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-order Van Hove point, is an unstable fixed point in our case.
The phase diagram of the two-dimensional extended one-band U-V-J Hubbard model is considered within a mean-field approximation and two- and many-patch renormalization group (RG) approaches near the van Hove band fillings. At small t' and J>0 mean-field and many-patch RG approaches give similar results for the leading spin-density-wave (SDW) instability, while the two-patch RG approach, which predicts a wide region of charge-flux (CF) phase becomes unreliable due to nesting effect. At the same time, there is a complex competition between SDW, CF phases, and d-wave superconductivity in two- and …
Phase diagrams of the two-dimensional one-band t-t' Hubbard model are obtained within the two-patch and the temperature-cutoff many-patch renormalization group approach. At small t' and at van Hove band fillings antiferromagnetism dominates, while with increasing t' or changing filling antiferromagnetism is replaced by d-wave superconductivity. Near t'=t/2 and close to van Hove band fillings the system is unstable towards ferromagnetism. Away from van Hove band fillings this ferromagnetic instability is replaced by a region with dominating triplet p-wave superconducting correlations. The resul…
The electronic orders in Hubbard models on a Kagome lattice at van Hove filling are of intense current interest and debate. We study this issue using the singular-mode functional renormalization group theory. We discover a rich variety of electronic instabilities under short range interactions. With increasing on-site repulsion $U$, the system develops successively ferromagnetism, intra unit-cell antiferromagnetism, and charge bond order. With nearest-neighbor Coulomb interaction $V$ alone (U=0), the system develops intra-unit-cell charge density wave order for small $V$, s-wave superconductiv…
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）
We use a novel temperature-flow renormalization group technique to analyze magnetic and superconducting instabilities in the two-dimensional t-t' Hubbard model for particle densities close to the van Hove filling as a function of the next-nearest neighbor hopping t'. In the one-loop flow at the van Hove filling, the characteristic temperature for the flow to strong coupling is suppressed drastically around t'_c approx. -0.33t, suggesting a quantum critical point between d-wave pairing at moderate t'>t'_c and ferromagnetism for t'<t'_c. Upon increasing the particle density in the latter regime …
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 use a diagrammatic approach to study low energy physics of a two dimensional electron system where the Fermi level is near van-Hove singularies in the energy spectrum. We find that in most regions of the $ε_F-T$ phase diagram the system behaves as a normal Fermi liquid rather than a marginal Fermi liquid. Particularly, the imaginary part of the self energy is much smaller than the excitation energy, which implies well defined quasiparticle excitations, and single particle properties are only weakly affected by the presence of the van-Hove singularities. The relevance to high temperature sup…
Recent Raman experiments [F. Venturini et al., Phys. Rev. Lett. {\bf 89}, 107003-1,(2002)] done in $Bi_2 Sr_2 Ca Cu_2 O_4$ have found that antinodal quasiparticles become insulating when the doping is varied from overdoped to optimally doped while nodal quasiparticles remain metallic. We propose a simple explanation based on the incoherence of the spectral function in the antinodal direction due to the strong scattering suffered by the quasiparticles in the proximity of the Van Hove singularity.
We devise a computational approach to the Hubbard model that captures the strong coupling dynamics arising when the Fermi level is at a Van Hove singularity in the density of states. We rely on an approximate degeneracy among the many-body states accounting for the main instabilities of the system (antiferromagnetism, d-wave superconductivity). The Fermi line turns out to be deformed in a manner consistent with the pinning of the Fermi level to the Van Hove singularity. For a doping rate $δ\sim 0.2$, the ground state is characterized by d-wave symmetry, quasiparticles gapped only at the saddle…
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…
In two dimensions the non-interacting density of states displays a Van Hove singularity (VHS) which introduces an intrinsic electron-hole asymmetry, absent in three dimensions. We show that due to this VHS the strong-coupling analysis of tunneling spectra in high-$T_c$ superconductors must be reconsidered. Based on a microscopic model which reproduces the experimental data with great accuracy, we elucidate the peculiar role played by the VHS in shaping the tunneling spectra, and show that more conventional analyses of strong-coupling effects can lead to severe errors.
