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 Stoner criterion. A comparison with the functional renormalization group results and mean-field approximation which yields a phase separation is also performed.
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…
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…
The interplay of magnetic and superconducting fluctuations in two dimensional systems with van Hove singularities in the electronic spectrum is considered within the functional renormalization group (fRG) approach. While the fRG flow has to be stoped at a certain minimal temperature T_RG^min, we study temperature dependence of magnetic and superconducting susceptibilities both, above and below T_RG^min, which allows to obtain the resulting ground state phase diagram. Close to half filling the fRG approach yields two quantum phase transitions: from commensurate antiferromagnetic to incommensura…
We investigate a competition of tendencies towards ferromagnetic and incommensurate order in two-dimensional fermionic systems within functional renormalization group technique using temperature as a scale parameter. We assume that the Fermi surface (FS) is substantially curved, lies in the vicinity of van Hove singularity points and perform an account of the self-energy corrections. It is shown that the character of magnetic fluctuations is strongly asymmetric with respect to the Fermi level position relatively to van Hove singularity (VHS). For the Fermi level above VHS we find at low temper…
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…
Theoretical studies of the metamagnetism and anomalous phase of Sr3Ru2O7 have focused on the role of van Hove singularities, although much experimental evidence points towards quantum criticality having a large effect. We investigate the magnetic and thermodynamic properties of systems where magnetic field tunes through such a peak in the electronic density of states. We study the generic case of a van Hove singularity in 2D. We see that in combination with the requirement of number conservation and interaction effects the peak in the density of states produces several interesting phenomena in…
We study symmetry-broken phases in twisted bilayer graphene at small filling above charge neutrality and at Van Hove filling. We argue that the Landau functionals for the particle-hole order parameters at these fillings both have an approximate SU(4) symmetry, but differ in the sign of quartic terms. We determine the order parameter manifold of the ground state and analyze its excitations. For small fillings, we find a strong 1st-order transition to an SU(3)$\otimes$U(1) manifold of orders that break spin-valley symmetry and induce a 3-1 splitting of fermionic excitations. For Van Hove filling…
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 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…
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…
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…
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 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 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 …
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…
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…
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.
We report, for the first time, measurements of the third order, $χ_3$ and fifth order, $χ_5$, susceptibilities in an itinerant oxide metamagnet, Sr$_3$Ru$_2$O$_7$ for magnetic fields both parallel and perpendicular to the c-axis. These susceptibilities exhibit maxima in their temperature dependence such that $T_1 \approx 2T_3 \approx 4T_5$ where the $T_i$ are the position in temperature where a peak in the $i$-th order susceptibility occurs. These features taken together with the scaling of the critical field with the temperature $T_1$ observed in a diverse variety of itinerant metamagnets fin…
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…
The t-t' Hubbard model for the Fermi level near the Van Hove singularity is considered within the renormalization group and parquet approaches. The interplay of ferromagnetic, antiferromagnetic, and superconducting channels is investigated, and the phase diagram of the model is constructed. In comparison with previous approaches, the account of ferromagnetic fluctuations suppresses superconducting pairing and, vice versa, the influence of the Cooper channel decreases the Curie temperature, so that the Stoner criterion is inapplicable even qualitatively.
A numerical renormalization group (NRG) investigation of the one-centre $t-t'$ Kondo problem is performed for the square lattice with account of logarithmic Van Hove singularities (VHS) in the electron density of states. The magnetic susceptibility, entropy and specific heat are calculated. The temperature dependences of the thermodynamic properties in the presence of VHS turn out to be non-trivial. For finite $t'$ inverse logarithm of the corresponding Kondo temperature $T_K$ demonstrates a crossover from the square-root to standard linear dependence on the $s-d$ exchange coupling. The low-te…
Recent experiments revealed non-Fermi-liquid resistivity in the unconventional superconductor Sr$_{2}$RuO$_{4}$ when strain pushes one of the Fermi surfaces close to a van Hove singularity. The origin of this behavior and whether it can be understood from a picture of well defined quasiparticles is unclear. We employ a Boltzmann transport analysis beyond the single relaxation-time approximation based on a single band which undergoes a Lifshitz transition, where the Fermi surface crosses a van Hove singularity, either due to uni-axial or epitaxial strain. First analytically investigating impuri…
We study the impact of the fermionic self-energy on one-loop functional renormalization group flows of the two-dimensional $t$-$t'$ Hubbard model, with emphasis on electronic densities away from van Hove filling. In the presence of antiferromagnetic hot spots, antiferromagnetic fluctuations lead to a flattening of the Fermi surface, shift magnetic phase boundaries and significantly enhance critical scales. We trace back this effect to the presence of a magnetic first order transition. For some parameters, the first order character of the latter is reduced by self-energy effects. For reliably d…
