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Topological materials are typically characterized by gapless boundary states originated from nontrivial bulk band topology, known as topological bulk-boundary correspondence. Recently, this fundamental concept has been generalized in higher-order topological insulators (HOTIs). E.g., a second-order three-dimensional (3D) TI hosts one-dimensional (1D) topological hinge states winding around the crystal. However, a complete verification of higher-order topology is still lacking as it requires probing all the crystal boundaries. Here we studied a promising candidate of second-order TI, bismuth (Bi), in the form of mesoscopic crystals grown on superconducting V3Si. Using low-temperature scanning tunneling microscopy, we directly observed dispersive 1D states on various hinges of the crystal. Upon introducing magnetic scatterers, new scattering channels emerged selectively on certain hinges, revealing their spin-helical nature. Combining first-principle calculation and global symmetry analysis, we find these hinge states are topological and formed a closed loop encircling the crystal. This provides direct evidence on the higher-order topology in Bi. Moreover, proximity superconductivity is observed in the topological hinge states, enabling HOTI as a promising platform for realizing topological superconductivity and Majorana quasiparticles., Comment: 28 pages,15 figures

Two-dimensional (2D) van der Waals (vdW) magnets present a promising platform for spintronic applications due to their unique structural and electronic properties. The ability to electrostatically control their interlayer magnetic coupling between ferromagnetic and antiferromagnetic phases is particularly advantageous for the development of energy-efficient spintronic components. While effective in bilayer CrI3, achieving this control in other 2D magnets remains a challenge. In this work, we demonstrate that bilayer Cr2Ge2Te6 can achieve efficient electrostatic control through interlayer hopping modulation. We show that an external electric field can effectively manipulate the FM-AFM phase transition when interlayer hopping is enhanced by pressure or sliding. We further develop a four-site interlayer hopping model, revealing that the phase transition is driven by a combined effect of on-site energy splitting and interlayer electronic hopping. These findings pave the way for designing novel, electrically tunable spintronic devices, offering substantial potential for energy-efficient information processing and storage., Comment: 4 figures

In the past, quasi coherent modes were reported for nearly all tokamaks. The general definition describes modes as quasi coherent when the magnitude squared coherence is in the range of \SIrange{0.3}{0.6}{}. Quasi coherent modes are observed in the plasma core as well as in the plasma edge and can have quite different physical origins. The one in the core are observed in plasmas with low collisionality, where the electron temperature exceeds the ion temperature in the plasma core. This is the case for electron cyclotron heating in general. The origin of these modes are electrons trapped within a magnetic mirror, as reported in the past from various fusion devices. The so-called trapped-electron modes (TEMs) belong to drift wave instabilities and can be destabilized by electron-temperature gradients in the plasma core. From the diagnostic point of view, quasi coherent modes appear as fluctuations in electron density and temperature. Therefore, the microwave reflectometer is very well suited to monitor these modes. This paper describes experiments, conducted at the Wendelstein 7-X stellarator (W7-X), which aim at detecting quasi coherent modes at low wave numbers. A Poloidal Correlation Reflectometer (PCR) installed at W7-X, is able to measure low wave numbers ($k_\perp\le 3.5$ cm$^{-1}$). For different magnetic configurations and plasma parameters, broad quasi-coherent structures are observed in the coherence spectra. From the analysis of the rotation and the poloidal structure, these quasi coherent (QC) modes show the properties of electron-temperature-gradient driven TEMs. A linear relation between the mode velocity and the rotation frequency is found. The relation is uniform and confirms the nature of QC-mode observation as TEM in tokamaks, too., Comment: Some revisions asked by referees included

