The properties of correlated electron materials are often intricately linked to Van Hove singularities (VHS) in the vicinity of the Fermi energy. The class of these VHS is of great importance, with higher-order ones -- with power-law divergence in the density of states -- leaving frequently distinct signatures in physical properties. We use a new theoretical method to detect and analyse higher-order VHS (HOVHS) in two-dimensional materials and apply it to the electronic structure of the surface layer of Sr$_2$RuO$_4$. We then constrain a low energy model of the VHS of the surface layer of Sr$_2$RuO$_4$ against angle-resolved photoemission spectroscopy and quasiparticle interference data to analyse the VHS near the Fermi level. We show how these VHS can be engineered into HOVHS.
Van Hove singularity are electronic instabilities that lead to many fascinating interactions, such as superconductivity and charge-density waves. And despite much interest, the nexus of emergent correlation effects from van Hove singularities and topological states of matter remains little explored in experiments. By utilizing synchrotron-based angle-resolved photoemission spectroscopy and Density Functional Theory, here we provide the first discovery of the helicoid quantum nature of topological Fermi arcs inducing van Hove singularities. In particular, in topological chiral conductors RhSi a…
We present a practical method to detect, diagnose and engineer higher order Van Hove singularities in multiband systems, with no restrictions on the number of bands and hopping terms. The method allows us to directly compute the Taylor expansion of the dispersion of any band at arbitrary points in momentum space, using a generalised extension of the Feynman Hellmann theorem, which we state and prove. Being fairly general in scope, it also allows us to incorporate and analyse the effect of tuning parameters on the low energy dispersions, which can greatly aid the engineering of higher order Van…
We discuss the evolution of high-order Van Hove singularities (hoVHSs) that carry faster-than logarithmic divergences over a wide range of parameters in cuprate-like electronic band dispersions. Numerical analysis gives insight into the quantization of the VHS power-law-exponent pV and into transitions between hoVHSs with different values of pV. The cuprates are found to lie in the parameter regime where the amplitude of the hoVHS is not too large. Our study indicates that the occurrence of high-temperature superconductivity requires simultaneous tuning of two different competing orders (antif…
Magnetic correlations and superconducting pairing near higher-order Van Hove singularities
School of Physics and Astronomy, and Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学物理与天文学院，多尺度自旋物理教育部重点实验室）
Beyond the two-dimensional (2D) saddle-point Van Hove singularities (VHSs) with logarithmic divergences in the density of states (DOS), recent studies have identified higher-order VHSs with faster-than-logarithmic divergences that can amplify electron correlation effects. Here we show that the cuprate high-Tc superconductors harbor high-order VHSs in their electronic spectra and unveil a new correlation that the cuprates with high-order VHSs display higher Tc. Our analysis indicates that the normal and higher-order VHSs can provide a straightforward new marker for identifying propensity of a m…
Square-octagon lattice underlies the description of a family of two-dimensional materials such as tetragraphene. In the present paper we show that the tight-binding model of square-octagon lattice contains both conventional and high-order van Hove points. In particular, the spectrum of the model contains flat lines along some directions composed of high-order saddle points. Their role is analyzed by calculating orbital susceptibility of electrons. We find that the presence of van Hove singularities of different kinds in the density of states leads to strong responses: paramagnetic for ordinary…
The unconventional temperature variation of the Knight shift (static spin susceptibility) that has been observed in Fe-based superconductors AFe$_2$As$_2$ (A = K, Rb, Cs) is explained in terms of proximity to a van Hove singularity. Using the Hubbard model we show that when the Fermi energy is in the vicinity of a van Hove singularity, a downturn in spin susceptibility occurs as the temperature is lowered. This behavior is characterized by a temperature, $T^*$, which is determined by the difference in energy between the Fermi level and the van Hove singularity. When vertex corrections are take…
We theoretically show that in the presence of conventional or higher order van Hove singularities(VHS), the bare finite momentum pairing, also known as the pair density wave (PDW), susceptibility can be promoted to the same order of the most divergent bare BCS susceptibility through a valley-contrasting flux 3$ϕ$ in each triangular plaquette at $ϕ=\fracπ{3}$ and $ϕ=\fracπ{6}$ in moiré systems. This makes the PDW order a possible leading instability for an electronic system with repulsive interactions. We confirm that it indeed wins over all other instabilities and becomes the ground state unde…
All van Hove singularities in the density of states (DOS) of face-centered cubic lattice in the nearest and next-nearest neighbour approximation, focusing on higher-order ones, are found and classified. At special values of the ratio $τ$ of nearest and next-nearest neighbour hopping integrals, $t$ and $t'$, giant DOS singularities, caused by van Hove lines or surfaces, are formed. An exact formula for DOS which provides efficient numerical implementation is proposed. The standard tetrahedron method is demonstrated to be inapplicable due to its poor convergence in the vicinity of kinks caused b…
