Abstract Charge density wave (CDW) orders in vanadium-based kagome metals have recently received tremendous attention, yet their origin remains a topic of debate. The discovery of ScV6Sn6, a bilayer kagome metal featuring an intriguing $$\sqrt{3}\times\sqrt{3}\times3$$ 3 × 3 × 3 CDW order, offers a novel platform to explore the underlying mechanism behind the unconventional CDW. Here, we combine high-resolution angle-resolved photoemission spectroscopy, Raman scattering and density functional theory to investigate the electronic structure and phonon modes of ScV6Sn6. We identify topologically nontrivial surface states and multiple van Hove singularities (VHSs) in the vicinity of the Fermi level, with one VHS aligning with the in-plane component of the CDW vector near the $$\bar{K}$$ K ¯ point. Additionally, Raman measurements indicate a strong electron-phonon coupling, as evidenced by a two-phonon mode and new emergent modes. Our findings highlight the fundamental role of lattice degrees of freedom in promoting the CDW in ScV6Sn6.

Based on first-principles calculations, we investigate the electronic band structures and topological properties of heterostructure BiTeCl/HfTe2 under c-direction strain. In the primitive structure, this material undergoes a phase transition from an insulator with a narrow indirect gap to a metal by strong spin-orbital coupling. When strain effect is considered, band inversion at time-reversal invariant point Z is responsible for the topological phase transition. These nontrivial topologies are caused by two different types of band crossings. The observable topological surface states in (110) surface also support that this material experiences topological phase transition twice. The layered heterostructure with van der Waals force provides us with a new desirable platform upon which to control topological phase transition and construct topological superconductors.

Based on the first-principles calculation, we have studied the electronic band structures and topological properties of CoSb2-type binary monoclinic compound RhSb2 and superconductor RhBi2. By substituting congeners Bi for chemical element Sb, the compounds exhibit the transition from trivial semiconductor to nontrivial metal in the normal state. The three-dimensional strong topological insulator phase exists in the superconductor RhBi2 and the corresponding topological surface states on the (100) surface near Fermi level. By adding different compressed strains, topological phase transition and superconductivity can also be achieved in the compound RhSb2. The natural combination of nontrivial topology and superconductivity in monoclinic superconductors RhX2 (X=Sb,Bi) provides us a new promising platform to study topological superconductivity.

By using the first-principles electronic structure calculation, we have studied electronic band structures and topological properties of CsCl type binary superconductors RuTi and OsTi. Due to the protection of higher crystal symmetry, there are three-dimensional nodal rings around high symmetry points X, Y and Z without spin-orbital coupling (SOC). When SOC is considered, we find the topological phase transition from strong topological insulator phase in RuTi to Dirac semimetal in OsTi. The corresponding surface states are consistent with these nontrivial topologies. We also find strong topological insulator phases near Fermi level in isostructure material MgRh. Based on the topological surface states, the interface of heterostructure of superconductor RuTi (OsTi) and doped topological material MgRh could realize observable topological superconductivity. The nontrivial topological properties in binary superconductors RuTi and OsTi provide us new desirable avenues to study Majorana bound states in vortex cores of topological superconductor.

The recently discovered cuprate superconductor ${\mathrm{Ba}}_{2}\mathrm{Cu}{\mathrm{O}}_{3+\ensuremath{\delta}}$ exhibits a high ${T}_{c}\ensuremath{\simeq}73\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ at $\ensuremath{\delta}\ensuremath{\simeq}0.2$. The polycrystal grown under high pressure has a structure similar to ${\mathrm{La}}_{2}\mathrm{Cu}{\mathrm{O}}_{4}$ but with dramatically different lattice parameters due to the $\mathrm{Cu}{\mathrm{O}}_{6}$ octahedron compression. The crystal field in the compressed ${\mathrm{Ba}}_{2}\mathrm{Cu}{\mathrm{O}}_{4}$ leads to an inverted Cu $3d\phantom{\rule{4pt}{0ex}}{e}_{g}$ complex with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbital sitting below the ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ and an electronic structure highly unusual compared to the conventional cuprates. We construct a two-orbital Hubbard model for the Cu ${d}^{9}$ state at hole doping $x=2\ensuremath{\delta}$ and study the orbital-dependent strong correlation and superconductivity. For the undoped case at $x=0$, we found that strong correlation drives an orbital-polarized Mott-insulating state with the spin-$1/2$ moment of the localized ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbital. In contrast to the single-band cuprates where superconductivity is suppressed in the overdoped regime, hole doping the two-orbital Mott insulator leads to orbital-dependent correlations and the robust spin and orbital exchange interactions produce a high-${T}_{c}$ antiphase $d$-wave superconductor even in the heavily doped regime at $x=0.4$. We conjecture that ${\mathrm{Ba}}_{2}\mathrm{Cu}{\mathrm{O}}_{3+\ensuremath{\delta}}$ realizes mixtures of such heavily hole-doped superconducting ${\mathrm{Ba}}_{2}\mathrm{Cu}{\mathrm{O}}_{4}$ and disordered ${\mathrm{Ba}}_{2}\mathrm{Cu}{\mathrm{O}}_{3}$ chains in a single-layer or predominately separated bilayer structure. Our findings suggest that unconventional cuprates with liberated orbitals as doped two-band Mott insulators can be a direction for realizing high-${T}_{c}$ superconductivity with enhanced transition temperature ${T}_{c}$.