Traditional ferroelectrics are limited by Neumann's principle, which confines exploration of ferroelectrics within polar point groups. Our recent work [Nat. Commun. 15, 135, (2024)] proposes the concept of fractional quantum ferroelectricity (FQFE) that extend the playground of ferroelectricity to non-polar point groups. Here, we apply group theory and introduce an efficient symmetry strategy to identify FQFE candidates. Integrated with a high-throughput screening scheme, we go through 171,527 materials and identify 202 potential FQFE candidates, which are already experimentally synthesized. In addition, we point out that the essence of FQFE is fractional atomic displacements with respect to lattice vectors, which can actually result in both fractional (type-I) and integer (type-II) quantized polarization, respectively. Through performing first-principles calculations, we verify the symmetry-predicted switchable FQFE properties in bulk AlAgS2 and monolayer HgI2. Notably, AlAgS2 exhibits an ultra-low switching barrier of 23 meV/f.u. and interlocked in-plane/out-of-plane polarization, while HgI2 demonstrates large spontaneous polarization of 42 {\mu}C/cm2. Our findings not only advance the understanding on FQFE, but also offer guidance for experimental exploration and design of novel ferroelectric materials., Comment: 16 pages, 4 figures

Nonlinear Hall effects have been previously investigated in non-centrosymmetric systems for electronic systems. However, they only exist in metallic systems and are not compatible with ferroelectrics since these latter are insulators, hence limiting their applications. On the other hand, ferroelectrics naturally break inversion symmetry and can induce a non-zero Berry curvature. Here, we show that a non-volatile electric-field control of heat current can be realized in ferroelectrics through the nonlinear phonon Hall effects. More precisely, based on Boltzmann equation under the relaxation-time approximation, we derive the equation for nonlinear phonon Hall effects, and further show that the behaviors of nonlinear phonon (Boson) Hall effects are very different from nonlinear Hall effects for electrons (Fermion). Our work provides a route for electric-field control of thermal Hall current in ferroelectrics., Comment: 16 pages, 2 figures

Non-volatile manipulation of valley polarization in solids has long been desired for valleytronics applications but remains challenging. Here, we propose a novel strategy for non-volatile manipulating valleys through bilayer stacking, which enables spontaneous valley polarization without breaking time-reversal symmetry. We call this noval physics as bilayer stacking ferrovalley (BSFV). The group theory analysis reveals that the two-dimensional (2D) valley materials with hexagonal and square lattices can host BSFV. By searching the 2D material database, we discovered 14 monolayer 2D materials with direct gaps that are candidates for realizing BSFV. Further first-principles calculations demonstrate that BSFV exists in RhCl3 and InI bilayers. The bilayer stacking breaks their three- and four-fold rotation symmetry, resulting in 39 and 326 meV valley polarization, respectively. More interestingly, the valley polarization in our systems can be switched by interlayer sliding. Our study opens up a new direction for designing ferrovalley materials and thus greatly enriches the platform for the research of valleytronics., Comment: 13 pages, 3 figures

The physical properties of crystals are governed by their symmetry according to Neumann's principle. However, we present a case that contradicts this principle wherein the polarization is not invariant under its symmetry. We term this phenomenon as unconventional ferroelectricity in violation of Neumann's principle (UFVNP). Our group theory analysis reveals that 33 symmorphic space groups have the potential for UFVNP, with 26 of these symmorphic space groups belonging to non-polar groups. Notably, the polarization component in UFVNP materials is quantized. Our theory can explain the experimentally proven in-plane polarization of the monolayer {\alpha}-In2Se3, which has C3v symmetry. Additionally, we employ first-principles calculations to demonstrate the existence of UFVNP in Td phase AgBr, which was not initially anticipated to exhibit polarization. Thus, UFVNP plays an integral role in characterizing and exploring the possible applications of ferroelectrics, significantly expanding the range of available materials for study., Comment: 14 pages, 3 figures, 1 tables

Two-dimensional (2D) ferroelectrics, which is rare in nature, enable high-density non-volatile memory with low energy consumption. Here, we propose a theory of bilayer stacking ferroelectricity (BSF), in which, two stacked layers of the same 2D material, with different rotation and translation, exhibits ferroelectricity. By performing systematic group theory analysis, we find out all the possible BSF in all the 80 layer groups (LGs) and discover the rules about the creation and annihilation of symmetries in the bilayer. Our general theory can not only explain all the previous findings (including sliding ferroelectricity), but also provide new perspective. Interestingly, the direction of the electric polarization of the bilayer could be totally different from that of the single layer. In particular, the bilayer could become ferroelectric after properly stacking two centrosymmetric non-polar monolayers. By means of first-principles simulations, we demonstrate that the ferroelectricity and thus multiferroicity can be introduced to the prototypical 2D ferromagnetic centrosymmetric material CrI3 by stacking. Furthermore, we find that the out-of-plane electric polarization in bilayer CrI3 is interlocked with the in-plane electric polarization, suggesting that the out-of-plane polarization can be manipulated in a deterministic way through the application of an in-plane electric field. The present BSF theory lays a solid foundation for designing a large number of bilayer ferroelectrics and thus colorful platforms for fundamental studies and applications., Comment: 18 pages, 2 figures