The recently discovered layered kagome metals AV$_3$Sb$_5$ (A=K, Rb, Cs) exhibit diverse correlated phenomena, which are intertwined with a topological electronic structure with multiple van Hove singularities (VHSs) in the vicinity of the Fermi level. As the VHSs with their large density of states enhance correlation effects, it is of crucial importance to determine their nature and properties. Here, we combine polarization-dependent angle-resolved photoemission spectroscopy with density functional theory to directly reveal the sublattice properties of 3d-orbital VHSs in CsV$_3$Sb$_5$. Four V…
Recent experiments on kagome metals AV$_3$Sb$_5$ (A=K,Rb,Cs) [M. Kang et al., Nat. Phys. 18, 301-308 (2022)] identify twofold van Hove singularities (TvHS) with opposite concavity near the Fermi energy, generating two approximately hexagonal Fermi surfaces -- one electron-like and the other hole-like. Here we propose that a TvHS generates a novel time-reversal symmetry breaking excitonic order -- arising due to bound pairs of electrons and holes located at opposite concavity van Hove singularities. We introduce a minimal model for the TvHS and investigate interaction induced many-body instabil…
Transition-metal-based kagome materials at van Hove filling are a rich frontier for the investigation of novel topological electronic states and correlated phenomena. To date, in the idealized two-dimensional kagome lattice, topologically nontrivial Dirac surface states (TDSSs) have not been unambiguously observed, and the manipulation of TDSSs and van Hove singularities (VHSs) remains largely unexplored. Here, we reveal TDSSs originating from a Z${_2}$ bulk topology and identify multiple VHSs near the Fermi level ($\textit{E}$${_F}$) in magnetic kagome material GdV${_6}$Sn${_6}$. Using in-sit…
We study unconventional superconductivity induced by weak repulsive interactions in 2D electronic systems at Van Hove singularity (VHS) where density of states is logarithmically divergent. We define two types of VHS. For systems at type-I VHS, weak repulsive interactions generically induce unconventional singlet pairing. However and more interestingly, for type-II VHS renormalization group (RG) analysis shows that weak repulsive interactions favor triplet pairing (e.g. p-wave) when the Fermi surface is not sufficiently nested. For type-II VHS systems respecting tetragonal symmetry, topologica…
We study systems with energy bands in two dimensions, hosting higher order Van Hove singularities (HOVHS) in the presence of disorder, using standard diagrammatic techniques for impurity averaging. In the clean limit, such singularities cause power-law divergence in the density of states (DOS), and this is expected to strongly affect electronic correlation. In order to analyse the signatures of these singularities in disordered systems, we employ various Born approximations, culminating in the self-consistent (non) Born approximation. Although the divergence of the DOS is smeared, we find that…
The emergence of flat bands in twisted bilayer graphene leads to an enhancement of interaction effects, and thus to insulating and superconducting phases at low temperatures, even though the exact mechanism is still widely debated. The position and splitting of the flat bands is also very sensitive to the residual interactions. Moreover, the low energy bands of twisted graphene bilayers show a rich structure of singularities in the density of states, van Hove singularities, which can enhance further the role of interactions. We study the effect of the long-range interactions on the band struct…
A renormalization group treatment of the Kondo model with logarithmic Van Hove singularity in the electron density of states is performed within next-leading order scaling, different magnetic phases being considered. The effective coupling constant remains small, renormalized magnetic moment and spin-fluctuation frequency decreasing by several orders of magnitude. Thus wide non-Fermi-liquid behavior regions are found from the scaling trajectories in a broad interval of the bare coupling parameter. Applications to itinerant magnetism theory are discussed.
We investigate the electronic structure of the new family of kagome metals AV$_{3}$Sb$_{5}$ (A = K, Rb, Cs) using first-principles calculations. We analyze systematically the evolution of the van Hove singularities (vHss) across the entire family upon applied pressure and hole doping, specifically focusing on the two vHss closer to the Fermi energy. With pressure, these two saddle points shift away from the Fermi level. At the same time, the Fermi surface undergoes a large reconstruction with respect to the Sb bands while the V bands remain largely unchanged, pointing to the relevant role of t…
Van Hove points are special points in the energy dispersion, where the density of states exhibits analytic singularities. When a Van Hove point is close to the Fermi level, tendencies towards density wave orders, Pomeranchuk orders, and superconductivity can all be enhanced, often in more than one channel, leading to a competition between different orders and unconventional ground states. Here we consider the effects from higher-order Van Hove points, around which the dispersion is flatter than near a conventional Van Hove point, and the density of states has a power-law divergence. We argue t…
Densities of states for simple (sc) and base-centered (bcc) cubic lattices with account of nearest and next-nearest neighbour hopping integrals $t$ and $t'$ are investigated in detail. It is shown that at values of $τ\equiv t'/t = τ_\ast$, corresponding to the change of isoenergetic surface topology, the formation of van Hove $\bf k$ lines takes place. At small deviation from these special values, the weakly dispersive spectrum in the vicinity of van Hove lines is replaced by a weak $\bf k$-dependence in the vicinity of few van Hove points which possess huge masses proportional to $|τ- τ_\ast|…