Based on the random phase approximation calculation in two-orbital honeycomb lattice model, we investigate the pairing symmetry of Ni-based transition-metal trichalcogenides by electron doping access to type-II van Hove singularities (vHs). We find that chiral even-parity d + id-wave (Eg) state is suppressed by odd-parity p + ip-wave (Eu) state when electron doping approaches the type-II vHs. The type-II vHs peak in density of states (DOS) enables to strengthen the ferromagnetic fluctuation, which is responsible for triplet pairing. The competition between antiferromagnetic and ferromagnetic fluctuation results in pairing phase transition from singlet to triplet pairing. The Ni-based transition-metal trichalcogenides provide a promising platform to unconventional superconductor emerging from electronic DOS.

The prediction of topological states in rare-earth monopnictide compounds has attracted renewed interest. Extreme magnetoresistance (XMR) has also been observed in several nonmagnetic rare-earth monopnictide compounds. The origin of XMR in these compounds could be attributed to several mechanisms, such as topologically nontrivial electronic structures and electron-hole carrier balance. YBi is a typical rare-earth monopnictide exhibiting XMR and is expected to have a nontrivial electronic structure. In this work, we perform a direct investigation of the electronic structure of YBi by combining angle-resolved photoemission spectroscopy and theoretical calculations. Our results show that YBi is topologically trivial without the expected band inversion, and they rule out the topological effect as the cause of XMR in YBi. Furthermore, we directly observed nearly perfect electron-hole compensation in the electronic structure of YBi, which could be the primary mechanism accounting for the XMR.

Nontrivial topology and unconventional pairing are two central guiding principles in the contemporary search for and analysis of superconducting materials and heterostructure compounds. Previously, a topological superconductor has been predominantly conceived to result from a topologically nontrivial band subject to an intrinsic or external superconducting proximity effect. Here, we propose a new class of topological superconductors that are uniquely induced by unconventional pairing. They exhibit a boundary-obstructed higher-order topological character and, depending on their dimensionality, feature unprecedently robust Majorana bound states or hinge modes protected by chiral symmetry. We predict the 112 family of iron pnictides, such as Ca(1-)xLa(x)FeAs(2), to be highly suited material candidates for our proposal, which can be tested by edge spectroscopy. Because of the boundary obstruction, the topologically nontrivial feature of the 112 pnictides does not reveal itself for a bulk-only torus band analysis without boundaries, and as such, it had evaded previous investigations. Our proposal not only opens a new arena for highly stable Majorana modes in high-temperature superconductors but also provides the smoking gun for extended s-wave order in the iron pnictides.

We predict that the non-centrosymmetric materials Zn3In2Se6 and In2Se3 are the symmetry protected topological critical triple point metals based on first principles calculation. The dispersion along the Γ-Z line almost vanishes because of the particular crystal structure, and the strain along the c direction maybe drives accidental Dirac point to triple point. An effective theory is developed to describe accidental Dirac points and triple points, by which we calculate the surface states. These materials provide us a new platform to discuss the relation between the triple points and Dirac points.

We study the recently discovered $73$K high-$T_c$ superconductor Ba$_2$CuO$_{3+\delta}$ at $\delta\simeq0.2$ grown under high pressure. Neutron experiments find that the polycrystal exhibits a structure similar to La$_2$CuO$_4$, but with dramatically different lattice parameters due to the CuO$_6$ octahedron compression. The resulting crystal field leads to an inverted Cu $3d$ $e_g$ complex with the $d_{x^2-y^2}$ orbital sitting below the $d_{3z^2-r^2}$ orbital and an electronic structure highly unusual compared to the conventional cuprates. We conjecture that the material realizes a new path of in-plane positional oxygen doping, where the doped oxygens create matrices of compressed Ba$_2$CuO$_4$ embedded in Ba$_2$CuO$_{3}$. Constructing a strongly correlated two-orbital model at hole doping $x=2\delta$ of the Cu $d^9$ state, we show that the spin-orbital exchange interactions lead to a multiband antiphase $d$-wave superconducting state, i.e. a nodal $d_\pm$ pairing state. These findings suggest that the class of unconventional cuprates with liberated orbitals as doped two-band Mott insulators can be a direction for realizing high-T$_c$ superconductivity with enhanced transition temperature $T_c$.

Based on a two-orbital honeycomb lattice model and random phase approximation, we investigate the pairing symmetry of the Ni-based transition-metal trichalcogenide. We find that an I-wave (A2g) state and a chiral d-wave state are dominant and nearly degenerate for typical electron and hole dopings. These two states carry nontrivial topological properties, which are manifested by the presence of chiral edge states in the d+id-wave state and dispersionless Andreev bound state at zero energy in the I-wave state. Ni-based transition-metal trichalcogenides provide us a new platform to study the exotic phenomena emerged from electron-electron correlation effects.