We study the quantum corrections to the Fermi energy of a two-dimensional electron system, showing that it is attracted towards the Van Hove singularity for a certain range of doping levels. The scaling of the Fermi level allows to cure the infrared singularities left in the BCS channel after renormalization of the leading logarithm near the divergent density of states. A phase of d-wave superconductivity arises beyond the point of optimal doping corresponding to the peak of the superconducting instability. For lower doping levels, the condensation of particle-hole pairs due to the nesting of …
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…
The proximity of the Fermi surface to van Hove singularities drastically enhances interaction effects and leads to essentially new physics. In this work we address the formation of flat bands ("Fermi condensation") within the Hubbard model on the triangular lattice and provide a detailed analysis from an analytical and numerical perspective. To describe the effect we consider both weak-coupling and strong-coupling approaches, namely the renormalization group and dual fermion methods. It is shown that the band flattening is driven by correlations and is well pronounced even at sufficiently high…
A van Hove singularity (VHS) often significantly amplifies the electronic instability of a crystalline solid, including correlation-induced phenomena such as Hund's metallicity. We perform a systematic study on the interplay between Hund's coupling and electronic structures with a VHS focusing on Hund's metallicity. We construct a simplified tight-binding model targeting cubic perovskite materials and test the effects of the VHS utilizing dynamical mean-field theory with an exact diagonalization solver. The quasiparticle weight and the low-frequency power exponent of the self-energy provide a …
We investigate the magnetic instabilities of the nondegenerate (s-band) and a degenerate (d-band) Hubbard model in two dimensions using many-body effects due to the particle-particle diagrams and Hund's rule local correlations. The density of states and the position of Van Hove singularity change depending on the value of next-nearest neighbor hopping t'. The Stoner parameter is strongly reduced in the s-band case, and ferromagnetism survives only if electron density is small, and the band is almost flat at small momenta due to next-nearest neighbor hopping. In contrast, for the d-band case th…
We have applied nuclear magnetic resonance spectroscopy to study the distinctive network of nodal lines in the Dirac semimetal ZrSiTe. The low-$T$ behavior is dominated by a symmetry-protected nodal line, with NMR providing a sensitive probe of the diamagnetic response of the associated carriers. A sharp low-$T$ minimum in NMR shift and $(T_1T)^{-1}$ provides a quantitative measure of the dispersionless, quasi-2D behavior of this nodal line. We also identify a van Hove singularity closely connected to this nodal line, and an associated $T$-induced Lifshitz transition. A disconnect in the NMR s…
First-principles density functional theory calculations are performed to understand the electronic structure and interaction parameters for recently discovered superconducting Kagome metal CsV$_3$Sb$_5$. A systematic analysis of the tight-binding parameters based on maximally localized Wannier function method demonstrates that the out-of-plane Sb$^{\rm out}$-$p$ orbital is a key element in complete description of the three Van Hove singularity structures known in this material at $M$ point near the Fermi level. Further, the correlation strengths are also largely determined by Sb$^{\rm out}$-$p…
We report the results of a combined study of the normal state resistivity and superconducting transition temperature $T_c$ of the unconventional superconductor Sr$_2$RuO$_4$ under uniaxial pressure. There is strong evidence that as well as driving $T_c$ through a maximum at $\sim$3.5 K, compressive strains $\varepsilon$ of nearly 1 % along the crystallographic [100] axis drive the $γ$ Fermi surface sheet through a Van Hove singularity, changing the temperature dependence of the resistivity from $T^2$ above and below the transition region to $T^{1.5}$ within it. This occurs in extremely pure si…
Divergent density of states (DOS) can induce extraordinary phenomena such as significant enhancement of superconductivity and unexpected phase transitions. Moreover, van Hove singularities (VHSs) are known to lead to divergent DOS in two-dimensional (2D) systems. Despite the recent interest in VHSs, only a few controllable cases have been reported to date. In this work, we investigate the electronic band structures of a 2D VHS with angle-resolved photoemission spectroscopy and control transport properties by utilizing an atomically ultrathin SrRuO$_3$ film. By applying electric fields with alk…
When a van-Hove singularity is located in the vicinity of the Fermi level, the electronic scattering rate acquires a non-analytic contribution. This invalidates basic assumptions of Fermi liquid theory and within perturbative treatments leads to a non-Fermi liquid self-energy and transport properties.Such anomalies are shown to also occur in the strongly correlated metallic state. We consider the Hubbard model on a two-dimensional square lattice with nearest and next-nearest neighbor hopping within the single-site dynamical mean-field theory. At temperatures on the order of the low-energy scal…
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…
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…
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…
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…
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…
We study the electronic instabilities of doped bilayer silicene using the random phase approximation. In contrast to the singlet $d+id'$ superconductivity at the low doping region, we find that the system is an itinerant ferromagnet in the narrow doping regions around the Van Hove singularities, and a triplet $p+ip'$ superconductor in the vicinity of these regions. Adding a weak Kane-Mele spin-orbit coupling to the system further singles out the time-reversal invariant equal-spin helical $p+ip'$ pairing as the leading instability. The triplet pairing identified here is driven by the ferromagne…
