of milli-electron volts. There must be other in-gap conduction channels that do not freeze out until a much lower temperature. Here we grow ultra-thin topological insulator Bi<jats:sub>2</jats:sub>Te<jats:sub>3</jats:sub> and Sb<jats:sub>2</jats:sub>Te<jats:sub>3</jats:sub> films by molecular beam epitaxy and investigate the structures of domain boundaries in these films. By scanning tunneling microscopy and spectroscopy we find that the domain boundaries with large rotation angles have pronounced in-gap bound states, through which one-dimensional conduction channels are suggested to form, as visualized by spatially resolved spectroscopy. Our work indicates the critical role played by domain boundaries in degrading the transport properties.</jats:p>

<jats:p>Topological superconductors (TSCs) have been widely investigated in recent years due to their novel physics and ability to host Majorana fermions (MFs) which are key to topological quantum computation. Despite the great interest, only a few compounds have been proposed as candidates of intrinsic TSCs, such as iron-based superconductor FeSe<jats:sub>0.55</jats:sub>Te<jats:sub>0.45</jats:sub> and 2M-WS<jats:sub>2</jats:sub>. Among them, quasi-one-dimensional superconductor TaSe<jats:sub>3</jats:sub> possesses fascinating properties such as its simple stoichiometry, layered nature and chemical stability. Here, using scanning tunneling microscope/spectroscopy (STM/STS), we systematically investigate the topography and electronic structure of TaSe<jats:sub>3</jats:sub>. Our STM/STS measurement reveals large atomically flat, defect-free surfaces suitable for the search of MF; electronic density of states consistent with our angle-resolved photoemission result and band-structure calculations, and a uniform superconducting gap with a typical size of ∼ 0.25 meV. Remarkably, additional edge states are observed in the vicinity of the terrace edge, suggesting they may have a topological origin. Our result proves the coexistence of superconductivity and topological electronic structure in TaSe<jats:sub>3</jats:sub>, making it an intriguing platform to investigate topological superconductivity.</jats:p>

<jats:p>We propose a new method to construct low-dimensional quantum devices consisting of the magnetic topological insulators. Unlike previous systems based on locally depleting two-dimensional electron gas in semiconductor heterojunctions, magnetization provides a simpler and rewriteable fabrication way. The motion of electrons can be manipulated through the domain wall formed by the boundary between different magnetic domains. Here, three devices designed by local magnetization are presented. For the quantum point contact, conductance exhibits quantized plateaus with the increasing silt width between two magnetic domains. For the quantum dot, conductance shows pronounced peaks as the change of gate voltage. Finally, for the Aharonov–Bohm ring, conductance oscillates periodically with the external magnetic field. Numerical results show that the transport of these local magnetization systems is identical to that of the previous systems based on depleting two-dimensional electron gas, and the only difference is the approach of construction. These findings may pave the way for realization of low-power-consumption devices based on magnetic domain walls.</jats:p>

<jats:p>We introduce a generalized Rashba coupling approximation to analytically solve confined two-dimensional electron systems with both the Rashba and Dresselhaus spin–orbit couplings in an external magnetic field. A solvable Hamiltonian is obtained by performing a simple change of basis, which has the same form as that with only Rashba coupling. Each Landau state becomes a new displaced-Fock state instead of the original Harmonic oscillator Fock state. Analytical energies are consistent with the numerical ones in a wide range of coupling strength even for a strong Zeeman splitting, exhibiting the validity of the analytical approximation. By using the eigenstates, spin polarization correctly displays a jump at the energy-level crossing point, where the corresponding spin conductance exhibits a pronounced resonant peak. As the component of the Dresselhaus coupling increases, the resonant point shifts to a smaller value of the magnetic field. In contrast to pure Rashba couplings, we find that the Dresselhaus coupling and Zeeman splittings tend to suppress the resonant spin Hall effect. Our method provides an easy-to-implement analytical treatment to two-dimensional electron gas systems with both types of spin–orbit couplings by applying a magnetic field.</jats:p>

<jats:p>We report an implementation of the momentum space quantum Monte Carlo (QMC) method on the interaction model for the twisted bilayer graphene (TBG). The long-range Coulomb repulsion is treated exactly with the flat bands, spin and valley degrees of freedom of electrons taking into account. We prove the absence of the minus sign problem for QMC simulation when either the two valleys or the two spin degrees of freedom are considered. By taking the realistic parameters of the twist angle and interlayer tunnelings into the simulation, we benchmark the QMC data with the exact band gap obtained at the chiral limit, to reveal the insulating ground states at the charge neutrality point (CNP). Then, with the exact Green’s functions from QMC, we perform stochastic analytic continuation to obtain the first set of single-particle spectral function for the TBG model at CNP. Our momentum space QMC scheme therefore offers the controlled computation pathway for systematic investigation of the electronic states in realistic TBG model at various electron fillings.</jats:p>

