The superconducting transition temperature $T_c$ of the two-dimensional attractive Hubbard model is computed in the vicinity of both ordinary (logarithmic) and higher-order (power-law) Van Hove singularities using determinant quantum Monte Carlo simulations. For interaction strengths $|U| \lesssim W/3$, where $W$ is the electronic bandwidth, $T_c$ is enhanced in the neighborhood of the Van Hove point, albeit more weakly than expected from weak-coupling BCS theory. Enhancing the Van Hove singularity from logarithmic to power-law yields only a minor additional enhancement of $T_c$. For $|U| \gtrsim W/3$, the maximum $T_c$ shifts away from the Van Hove point and instead occurs at a density unrelated to any features in the non-interacting density of states, consistent with a strong-coupling interpretation. We find that the maximal $T_c$ in the model is achieved at intermediate $U$ and at a density away from the Van Hove point.
Higher-order Van Hove singularities in strongly correlated electron systems provide a fertile ground for emergent electronic orders and superconductivity. This study investigates the interplay between magnetic fluctuations and superconducting pairing near higher-order Van Hove singularities on the honeycomb lattice, a paradigmatic platform relevant to graphene. By incorporating third-nearest-neighbor hopping \(t''\), we uncover a universal crossover: ferromagnetic fluctuations dominate below the higher-order Van Hove filling, while antiferromagnetic fluctuations take over toward half filling. A key finding is that the already dominant \(f_n\)-wave pairing is enhanced in the critical region of this magnetic crossover by the higher-order Van Hove. This enhancement is driven by the synergistic effect of the higher-order Van Hove singularities-induced divergent density of states and the competing magnetic fluctuations. Although increased hopping parameters generally suppress superconducting correlation, we identify a critical \(t''\) that anomalously enhances pairing via the higher-order Van Hove renormalization. Furthermore, the nearest-neighbor Coulomb interaction suppresses the pair
The kagome-lattice Hubbard model attracts widespread interest due to its flat-band and Van Hove singularity features, which can give rise to unconventional magnetism. We employ determinant quantum Monte Carlo simulations to systematically investigate the uniform magnetic susceptibility across a range of on-site interactions and electron fillings on a two-dimensional kagome lattice. Beyond the Van Hove singularity, dominant ferromagnetic fluctuations emerge. Magnetic susceptibility grows markedly with increasing interaction strength and decreasing temperature, indicating that the Van Hove singularity acts as a critical point for the crossover of dominant magnetic fluctuations. Finite-size analysis further suggests the potential stabilization of a finite-temperature ferromagnetic phase. We also examine the sign problem to identify numerically reliable parameter regimes. These results provide valuable insights into controlling magnetic fluctuations in kagome systems and establish a computational framework for exploring flat-band physics in regimes characterized by novel quantum phases and competing orders.
Realizing two-dimensional (2D) altermagnets is important for spintronics applications. Here we propose a microscopic template for stabilizing 2D altermagnetism through Van Hove singularities that are coincident in both energy and momentum. These coincident Van Hove singularities are a generic consequence of non-symmorphic symmetries in nine 2D space groups. Due to nontrivial symmetry properties of the Hamiltonian, these coincident Van Hove singularities allow new hopping interactions between the Van Hove singularities that do not appear in analogous Van Hove singularity based patch models for cuprates and graphene. We show these new interactions can give rise to various weak coupling, and BCS-based instabilities, including altermagnetism, nematicity, inter-band d-wave superconductivity, and orbital altermagnetic order. We apply our results to quasi-2D organic $κ$-Cl in which altermagnetism is known to appear.