Two-dimensional (2D) van der Waals (vdW) magnets provide an ideal platform for exploring, on the fundamental side, new microscopic mechanisms and for developing, on the technological side, ultra-compact spintronic applications. So far, bilinear spin Hamiltonians have been commonly adopted to investigate the magnetic properties of 2D magnets, neglecting higher order magnetic interactions. However, we here provide quantitative evidence of giant biquadratic exchange interactions in monolayer NiX2 (X=Cl, Br and I), by combining first-principles calculations and the newly developed machine learning method for constructing Hamiltonian. Interestingly, we show that the ferromagnetic ground state within NiCl2 single layers cannot be explained by means of bilinear Heisenberg Hamiltonian; rather, the nearest-neighbor biquadratic interaction is found to be crucial. Furthermore, using a three-orbitals Hubbard model, we propose that the giant biquadratic exchange interaction originates from large hopping between unoccupied and occupied orbitals on neighboring magnetic ions. On a general framework, our work suggests biquadratic exchange interactions to be important in 2D magnets with edge-shared octahedra., Comment: 3 figures

The layered magnetic topological insulator MnBi$_2$Te$_4$ is a promising platform to realize the quantum anomalous Hall effect because its layers possess intrinsic ferromagnetism. However, it is not well understood why the high-spin $d^5$ magnetic ions Mn$^{2+}$ forming the Mn-Te-Mn spin exchange paths prefer ferromagnetic (FM) coupling, contrary to the prediction of the Goodenough-Kanamori rule that a TM-L-TM spin exchange, where TM and L are a transition-metal magnetic cation and a main group ligand, respectively, is antiferromagnetic (AFM) even when the bond angle of the exchange path is 90$^{\circ}$. Using density functional theory (DFT) calculations, we show that the presence of Bi$^{3+}$ ions is essential for the FM coupling in MnBi$_2$Te$_4$. Then, using a tight-binding model Hamiltonian, we find that high-spin $d^5$ ions (S = 5/2) in TM-L-TM spin exchange paths prefer FM coupling if the empty p-orbitals of a nonmagnetic cation M (e.g., Bi$^{3+}$ ion) hybridize strongly with those of the bridging ligand L, but AFM coupling otherwise., Comment: 13 pages, 4 figures

Intense laser pulses have recently emerged as a tool to tune between different orders in complex quantum materials. Among different light-induced phenomena, transient superconductivity far above the equilibrium transition temperature in cuprates is particularly attractive. Key to those experiments was the resonant pumping of specific phonon modes, which was believed to induce superconducting phase coherence by suppressing the competing orders or modifying the structure slightly. Here, we present a comprehensive study of photo-induced nonequilibrium response in underdoped YBa$_2$Cu$_3$O$_{6+x}$. We find that upon photo-excitations, Josephson plasma edge in superconducting state is initially removed accompanied by quasiparticle excitations, and subsequently reappears at frequency lower than the static plasma edge within short time. In normal state, an enhancement or weaker edge-like shape is indeed induced by pump pulses in the reflectance spectrum accompanied by simultaneous rises in both real and imaginary parts of conductivity. We compare the pump-induced effects between near- and mid-infrared excitations and exclude phonon pumping as a scenario for the photo-induced effects above. We further elaborate the transient responses in normal state are unlikely to be explained by photo-induced superconductivity., Comment: 8 pages, 4 figures and supplementary

Materials with a coexistence of magnetic and ferroelectric order (i.e., multiferroics) provide an efficient route for the control of magnetism by electric fields. Unfortunately, a long-sought room temperature multiferroic with strongly coupled ferroelectric and ferromagnetic (or ferrimagnetic) orderings is still lacking. Here, we propose that hydrogen intercalation in antiferromagnetic transition metal oxides is a promising way to realize multiferroics with strong magnetoelectric coupling. Taking brownmillerite SrCoO2.5 as an example, we show that hydrogen intercalated SrCoO2.5 displays strong ferrimagnetism and large electric polarization in which the hydroxide acts as a new knob to simultaneously control the magnetization and polarization at room temperature. We expect that ion intercalation will become a general way to design magnetoelectric and spintronic functional materials.