We apply a wilsonian renormalization group approach to the continuum limit of the attractive $t-t'$ Hubbard model, taken when the Fermi level is at the Van Hove singularity of the density of states. The model has well-defined scaling properties and the effective couplings display an unbounded flow in the infrared. We determine the leading instabilities by computing the different response functions up to $t' = 0.5 t$. The phase diagram shows a large boundary between superconducting and charge-density-wave phases, that merge in a triple point with a phase separation instability. The latter is re…
Using the functional renormalization group, we investigate the electron instability in the single-sheet BC$_3$ when the electron filling is near a type-II van Hove singularity. For a finite Hubbard interaction, the ferromagnetic-like spin density wave order dominates in the immediate vicinity of the singularity. Elsewhere near the singularity the p-wave superconductivity prevails. We also find that a small nearest-neighbor Coulomb repulsion can enhance the superconductivity. Our results show that BC$_3$ would be a promising candidate to realize topological $p+ip'$ superconductivity, but the tr…
A mechanism of self-organized one-dimensionality in correlated electron system coupled to optical phonon mode is proposed. It is found that a lattice vibration may compactify electron motion effectively to a one-dimensional space and trigger quantum phase transition into ordered state with "extended van Hove singularities" in the electronic Floquet modes spectrum. This mechanism may be of relevance for observed enhancement of the ordering instability in the anti-nodal regions of the Fermi surface in the high-Tc cuprates, which is accompanied by anomalous softening of some optical phonon modes.…
We propose a new parametrization of the four-point vertex function in the one-loop one-particle irreducible renormalization group (RG) scheme for fermions. It is based on a decomposition of the effective two-fermion interaction into fermion bilinears that interact via exchange bosons. The numerical computation of the RG flow of the boson propagators reproduces the leading weak coupling instabilities of the two-dimensional Hubbard model at Van Hove filling, as they were previously obtained by a temperature RG flow. Instead of regularizing with temperature, we here use a soft frequency $Ω$-regul…
We present a stability analysis of the two-dimensional t-t' Hubbard model for various values of the next-nearest-neighbor hopping t', and electron concentrations close to the Van Hove filling by means of the flow equation method. For t' > -t/3 a d_{x^2-y^2}-wave Pomeranchuk instability dominates (apart from antiferromagnetism at small t'). At t' < -t/3 the leading instabilities are a g-wave Pomeranchuk instability and p-wave particle-hole instability in the triplet channel at temperatures T < 0.15t, and an s^*-magnetic phase for T > 0.15t; upon increasing the electron concentration the triplet…
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…
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 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…
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 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 ca…
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 introduce a new type of van Hove singularity in two dimensions, where a saddle point in momentum space is changed from second-order to high-order. Correspondingly, the density of states near such ``high-order van Hove singularity'' is significantly enhanced from logarithmic to power-law divergence, which promises stronger electron correlation effects. High-order van Hove singularity can be generally achieved by tuning the band structure with a single parameter in moiré superlattices, such as twisted bilayer graphene by tuning twist angle or applying pressure, and trilayer graphene by applyi…
The Fermi surface of most hole-doped cuprates is close to a Van Hove singularity at the M point. A two-dimensional electronic system, whose Fermi surface is close to a Van Hove singularity shows a variety of weak coupling instabilities. It is a convenient model to study the interplay between antiferromagnetism and anisotropic superconductivity. The renormalization group approach is reviewed with emphasis on the underlying physical processes. General properties of the phase diagram and possible deformations of the Fermi surface due to the Van Hove proximity are described.
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 analyze the weak-coupling instabilities that may arise when multiple high-order Van Hove points are present inside the Brillouin zone. The model we consider is inspired by twisted bilayer graphene, although the analysis should be more generally applicable. We employ a parquet renormalization group analysis to identify the leading weak-coupling instabilities, supplemented with a Ginzburg-Landau treatment to resolve any degeneracies. Hence we identify the leading instabilities that can occur from weak repulsion with the power-law divergent density of states. Five correlated phases are uncover…
We study quantum phase transitions in graphene superlattices in external magnetic fields, where a framework is presented to classify multiflavor Dirac fermion critical points describing hopping tuned topological phase transitions of integer and fractional Hofstadter-Chern insulators. We argue and provide numerical support for the existence of transitions that can be explained by a nontrivial interplay of Chern bands and van Hove singularities near charge neutrality. This work provides a route to critical phenomena beyond conventional quantum Hall plateau transitions.