In two-dimensional electronic lattices, changes in the topology of the Fermi surface (Lifshitz transitions) lead to Van Hove singularities characterized by a divergence in the electronic density of states. Van Hove singularities can enhance the effect of electronic interactions, providing a platform to explore novel correlated electronic states. In this work, we investigate the emergence of topological Chern bands on the surface of three-dimensional topological insulators, which host higher-order Van Hove singularities that are characterized by the power-law diverging density of states. These singularities can arise from the interplay between a time-reversal breaking Zeeman field induced by proximity to a ferromagnetic insulator and a time-reversal invariant moiré potential on the surface electrons, created by quintuple layer misalignment in a family of topological insulators such as Bi$_2$Se$_3$ and Bi$_2$Te$_3$, which host a single surface Dirac fermion. We establish the onset of Chern bands near charge neutrality with Chern numbers $C = \pm 1$ that also possess a manifold of higher-order Van Hove singularities on the moiré Brillouin zone valleys controlled by the Zeeman and moir
Twisted bilayers of transition metal dichalcogenide semiconductors have enabled the discovery of superconductivity, ferromagnetism, correlated insulators and a series of new topological phases of matter. However, the connection between these electronic phases and the underlying band structure singularities in these materials has remained largely unexplored. Here, combining the magnetic circular dichroism and electronic compressibility measurements, we investigate the influence of a van Hove singularity on the correlated phases in bilayer WSe2 with twist angle between 2-3 degrees. We demonstrate stabilizing the Stoner ferromagnetism below moiré lattice filling one and Chern insulators at filling one by tuning the van Hove singularity cross the Fermi level using the electric and magnetic fields. The experimental observations are supported by the continuum model band structure calculations. Our results highlight the prospect of engineering the electronic phases by tunable van Hove singularities.
We theoretically study the two-dimensional metal that is coupled to critical magnons and features van Hove singularities on the Fermi surface. When there is only translationally invariant SYK-liked Yukawa interaction, van Hove points suppress the contribution from the part of the Fermi surface away from them, dominating and exhibiting non-Fermi-liquid behavior. When introducing disordered Yukawa coupling, it leads to a crossover from non-Fermi-liquid to marginal-Fermi-liquid, and the marginal-Fermi-liquid region exhibits the $T\ln (1/T)$ specific heat and temperature-linear resistivity of strange metal. By solving the gap equation, we provide the critical temperature for superconductor induced by van Hove singularities and point out the possible emergence of pair-density-wave superconductor. Our theory may become a new mechanism for understanding non-Fermi-liquid or marginal-Fermi-liquid phenomenons.
Kagome metals with van Hove singularities near the Fermi level can host intriguing quantum phenomena such as chiral loop currents, electronic nematicity, and unconventional superconductivity. However, to our best knowledge, unconventional magnetic states driven by van Hove singularities--like spin-density waves--have not been observed experimentally in kagome metals. Here, we report the magnetic and electronic structure of the layered kagome metal CeTi3Bi4, where Ti kagome electronic structure interacts with a magnetic sublattice of Ce3+ Jeff = 1/2 moments. Neutron diffraction reveals an incommensurate spin-density wave ground state of the Ce3+ moments, coexisting with commensurate antiferromagnetic order across most of the temperature-field phase diagram. The commensurate component is preferentially suppressed by thermal fluctuations and magnetic field, yielding a rich phase diagram involving an intermediate single-Q spin-density wave phase. First-principles calculations and angle-resolved photoemission spectroscopy identify van Hove singularities near the Fermi level, with the observed magnetic propagation vectors connecting their high density of states, strongly suggesting a van
The flattening of single-particle band structures plays an important role in the quest for novel quantum states of matter due to the crucial role of interactions. Recent advances in theory and experiment made it possible to construct and tune systems with nearly flat bands, ranging from graphene multilayers and moire' materials to kagome' metals and ruthenates. While theoretical models predict exactly flat bands under certain ideal conditions, evidence was provided that these systems host high-order Van Hove points, i.e., points of high local band flatness and power-law divergence in energy of the density of states. In this review, we examine recent developments in engineering and realising such weakly dispersive bands. We focus on high-order Van Hove singularities and explore their connection to exactly flat bands. We provide classification schemes and discuss interaction effects. We also review experimental evidence for high-order Van Hove singularities and point out future research directions.
We show that an interacting electronic system with a single ordinary or extended Van Hove point, which crosses the Fermi energy, is unstable against triplet superconductivity. The pairing mechanism is unconventional. There is no Cooper instability. Instead, pairing is due to the divergence of the density of states at a Van Hove point, leading to a superconducting quantum critical point at a finite detuning from the Van Hove point. The transition temperature is universally determined by the exponent governing the divergence of the density of states. Enhancing this exponent drastically increases $T_c$. The Cooper pair wave function has a non-monotonic momentum dependence with a steep slope near the gap nodes. In the absence of spin-orbit coupling, pairing fluctuations suppress a $2e$ spin-triplet state, but allow pairs of triplets to condense into a charge-$4e$ singlet state at a temperature of similar order as our result.
