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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.
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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 many-patch RG approaches. While the spin-flux (SF) phase is not stable at the mean-field level, it is identified as a possible ground state at J<0 in both RG approaches. With increasing t the results of all three approaches merge: d-wave superconductivity at J>0 and ferromagnetism at J<0 become the leading instabilities. For large enough V the charge-density-wave (CDW) state occurs.
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 the electronic dimensionality of the system being lower than the dimensionality of the lattice. The order of VHS is found to correlate with the superconducting Tc such that materials with higher order VHSs display higher Tcs. We further show that the presence of the normal and higher-order VHSs in the electronic spectrum can provide a straightforward marker for identifying the propensity of a material toward correlated phases such as excitonic insulators or supermetals. Our study opens up a new materials playground for exploring the interplay between high-order VHSs, superconducting transition temperatures and electron correlation effects in the cuprates and related high-Tc superconductors.
The electronic band structure of the 2D kagome net hosts two different types of van Hove singularities (vHs) arising from an intrinsic electron-hole asymmetry. The distinct sublattice flavors (pure and mixed, p-type and m-type) and pairing instabilities associated to the two types of vHs are key to understand the unconventional many-body phases of the kagome lattice. Here, in a recently discovered kagome metal CsV3Sb5 exhibiting charge order and superconductivity, we have examined the vHs, Fermi surface nesting, and many-body gap opening. Using high-resolution angle-resolved photoemission spectroscopy (ARPES), we identify multiple vHs coexisting near the Fermi level of CsV3Sb5, including both p- and m-types of vHs emerging from dxz/dyz kagome bands and a p-type vHs from dxy/dx2-y2 kagome bands. Among the multiple vHs, the m-type vHs is located closest to the Fermi level and is characterized by sharp Fermi surface nesting and gap opening across the charge order transition. Our work reveals the essential role of kagome-derived vHs as a driving mechanism for the collective phenomena realized in the AV3Sb5 family (A = K, Rb, Cs) and paves the way for a deeper understanding of strongly correlated topological kagome systems.
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. A destruction of the effect by special microwave radiation is predicted, followed by a partial release of the zero-point vibration energy of the coupled optical phonon mode.
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 results of the renormalization-group approach are compared with the mean-field results and the results of the T-matrix approximation.
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