A two dimensional electronic system, where the Fermi surface is close to a Van Hove singularity, shows a variety of weak coupling instabilities, and it is a convenient model to study the interplay between antiferromagnetism and anisotropic superconductivity. We present a detailed analysis of the kinematics of the electron scattering in this model. The similitudes, and differences, between a standard Renormalization Group approach and previous work based on parquet summations of log$^2$ divergences are analyzed, with emphasis on the underlying physical processes. General properties of the phase…
Sr$_2$MoO$_4$ is isostructural to the unconventional superconductor Sr$_2$RuO$_4$ but with two electrons instead of two holes in the Mo/Ru-t$_{2g}$ orbitals. Both materials are Hund's metals, but while Sr$_2$RuO$_4$ has a van Hove singularity in close proximity to the Fermi surface, the van Hove singularity of Sr$_2$MoO$_4$ is far from the Fermi surface. By using density functional plus dynamical mean-field theory we determine the relative influence of van Hove and Hund's metal physics on the correlation properties. We show that theoretically predicted signatures of Hund's metal physics occur …
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…
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…
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…
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 study the role of electron correlations in the formation of the surface charge-density-wave state in the Sn/Ge(111) interface. The Fermi energy of the overlayer is treated as a dynamical variable, which undergoes a substantial renormalization by the interaction. We show that the Fermi level turns out to be pinned to a Van Hove singularity in the density of states, which explains the formation of the charge-density-wave, the observation of a very flat band in photoemission experiments and the reduction of the spectral weight in the low-temperature phase.
The charge instabilities of electron systems in the square lattice are analyzed near the Van Hove singularity by means of a wilsonian renormalization group approach. We show that the method preserves the spin rotational invariance at all scales, allowing a rigorous determination of spin and charge instabilities of the $t-t'$ Hubbard model. For $t'$ above $\approx 0.276 t$, repulsive interactions fall into two different universality classes. One of them has nonsingular response functions in the charge sector, while the other is characterized by the splitting of the Van Hove singularity. At the …
A scaling consideration of the Kondo lattices is performed with account of logarithmic Van Hove singularities (VHS) in the electron density of states. The scaling trajectories are presented for different magnetic phases. It is demonstrated that VHS lead to a considerable increase of the non-Fermi-liquid behavior region owing to softening of magnon branches during the renormalization process. Although the effective coupling constant remains moderate, renormalized magnetic moment and spin-fluctuation frequency can decrease by several orders of magnitude. A possible application to f-systems and w…
Tuning of electronic density-of-states singularities is a common route to unconventional metal physics. Conceptually, van Hove singularities are realized only in clean two-dimensional systems. Little attention has therefore been given to the disordered (dirty) limit. Here, we provide a magnetotransport study of the dirty metamagnetic system calcium-doped strontium ruthenate. Fermi liquid properties persist across the metamagnetic transition, but with an unusually strong variation of the Kadowaki-Woods ratio. This is revealed by a strong decoupling of inelastic electron scattering and electroni…
We use the quasistatic approach to analyze the criterion of ferromagnetism for two-dimensional (2D) systems with the Fermi level near Van Hove singularities (VHS) of the electronic spectrum. It is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction I between electrons and paramagnons, which corresponds to the Hubbard on-site repulsion U, is sufficiently large. The critical interactions I_c and U_c remain finite at Van Hove filling and exceed considerably their values obtained from the Stoner criterion due to incommensurate spin fluctuations whic…
Magnetic fluctuations near the Van Hove singularity in the kagome-lattice Hubbard model at finite doping
Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University（燕山大学理学院河北省微观结构材料物理重点实验室）；School of Physics and Astronomy, and Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学物理学系与教育部多尺度自旋物理重点实验室）
The most salient features observed around a metamagnetic transition in Sr3Ru2O7 are well captured in a simple model for spontaneous Fermi surface symmetry breaking under a magnetic field, without invoking a putative quantum critical point. The Fermi surface symmetry breaking happens in both a majority and a minority spin band but with a different magnitude of the order parameter, when either band is tuned close to van Hove filling by the magnetic field. The transition is second order for high temperature T and changes into first order for low T. The first order transition is accompanied by a m…