The probability distribution of a measure of non-stabilizerness, also known as magic, is investigated for Haar-random pure quantum states. Focusing on the stabilizer Rényi entropies, the associated probability density functions (PDFs) are found to display distinct non-analytic features analogous to Van Hove singularities in condensed matter systems. For a single qubit, the stabilizer purity exhibits a logarithmic divergence at a critical value corresponding to a saddle point on the Bloch sphere. This divergence occurs at the $|H\rangle$-magic states, which hence can be identified as states for which the density of non-stabilizerness in the Hilbert space is infinite. An exact expression for the PDF is derived for the case $α= 2$, with analytical predictions confirmed by numerical simulations. The logarithmic divergence disappears for dimensions $d \ge 3$, in agreement with the behavior of ordinary Van Hove singularities on flat manifolds. In addition, it is shown that, for one qubit, the linear stabilizer entropy is directly related to the partial incompatibility of quantum measurements, one of the defining properties of quantum mechanics, at the basis of Stern-Gerlach experiments.
In this paper we study the semiclassical limit $\hslash\to 0$ of a completely solvable model in quantum field theory: the van Hove model, describing a scalar field created and annihilated by an immovable source. Despite its simplicity, the van Hove model possesses many characterizing features of quantum fields, especially in the infrared region. In particular, the existence of non-Fock ground and equilibrium states in the presence of infrared singular sources makes a representation-independent algebraic approach of utmost importance. We make use of recent representation-independent techniques of infinite dimensional semiclassical analysis to establish the Bohr correspondence principle for the dynamics, equilibrium states, and long-time asymptotics in the van Hove model.
The appearance of van Hove singularities near the Fermi level leads to prominent phenomena, including superconductivity, charge density wave, and ferromagnetism. Here a bilayer Kagome lattice with multiple van Hove singularities is designed and a novel borophene with such lattice (BK-borophene) is proposed by the first-principles calculations. BK-borophene, which is formed via three-center two-electron (3c-2e) sigma-type bonds, is predicted to be energetically, dynamically, thermodynamically, and mechanically stable. The electronic structure hosts both conventional and high-order van Hove singularities in one band. The conventional van Hove singularity resulting from the horse saddle is 0.065 eV lower than the Fermi level, while the high-order one resulting from the monkey saddle is 0.385 eV below the Fermi level. Both the singularities lead to the divergence of electronic density of states. Besides, the high-order singularity is just intersected to a Dirac-like cone, where the Fermi velocity can reach 1340000 m/s. The interaction between the two Kagome lattices is critical for the appearance of high-order van Hove singularities. The novel bilayer Kagome borophene with rich and int
Motivated by the growing interest in band structures featuring higher-order Van Hove singularities (HOVHS), we investigate a spinless fermion kagome system characterized by nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping amplitudes. While NN hopping preserves time-reversal symmetry, NNN hopping, akin to chiral hopping on the Haldane lattice, breaks time-reversal symmetry and leads to the formation of topological bands with Chern numbers ranging from $C = \pm 1$ to $ \pm 4$. We perform analytical and numerical analysis of the energy bands near the high-symmetry points $\boldsymbolΓ$, $\pm \boldsymbol{K}$, and $\boldsymbol{M_i}$ ($i=1,2,$ and $3$), which uncover a rich and complex landscape of HOVHS, controlled by the magnitude and phase of the NNN hopping. We observe power-law divergences in the density of states (DOS), $ρ(ε) \sim |ε|^{-ν}$, with exponents $ν= 1/2, 1/3, 1/4$, which can significantly affect the anomalous Hall response at low temperatures when the Fermi level crosses the HOVHS. Additionally, the NNN hopping induces the formation of higher Chern number bands $C = \pm 2, \pm 4$ in the middle of the spectrum obeying a sublattice interference whereupon elect
We study the damping process of electron cyclotron motion and the resulting emission in a waveguide using the classical Friedrichs model without relying on perturbation analysis such as Fermi's golden rule. A classical Van Hove singularity appears at the lower bound (or cut-off frequency) of the dispersion associated with each of the electromagnetic field modes in the waveguide. In the vicinity of the Van Hove singularity, we found that not only is the decay process associated with the resonance pole enhanced (amplification factor ~ $10^4$) but the branch-point effect is also comparably enhanced. As a result, the timescale on which most of the decay occurs is dramatically shortened. Further, this suggests that the non-Markovian branch point effect should be experimentally observable in the vicinity of the Van Hove singularity. Our treatment yields a physically-acceptable solution without the problematic runaway solution that is well known to appear in the traditional treatment of classical radiation damping based on the Abraham-Lorentz equation.