Honeycomb iridate Na2IrO3, a Jeff=1/2 magnet, is a potential platform for realizing the quantum spin liquid. Many experiments have shown that its magnetic ground state has a zigzag antiferromagnetic (AFM) order. However, there is still a lack of consensus on the theoretical model explaining such order, since its second nearest neighbor (NN) and long-range third NN magnetic interactions are highly unclear. By properly taking into account the orbital moments, achieved through constraining their directions in the first-principles calculations, we obtain that the relative angle between orbital and spin moments is fairly small and in the order of several degrees, which thus validates the Jeff=1/2 state in Na2IrO3. Surprisingly, we find that the long-range third NN Heisenberg interactions are sizable whereas the second NN magnetic interactions are negligible. Using maximally localized Wannier functions, we show that the sizable long-range third NN Heisenberg interaction results from the extended nature of the Jeff=1/2 state. Based on our study, we propose a minimal J1-K1-{\Gamma}_1-J3 model in which the magnetic excitations have an intensity peak at 5.6 meV, consistent with the inelastic neutron scattering experiment [Phys. Rev. Lett. 108, 127204 (2012)]. The present work demonstrates again that constraining orbital moments in the first-principles calculations is powerful to investigate the intriguing magnetism in the Jeff=1/2 magnets, and paves the way toward gaining a deep insight into the novel magnetism discovered in the honeycomb Jeff=1/2 magnets., Comment: four figures and 2 tables

We report a single crystal neutron and x-ray diffraction study of the hybrid improper multiferroic Ca3Mn1.9Ti0.1O7 (CMTO), a prototypical system where the electric polarization arises from the condensation of two lattice distortion modes.With increasing temperature (T ), the out-of-plane, antiphase tilt of MnO6 decreases in amplitude while the in-plane, in-phase rotation remains robust and experiences abrupt changes across the first-order structural transition. Application of hydrostatic pressure (P) to CMTO at room temperature shows a similar effect. The consistent behavior under both T and P reveals the softness of antiphase tilt and highlights the role of the partially occupied d orbital of the transition-metal ions in determining the stability of the octahedral distortion. Polarized neutron analysis indicates the symmetry-allowed canted ferromagnetic moment is less than the 0.04 {\mu}B/Mn site, despite a substantial out-of-plane tilt of the MnO6 octahedra., Comment: 5 figures

The structure of ABO3 perovskites is dominated by two types of unstable modes, namely, the oxygen octahedral rotation (AFD) and ferroelectric (FE) mode. It is generally believed that such AFD and FE modes tend to compete and suppress each other. Here we use first-principles methods to show that a dual nature of the AFD-FE coupling, which turns from competitive to cooperative as the AFD mode strengthens, occurs in numerous perovskite oxides. We provide a unified model of such a dual interaction by introducing novel high-order coupling terms, and explain the atomistic origin of the resulting new form of ferroelectricity in terms of universal steric mechanisms. We also predict that such a novel form of ferroelectricity leads to atypical behaviors, such as an enhancement of the electric polarization under hydrostatic pressure.