Two-dimensional (2D) Van Hove singularities (VHSs) associated with the saddle points or extrema of the energy dispersion usually show logarithmic divergences in the density of states (DOS). However, recent studies find that the VHSs originating from higher-order saddle-points have faster-than-logarithmic divergences, which can amplify electron correlation effects and create exotic states such as supermetals in 2D materials. Here we report the existence of 'high-order' VHSs in the cuprates and related high-Tc superconductors and show that the anomalous divergences in their spectra are driven by…
In the present paper we derive the general expressions for the differential entropy per particle near van Hove singularities (vHs) in the density of states. The dependence of entropy per particle on chemical potential and temperature demonstrates different behavior depending on the type of vHs, and distinguishes high-order vHs with different divergence exponents and flat bands. In addition, it allows one to test the ``flatness" of the band in experiment. We compare the analytic predictions with the numerical calculation of the differential entropy for tight-binding models of graphene, Lieb lat…
Searching for unconventional Cooper pairing states has been at the heart of superconductivity research since the discovery of BCS superconductors. In particular, spin-triplet odd-parity pairing states were recently revisited due to the possibility of tuning towards topological superconductors. In this context, it is interesting to note a recent proposal that such a spin-triplet pairing instability occurs when the band filling is near van Hove singularities (vHS) associated with momenta away from time-reversal invariant momenta named type-II vHS. However, this result was obtained within a weak …
We present optical measurements of the transition metal dichalcogenide PdTe$_{2}$. The reflectivity displays an unusual temperature and energy dependence in the far-infrared, which we show can only be explained by a collapse of the scattering rate at low temperature, resulting from the vicinity of a van Hove singularity near the Fermi energy. An analysis of the optical conductivity suggests that below 150 K a reduction in the available phase space for scattering takes place, resulting in long-lived quasiparticle excitations. We suggest that this reduction in phase space provides experimental e…
We report an angle-resolved photoemission spectroscopy (ARPES) study of KFe$_2$As$_2$ and CsFe$_2$As$_2$, revealing the existence of a van Hove singularity affecting the electronic properties. As a result of chemical pressure, we find a stronger three-dimensionality in KFe$_2$As$_2$ than in CsFe$_2$As$_2$, notably for the 3$d_{z^2}$ states responsible for the small three-dimensional hole-like Fermi surface pocket reported by quantum oscillations. Supported by first-principles calculations, our ARPES study shows that the van Hove singularity previously reported in KFe$_2$As$_2$ moves closer to …
We theoretically investigate the development of unconventional superconductivity in the Sb(111) thin film when its Fermi level is tuned to near type-II Van Hove singularities (VHS), which locate at non-time-reversal invariant momenta. Via patch renormalization group analysis, we show that the leading instability is a chiral p + ip-wave superconducting order. The origin of such pairing relies on the hexagonal structure of the VHS and strong spin-orbit coupling, resulting in the anisotropy of the electron-electron scattering to provide an attractive channel. Our study hence suggests that superco…
Influence of Fermi Surface Geometry and Van Hove Singularities on the Optical Response of Sr$_2$RuO$_4$
Bu-Ali Sina University（布阿利·西纳大学）；University of Toronto（多伦多大学）；DelQuanTech Inc.（DelQuanTech公司）；Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京应用数学与物理研究所）
The Mott insulating phase of the parent compounds is frequently taken as starting point for the underdoped high-$T_c$ cuprate superconductors. In particular, the pseudogap state is often considered as deriving from the Mott insulator. In this work, we systematically investigate different weakly-doped Mott insulators on the square and triangular lattice to clarify the relationship between the pseudogap and Mottness. We show that doping a two-dimensional Mott insulator does not necessarily lead to a pseudogap phase. Despite its inherent strong-coupling nature, we find that the existence or absen…
We study the presence of higher-order van Hove singularities in mirror-symmetric twisted trilayer graphene. This geometry has recently emerged experimentally as a fascinating playground for studying correlated and exotic superconducting phases. We find that the trilayer hosts a zero-energy higher-order van Hove singularity with an exponent -1/3. The singularity is protected by the threefold rotation symmetry and a combined mirror-particle-hole symmetry and it can be tuned with only the twist angle and a perpendicular electric field. It arises from the combined merging of van Hove singularities…
A van der Waals coupled Weyl semimetal material NbIrTe4 is investigated by combining scanning tunneling microscopy/spectroscopy and first principles calculations. We observe a sharp peak in the tunneling conductance near the zero bias energy, and its origin is ascribed to a van Hove singularity associated with a Lifshitz transition of the topologically none trivial Fermi arc states. Furthermore, tunneling spectroscopy measurements show a surprisingly large signature of electron boson coupling, which presumably represents anomalously enhanced electron phonon coupling through the enhanced charge…
The single-layered ruthenate Sr$_2$RuO$_4$ is one of the most enigmatic unconventional superconductors. While for many years it was thought to be the best candidate for a chiral $p$-wave superconducting ground state, desirable for topological quantum computations, recent experiments suggest a singlet state, ruling out the original $p$-wave scenario. The superconductivity as well as the properties of the multi-layered compounds of the ruthenate perovskites are strongly influenced by a van Hove singularity in proximity of the Fermi energy. Tiny structural distortions move the van Hove singularit…