Topological transitions in electronic band structures, resulting in van Hove singularities in the density of states, can considerably affect various types of orderings in quantum materials. Regular topological transitions (of neck formation or collapse) lead to a logarithmic divergence of the electronic density of states (DOS) as a function of energy in two-dimensions. In addition to the regular van Hove singularities, there are higher order van Hove singularities (HOVHS) with a power-law divergences in DOS. By employing renormalization group (RG) techniques, we study the fate of a spin-density wave phase formed by nested parts of the Fermi surface, when a HOVHS appears in parallel. We find that the phase formation can be boosted by the presence of the singularity, with the critical temperature increasing by orders of magnitude. We discuss possible applications of our findings to a range of quantum materials such as Sr$_3$Ru$_2$O$_7$, Sr$_2$RuO$_4$ and transition metal dichalcogenides.
We study a ferromagnetic tendency in the two-dimensional Hubbard model near van Hove filling by using a functional renormalization-group method. We compute temperature dependences of magnetic susceptibilities including incommensurate magnetism. The ferromagnetic tendency is found to occur in a dome-shaped region around van Hove filling with an asymmetric property: incommensurate magnetism is favored near the edge of the dome above van Hove filling whereas a first-order-like transition to the ferromagnetic ground state is expected below van Hove filling. The dome-shaped phase diagram is well captured in the Stoner theory by invoking a smaller Coulomb interaction. Triplet p-wave superconductivity tends to develop at low temperatures inside the dome and extends more than the ferromagnetic region above van Hove filling.
Motivated by the pseudogap state of the cuprates, we introduce the concept of an "exceptional" van Hove singularity that appears when strong electron-electron interaction splits an otherwise simply connected Fermi surface into multiply connected pieces. The singularity describes the touching of two pieces of the split Fermi surface. We show that this singularity is proximate to a second order van Hove singularity, which can be accessed by tuning a dispersion parameter. We argue that, in a wide class of cuprates, the end-point of the pseudogap is accessed only by triggering the exceptional van Hove singularity. The resulting Lifshitz transition is characterized by enhanced specific heat and nematic susceptibility, as seen in experiments.
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 that such points are present in intercalated graphene and other materials. We use an effective low-energy model for electrons near higher-order Van Hove points and analyze the competition between different ordering tendencies using an unbiased renormalization group approach. For purely repulsive interactions, we find that two key competitors are ferromagnetism and chiral superconductivity. For a small attractive exchange interaction, we find a new type of spin Pomeranchuk order, in which the spin order parameter winds around the Fermi surface. The supermetal state, predicted for a single higher
We report on the interplay between a van Hove singularity and a charge density wave state in 2H-TaSe$_{2}$. We use angle-resolved photoemission spectroscopy to investigate changes in the Fermi surface of this material under surface doping with potassium. At high doping, we observe modifications which imply the disappearance of the $(3\times 3)$ charge density wave and formation of a different correlated state. Using a tight-binding-based approach as well as an effective model, we explain our observations as a consequence of coupling between the single-particle Lifshitz transition during which the Fermi level passes a van Hove singularity and the charge density order. In this scenario, the high electronic density of states associated with the van Hove singularity induces a change in the periodicity of the charge density wave from the known $(3\times 3)$ to a new $(2\times 2)$ superlattice.