We reply to the objections raised in a recent Comment (arXiv:1706.03023) regarding our observation of slow magnetic fluctuations and critical slowing down of magnetic fluctuations in the pseudogap phase of YBa$_2$Cu$_3$O$_y$ by zero-field and longitudinal-field muon spin relaxation (arXiv:1703.06799)., Comment: 4 pages, 3 figures

The rotation of octahedra (octahedral tilting) is common in ABO3 perovskites and relevant to many physical phenomena, ranging from electronic and magnetic properties, metal-insulator transitions to improper ferroelectricity. Hydrostatic pressure is an efficient way to tune and control octahedral tiltings. However, the pressure behavior of such tiltings can dramatically differ from one material to another, with the origins of such differences remaining controversial. In this work, we discover several new mechanisms and formulate a set of simple rules that allow to understand how pressure affects oxygen octahedral tiltings, via the use and analysis of first-principles results for a variety of compounds. Besides the known A-O interactions, we reveal that the interactions between specific B-ions and oxygen ions contribute to the tilting instability. We explain the previously reported trend that the derivative of the oxygen octahedral tilting with respect to pressure (dR/dP) usually decreases with both the tolerance factor and the ionization state of the A-ion, by illustrating the key role of A-O interactions and their change under pressure. Furthermore, three new mechanisms/rules are discovered. We further predict that the polarization associated with the so-called hybrid improper ferroelectricity could be manipulated by hydrostatic pressure, by indirectly controlling the amplitude of octahedral rotations., Comment: Submitted to Phys. Rev

Evidence for intra-unit-cell (IUC) magnetic order in the pseudogap region of high-$T_c$ cuprates below a temperature $T^\ast$ is found in several studies, but NMR and $\mu$SR experiments do not observe the expected static local magnetic fields. It has been noted, however, that such fields could be averaged by fluctuations. Our measurements of muon spin relaxation rates in single crystals of YBa$_2$Cu$_3$O$_y$ reveal magnetic fluctuations of the expected order of magnitude that exhibit critical slowing down at $T^\ast$. These results are strong evidence for fluctuating IUC magnetic order in the pseudogap phase., Comment: 8 pages 7 figures including supplemental material; added discussion of statistics and other experiments

Quantum anomalous Hall (QAH) insulator is a topological phase which exhibits chiral edge states in the absence of magnetic field. The celebrated Haldane model is the first example of QAH effect, but difficult to realize. Here, we predict the two-dimensional single-atomic-layer V2O3 with a honeycomb-Kagome structure is a QAH insulator with a large band gap (large than 0.1 eV) and a high ferromagnetic Curie temperature (about 900 K). Combining the first-principle calculations with the effective Hamiltonian analysis, we find that the spin-majority dxy and dyz orbitals of V atoms on the honeycomb lattice form a massless Dirac cone near the Fermi level which becomes massive when the on-site spin-orbit coupling is included. Interestingly, we find that the large band gap is caused by a cooperative effect of electron correlation and spin-orbit coupling. Both first-principle calculations and the effective Hamiltonian analysis confirm that 2D V2O3 has a non-zero Chern number (i.e., one). Our work paves a new direction towards realizing the QAH effect at room temperature., Comment: Phys. Rev. B in press

Recent experiments reveal that the honeycomb ruthenium trichloride {\alpha}-RuCl3 is a prime candidate of the Kitaev quantum spin liquid (QSL). However, there is no theoretical model which can properly describe its experimental dynamical response, due to the lack of a full understanding of its magnetic interactions. Here, we propose a general scheme to calculate the magnetic interactions in systems (e.g., {\alpha}-RuCl3) with non-negligible orbital moments by constraining the directions of orbital moments. With this scheme, we put forward a minimal J1-K1-{\Gamma}1-J3-K3 model for {\alpha}-RuCl3 and find that: (I) The third nearest neighbor (NN) antiferromagnetic Heisenberg interaction J3 stabilizes the zigzag antiferromagnetic order; (II) The NN symmetric off-diagonal exchange {\Gamma}1 plays a pivotal role in determining the preferred direction of magnetic moments and generating the spin wave gap. Exact diagonalization study on this model shows that the Kitaev QSL can be realized by suppressing the NN symmetric off-diagonal exchange {\Gamma}1 and the third NN Heisenberg interaction J3. Thus, we not only propose a powerful general scheme for investigating the intriguing magnetism of Jeff=1/2 magnets, but also point out future directions for realizing the Kitaev QSL in the honeycomb ruthenium trichloride {\alpha}-RuCl3., Comment: 16 Pages, 4 Figures, 1 Table