Simple scaling consideration and NRG solution of the one- and two-channel Kondo model in the presence of a logarithmic Van Hove singularity at the Fermi level is given. The temperature dependences of local and impurity magnetic susceptibility and impurity entropy are calculated. The low-temperature behavior of the impurity susceptibility and impurity entropy turns out to be non-universal in the Kondo sense and independent of the $s-d$ coupling $J$. The resonant level model solution in the strong coupling regime confirms the NRG results. In the two-channel case the local susceptibility demonstr…
The low-energy electronic structure of the itinerant metamagnet Sr3Ru2O7 is investigated by angle resolved photoemission and density functional calculations. We find well-defined quasiparticle bands with resolution limited line widths and Fermi velocities up to an order of magnitude lower than in single layer Sr2RuO4. The complete topography, the cyclotron masses and the orbital character of the Fermi surface are determined, in agreement with bulk sensitive de Haas - van Alphen measurements. An analysis of the dxy band dispersion reveals a complex density of states including van Hove singulari…
The quasistatic approach is used to analyze the criterion of ferromagnetism for two-dimensional (2D) systems with the Fermi level near Van Hove (VH) singularities of the electron spectrum. It is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction between electrons and paramagnons, determined by the Hubbard on-site repulsion U, is sufficiently large. Due to incommensurate spin fluctuations near the ferromagnetic quantum phase transition, the critical interaction Uc remains finite at VH filling and exceeds considerably its value obtained from the …
We investigate the possibility of ferromagnetic ordering in the non-degenerate Hubbard model on the face-centered cubic lattice within the functional renormalization group technique using temperature as a scale parameter. We assume the relations between nearest, next-nearest, and next-next-nearest hopping parameters providing higher order (giant) van Hove singularity of the density of states. The ferromagnetic instability formation with lowering temperature is described consistently in the one-loop approximation for a one-particle irreducible vertex of two-particle electron interaction. The ch…
We consider the two-dimensional t-t' Hubbard model with the Fermi level being close to the van Hove singularities. The phase diagram of the model is discussed. In a broad energy region the self-energy at the singularity points has a nearly-linear energy dependence. The corresponding correction to the density of states is proportional to ln^3(e). Both real- and imaginary part of the self-energy increase near the quantum phase transition into magnetically ordered or superconducting phase which implies violation of the Fermi-liquid behavior. The application of the results to cuprates is discussed…
The optical properties of Sn-doped Bi$_{1.1}$Sb$_{0.9}$Te$_{2}$S, the most bulk-insulating topological insulator thus far, have been examined at different temperatures over a broad frequency range. No Drude response is detected in the low-frequency range down to 30~cm$^{-1}$, corroborating the excellent bulk-insulating property of this material. Intriguingly, we observe a sharp peak at about 2\,200~cm$^{-1}$ in the optical conductivity at 5~K. Further quantitative analyses of the line shape and temperature dependence of this sharp peak, in combination with first-principles calculations, sugges…
We propose a novel parametrization of the four-point vertex function in the one-loop one-particle irreducible renormalization group (RG) scheme for fermions. It is based on a decomposition of the effective two-fermion interaction into fermion bilinears that interact via exchange bosons. Besides being more efficient than previous N-patch schemes, this parametrization also reduces the ambiguity of introducing boson fields. We apply this parametrization to the two-dimensional (t,t')-Hubbard model using a novel $Ω$-frequency regularization.
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…
We study the weak-coupling limit of the $t-t^\prime-U$ Hubbard model on a two-dimensional square lattice using a direct perturbative approach. Aided by symbolic computational tools, we compute the longitudinal density-density correlation functions in the $χ_{\uparrow \uparrow}$ and $χ_{\uparrow \downarrow}$ basis from which we can obtain the dynamical spin and charge susceptibilities at arbitrary doping and temperature. We find that for non-zero $t^\prime$, the zero frequency commensurate $\mathbf{q} = (π, π)$ spin and charge excitations are each strongest at different densities and we observe…