<jats:p>The recent observation of superconductivity in thin films of infinite-layer nickelate Nd<jats:sub>0.8</jats:sub>Sr<jats:sub>0.2</jats:sub>NiO<jats:sub>2</jats:sub> has received considerable attention. Despite the many efforts to understand the superconductivity in infinite-layer nickelates, a consensus on the underlying mechanism for the superconductivity has yet to be reached, partly owing to the challenges with the material synthesis. Here, we report the successful growth of superconducting infinite-layer Nd<jats:sub>0.8</jats:sub>Sr<jats:sub>0.2</jats:sub>NiO<jats:sub>2</jats:sub> films by pulsed laser deposition and soft chemical reduction. The details on the growth process are discussed.</jats:p>

<jats:p>We report <jats:sup>121/123</jats:sup>Sb nuclear quadrupole resonance (NQR) and <jats:sup>51</jats:sup>V nuclear magnetic resonance (NMR) measurements on kagome metal CsV<jats:sub>3</jats:sub>Sb<jats:sub>5</jats:sub> with <jats:italic>T</jats:italic> <jats:sub>c</jats:sub> = 2.5 K. Both <jats:sup>51</jats:sup>V NMR spectra and <jats:sup>121/123</jats:sup>Sb NQR spectra split after a charge density wave (CDW) transition, which demonstrates a commensurate CDW state. The coexistence of the high temperature phase and the CDW phase between 91 K and 94 K manifests that it is a first-order phase transition. At low temperature, electric-field-gradient fluctuations diminish and magnetic fluctuations become dominant. Superconductivity emerges in the charge order state. Knight shift decreases and 1/<jats:italic>T</jats:italic> <jats:sub>1</jats:sub> <jats:italic>T</jats:italic> shows a Hebel–Slichter coherence peak just below <jats:italic>T</jats:italic> <jats:sub>c</jats:sub>, indicating that CsV<jats:sub>3</jats:sub>Sb<jats:sub>5</jats:sub> is an s-wave superconductor.</jats:p>

<jats:p>The coupling between electric ordering and magnetic ordering in two-dimensional (2D) materials is important for both fundamental research of 2D multiferroics and future development of magnetism-based information storage and operation. Here, we introduce a scheme for realizing a magnetic phase transition through the transition of electric ordering. We take CuMoP<jats:sub>2</jats:sub>S<jats:sub>6</jats:sub> monolayer as an example, which is a member of the large 2D transition-metal chalcogen-phosphates family. Based on first-principles calculations, we find that it is a multiferroic with unprecedented characters, namely, it exhibits two different phases: an antiferroelectric-antiferromagnetic phase and a ferroelectric-ferromagnetic phase, in which the electric and magnetic orderings are strongly coupled. Importantly, the electric polarization is out-of-plane, so the magnetism can be readily switched by using the gate electric field. Our finding reveals a series of 2D multiferroics with special magnetoelectric coupling, which hold great promise for experimental realization and practical applications.</jats:p>

<jats:p>Starting from a general sixth-order nonlinear wave equation, we present its multiple kink solutions, which are related to the famous Hirota form. We also investigate the restrictions on the coefficients of this wave equation for possessing multiple kink structures. By introducing the velocity resonance mechanism to the multiple kink solutions, we obtain the soliton molecule solution and the breather-soliton molecule solution of the sixth-order nonlinear wave equation with particular coefficients. The three-dimensional image and the density map of these soliton molecule solutions with certain choices of the involved free parameters are well exhibited. After matching the parametric restrictions of the sixth-order nonlinear wave equation for having three-kink solution with the coefficients of the integrable bidirectional Sawada–Kotera–Caudrey–Dodd–Gibbons (SKCDG) equation, the breather-soliton molecule solution for the bidirectional SKCDG equation is also illustrated.</jats:p>

<jats:p>An integrable non-Hermitian generalized Rabi model is constructed. A twist matrix is introduced to the construction of Hamiltonian and generates the non-Hermitian properties. The Yang-Baxter integrability of the system is proven. The exact energy spectrum and eigenstates are obtained using the Bethe ansatz. The method given in this study provides a general way to construct integrable spin-boson models.</jats:p>