We investigate the electronic physics of layered Ni-based trichalcogenide NiPX3 (X = S, Se), a member of transition metal trichalcogenides (TMTs) with the chemical formula ABX(3). These Ni-based TMTs distinguish themselves from other TMTs as their low energy electronic physics can be effectively described by the two e(g) d orbitals. The major band kinematics is characterized by the unusual long-range effective hopping between two third nearest-neighbor (TNN) Ni sites in the two-dimensional Ni honeycomb lattice so that the Ni lattice can be equivalently viewed as four weakly coupled honeycomb sublattices. Within each sublattice, the electronic physics is described by a strongly correlated two-orbital graphene-type model that results in an antiferromagnetic (AFM) ground state near half-filling. We show that the low energy physics in a paramagnetic state is determined by the eight Dirac cones which locate at K, K', K/2, and K'/2 points in the first Brillouin zone with a strong AFM fluctuation between two K (K') and K'/2 (K/2) Dirac cones and carrier doping can sufficiently suppress the long-range AFM order and allow other competing orders, such as superconductivity, to emerge. The material can be an ideal system to study many exotic phenomena emerged from strong electron-electron correlation, including a potential d +/- id superconducting state at high temperature.

By using the method of Dyson–Maleev mean-field theory, we study the effect of bond alternation and longitudinal magnetic field in the model of ferrimagnetic spin chain. Based on the numerical results of self-consistent equations, properties of the excited spectrums, magnon internal energy, static susceptibility, magnetization plateau and specific heat are obtained with different bond alternation parameters δ and external magnetic field B. This method provides qualitative consistent results to describe the phase from ferrimagnetic state to bond altered state.

We use the mean-field approximation of Dyson–Maleev representation to study an XXZ Heisenberg ferrimagnetic spin chain with single-ion anisotropy. By solving the self-consistent equations with different anisotropies, λ and D respectively,the energy spectrums, internal energy, static susceptibility and specific heat are calculated. Especially, the quantum phase transition of the magnetization plateau induced by single-ion anisotropy D is obtained in the model of the ferrimagnetic spin chain by using Dyson–Maleev mean-field theory.

Anomalous surface states with Fermi arcs are commonly considered to be a fingerprint of Dirac semimetals (DSMs). In contrast to Weyl semimetals, however, Fermi arcs of DSMs are not topologically protected. Using first-principles calculations, we predict that β-cuprous iodide (β-CuI) is a peculiar DSM whose surface states form closed Fermi pockets instead of Fermi arcs. In such a fermiological Dirac semimetal, the deformation mechanism from Fermi arcs to Fermi pockets stems from a large cubic term preserving all crystal symmetries and from the small energy difference between the surface and bulk Dirac points. The cubic term in β-CuI, usually negligible in prototypical DSMs, becomes relevant because of the particular crystal structure. As such, we establish a concrete material example manifesting the lack of topological protection for surface Fermi arcs in DSMs.

Anomalous surface states with Fermi arcs are commonly considered to be a fingerprint of Dirac semimetals (DSMs). In contrast to Weyl semimetals, however, Fermi arcs of DSMs are not topologically protected. Using first-principles calculations, we predict that β-cuprous iodide (β-CuI) is a peculiar DSM whose surface states form closed Fermi pockets instead of Fermi arcs. In such a fermiological Dirac semimetal, the deformation mechanism from Fermi arcs to Fermi pockets stems from a large cubic term preserving all crystal symmetries and from the small energy difference between the surface and bulk Dirac points. The cubic term in β-CuI, usually negligible in prototypical DSMs, becomes relevant because of the particular crystal structure. As such, we establish a concrete material example manifesting the lack of topological protection for surface Fermi arcs in DSMs.

We investigate superconductivity that may exist in the doped BaCoSO, a multi-orbital Mott insulator with a strong antiferromagnetic ground state. The superconductivity is studied in both t-J type and Hubbard type multi-orbital models by mean field approach and random phase approximation (RPA) analysis. Even if there is no C 4 rotational symmetry, it is found that the system still carries a d-wave like pairing symmetry state with gapless nodes and sign changed superconducting order parameters on Fermi surfaces. The results are largely doping insensitive. In this superconducting state, the three t_2_g orbitals have very different superconducting form factors in momentum space. In particular, the intra-orbital pairing of the d_x^2 - y^2 orbital has an s-wave like pairing form factor. The two methods also predict very different pairing strength on different parts of Fermi surfaces. These results suggest that BaCoSO and related materials can be a new ground to test and establish fundamental principles for unconventional high temperature superconductivity.

Based on the method of Dyson–Maleev mean-field theory, we study the Heisenberg ferrimagnetic spin chain at zero temperature. The energy spectrum exhibits the coexistence of a nearly gapless branch and a gapful branch. Compared with numerical results of other methods, the energy gap, Δh=1.32, of Dyson–Maleev mean-field theory is reasonable and only a little bit lower. At finite temperature, the properties of energy gap, magnetization, uniform susceptibility, internal energy, specific heat are calculated respectively. The trends of these thermodynamic properties in this method are consistent with the existed results of other methods.