Robust topological superconductivity in spin-orbit coupled systems at higher-order van Hove filling
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学 Kavli 理论科学研究院）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所 北京凝聚态物理国家研究中心）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学 物理科学学院）；CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所 理论物理国家重点实验室）
Xinloong Han, Jun Zhan, Fu-chun Zhang, Jiangping Hu, Xianxin Wu
Van Hove奇异点（VHSs）接近费米能级会促进电子相互作用并产生多种竞争的不稳定性。此外，来自自旋轨道耦合（SOC）的非平凡 Berry 阶可以引入有趣的装饰到相互作用中，从而改变相关现象。然而，不清楚在VHSs和Berry相相互作用的系统中，如何以及会产生什么类型的新物理。在此，基于平方晶格上的通用Rashba模型，我们全面探讨了这种相互作用及其对竞争电子不稳定性的重要影响，通过进行parquet重整化群分析。尽管粒子-粒子和粒子-空穴通道中与更高阶VHSs相关的各种可比较波动存在，我们发现chiral p±ip配对在通用相互作用参数空间中作为两个稳定的固定轨迹出现，即系统成为鲁棒的拓扑超导体。chiral配对源于非平凡Berry相诱导的跃迁相互作用。讨论了可能的实验实现和影响。我们的工作为具有强SOC的量子材料中的相关态提供了新的视角，并为拓扑超导性的探索提供了新的见解。
英文摘要：
Van Hove singularities (VHSs) in proximity to the Fermi level promote electronic interactions and generate diverse competing instabilities. It is also known that a nontrivial Berry phase derived from spin-orbit coupling (SOC) can introduce an intriguing decoration into the interactions and thus alter correlated phenomena. However, it is unclear how and what type of new physics can emerge in a system featured by the interplay between VHSs and the Berry phase. Here, based on a general Rashba model on the square lattice, we comprehensively explore such an interplay and its significant influence on the competing electronic instabilities by performing a parquet renormalization group analysis. Despite the existence of a variety of comparable fluctuations in the particle-particle and particle-hole channels associated with higher-order VHSs, we find that the chiral $p \pm ip$ pairings emerge as two stable fixed trajectories within the generic interaction parameter space, namely the system becomes a robust topological superconductor. The chiral pairings stem from the hopping interaction induced by the nontrivial Berry phase. The possible experimental realization and implications are discussed. Our work sheds new light on the correlated states in quantum materials with strong SOC and offers fresh insights into the exploration of topological superconductivity.
Starting from a tight-binding model on the kagome lattice near the van Hove filling, the superconducting (SC) properties are investigated self-consistently using the Bogoliubov-de Gennes equation with the consideration of the inequivalent third-neighbor (TN) bonds. Near the van Hove filling, the most favorable SC pairings are found to derive from the electrons belonging to the same sublattice sites, including the on-site $s$-wave and the spin-singlet/triplet TN pairings. The inequivalent TN bonds will result in multiple SC components with different orbital angular momentums (OAM) for the TN SC…
Based on the random phase approximation calculation in two-orbital honeycomb lattice model, we investigate the pairing symmetry of Ni-based transition-metal trichalcogenides by electron doping access to type-II van Hove singularities (vHs). We find that chiral even-parity d+id-wave (Eg) state is suppressed by odd-parity p+ip-wave (Eu) state when electron doping approaches the type-II vHs. The type-II vHs peak in density of states (DOS) enables to strengthen the ferromagnetic fluctuation, which is responsible for triplet pairing. The competition between antiferromagnetic and ferromagnetic fluct…
Evidence of strong correlations at the van Hove singularity in the scanning tunneling spectra of superconducting Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} single crystals
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…
We study the occurrence and the origin of ferromagnetic fluctuations in the longitudinal spin susceptibility of the $t$-$t'$-Rashba-Hubbard model on the square lattice. The combined effect of the second-neighbor hopping $t'$ and the spin-orbit coupling leads to ferromagnetic fluctuations in a broad filling region. The spin-orbit coupling splits the energy bands, leading to two van Hove fillings, where the sheets of the Fermi surface change their topology. Between these two van Hove fillings the model shows ferromagnetic fluctuations. We find that these ferromagnetic fluctuations originate from…
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）
Motivated by experiments on twisted bilayer graphene, we study the emergence of superconductivity from $\textit{weak}$ repulsive interactions in the Hubbard model on a honeycomb lattice, with both spin and orbital degeneracies, and with the filling treated as a tunable control parameter. The attraction is generated through the Kohn-Luttinger mechanism. We find, similar to old studies of single layer graphene, that the leading superconducting instability is in a $d$-wave pairing channel close to Van Hove filling, and is in an $f$-wave pairing channel away from Van Hove filling. The $d$-wave pai…
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…
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…
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…
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…
Topological Odd-Parity Superconductivity at Type-II 2D Van Hove Singularities
我们研究了范霍夫奇点（VHS）处二维电子系统中弱排斥相互作用引起的非常规超导电性，其中态密度呈对数发散。我们定义了两种类型的VHS。对于I型VHS的系统，弱排斥相互作用一般诱导非常规单重态配对。然而，更有趣的是，对于II型VHS，重整化群（RG）分析表明，当费米面没有充分嵌套时，弱排斥相互作用有利于三重态配对（例如p波）。对于遵守四对称性的II型VHS系统，拓扑超导性（手性p+ip配对或时间反演不变的$Z_2$ p+ip配对）通常发生。我们还将讨论我们的研究的相关性材料，包括最近发现的超导体LaO $_{1-x}$ F $_x$ BiS $_2$，可以调整到II型VHS掺杂。
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 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…
