Recent discovery of both gapped and gapless topological phases in weakly correlated electron systems has introduced various relativistic particles and a number of exotic phenomena in condensed matter physics. The Weyl fermion is a prominent example of three dimensional (3D), gapless topological excitation, which has been experimentally identified in inversion symmetry breaking semimetals. However, their realization in spontaneously time reversal symmetry (TRS) breaking magnetically ordered states of correlated materials has so far remained hypothetical. Here, we report a set of experimental evidence for elusive magnetic Weyl fermions in Mn$_3$Sn, a non-collinear antiferromagnet that exhibits a large anomalous Hall effect even at room temperature. Detailed comparison between our angle resolved photoemission spectroscopy (ARPES) measurements and density functional theory (DFT) calculations reveals significant bandwidth renormalization and damping effects due to the strong correlation among Mn 3$d$ electrons. Moreover, our transport measurements have unveiled strong evidence for the chiral anomaly of Weyl fermions, namely, the emergence of positive magnetoconductance only in the presence of parallel electric and magnetic fields. The magnetic Weyl fermions of Mn$_3$Sn have a significant technological potential, since a weak field ($\sim$ 10 mT) is adequate for controlling the distribution of Weyl points and the large fictitious field ($\sim$ a few 100 T) in the momentum space. Our discovery thus lays the foundation for a new field of science and technology involving the magnetic Weyl excitations of strongly correlated electron systems.

Evidence for Magnetic Weyl Fermions in a Correlated Metal

${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ is a newly discovered ${Z}_{2}$ topological kagome metal showing the coexistence of a charge-density-wave (CDW)-like order at ${T}^{*}=94\text{ }\text{ }\mathrm{K}$ and superconductivity (SC) at ${T}_{c}=2.5\text{ }\text{ }\mathrm{K}$ at ambient pressure. Here, we study the interplay between CDW and SC in ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ via measurements of resistivity, dc and ac magnetic susceptibility under various pressures up to 6.6 GPa. We find that the CDW transition decreases with pressure and experience a subtle modification at ${P}_{c1}\ensuremath{\approx}0.6--0.9\text{ }\text{ }\mathrm{GPa}$ before it vanishes completely at ${P}_{c2}\ensuremath{\approx}2\text{ }\text{ }\mathrm{GPa}$. Correspondingly, ${T}_{c}(P)$ displays an unusual $M$-shaped double dome with two maxima around ${P}_{c1}$ and ${P}_{c2}$, respectively, leading to a tripled enhancement of ${T}_{c}$ to about 8 K at 2 GPa. The obtained temperature-pressure phase diagram resembles those of unconventional superconductors, illustrating an intimated competition between CDW-like order and SC. The competition is found to be particularly strong for the intermediate pressure range ${P}_{c1}\ensuremath{\le}P\ensuremath{\le}{P}_{c2}$ as evidenced by the broad superconducting transition and reduced superconducting volume fraction. The modification of CDW order around ${P}_{c1}$ has been discussed based on the band structure calculations. This work not only demonstrates the potential to raise ${T}_{c}$ of the V-based kagome superconductors, but also offers more insights into the rich physics related to the electron correlations in this novel family of topological kagome metals.

Double Superconducting Dome and Triple Enhancement of T_{c} in the Kagome Superconductor CsV_{3}Sb_{5} under High Pressure.

The recently discovered family of vanadium-based kagome metals with topological band structures offer a new opportunity to study frustrated, correlated and topological quantum states. These layered compounds are nonmagnetic and undergo charge density wave (CDW) transitions before developing superconductivity at low temperatures. Here we report the observation of unconventional superconductivity and pair density wave (PDW) in the vanadium-based kagome lattice CsV3Sb5 using scanning tunneling microscope/spectroscopy (STM/STS) and Josephson STS. The differential conductance exhibits a V-shaped pairing gap about 0.5 meV below a transition temperature Tc about 2.3 K. Superconducting phase coherence is observed by Josephson effect and Cooper-pair tunneling to a superconducting tip. We find that CsV3Sb5 is a strong-coupling superconductor (2delta/kBTc about 5) and coexists with 4a0 unidirectional and 2x2 charge order. Remarkably, we discover a 4a0/3 bidirectional PDW accompanied by spatial modulations of the coherence peak and gap-depth in the tunneling conductance. We term the latter as a roton-PDW that can produce a commensurate vortex-antivortex lattice to account for the observed conductance modulations. Above Tc, we observe long-range ordered 4a0 unidirectional and 2a0 bidirectional CDW and a large V-shaped pseudogap in the density of state. Electron-phonon calculations attribute the 2x2 CDW to phonon softening induced structural reconstruction, but the phonon mediated pairing cannot describe the observed strong-coupling superconductor. Our findings show that electron correlations in the charge sector can drive the 4a0 unidirectional CDW, unconventional superconductivity, and roton-PDW with striking analogies to the phenomenology of cuprate high-Tc superconductors, and provide the groundwork for understanding their microscopic origins in the vanadium-based kagome superconductors.

Roton pair density wave and unconventional strong-coupling superconductivity in a topological kagome metal

Kagome metals $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{K}$, Rb, and Cs) exhibit intriguing superconductivity below $0.9\ensuremath{\sim}2.5\text{ }\text{ }\mathrm{K}$, a charge density wave (CDW) transition around $80\ensuremath{\sim}100\text{ }\text{ }\mathrm{K}$, and ${\mathbb{Z}}_{2}$ topological surface states. The nature of the CDW phase and its relation to superconductivity remains elusive. In this work, we investigate the electronic and structural properties of CDW by first-principles calculations. We reveal an inverse Star of David deformation as the $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ CDW ground state of the kagome lattice. The kagome lattice shows softening breathing-phonon modes, indicating the structural instability. However, electrons play an essential role in the CDW transition via Fermi surface nesting and van Hove singularity. The inverse Star of David structure agrees with recent experiments by scanning tunneling microscopy (STM). The CDW phase inherits the nontrivial ${\mathbb{Z}}_{2}$-type topological band structure. Further, we find that the electron-phonon coupling is too weak to account for the superconductivity ${T}_{c}$ in all three materials. It implies the existence of unconventional pairing of these kagome metals. Our results provide essential knowledge toward understanding the superconductivity and topology in kagome metals.

Charge Density Waves and Electronic Properties of Superconducting Kagome Metals.

As one of the most fundamental physical phenomena, the anomalous Hall effect (AHE) typically occurs in ferromagnetic materials but is not expected in conventional superconductors. Here, the authors find a giant AHE in the kagome superconductor CsV${}_{3}$Sb${}_{5}$. Strikingly, the AHE develops spontaneously with the occurrence of a charge density wave (CDW), indicating a strong correlation between the CDW state and AHE. These discoveries make CsV${}_{3}$Sb${}_{5}$ an ideal platform to study the interplay among nontrivial band topology, CDW, and unconventional superconductivity

Concurrence of anomalous Hall effect and charge density wave in a superconducting topological kagome metal

We report the discovery of superconductivity and detailed normal-state physical properties of RbV3Sb5 single crystals with V kagome lattice. RbV3Sb5 single crystals show a superconducting transition at Tc ~ 0.92 K. Meanwhile, resistivity, magnetization and heat capacity measurements indicate that it exhibits anomalies of properties at T* ~ 102 - 103 K, possibly related to the formation of charge ordering state. When T is lower than T*, the Hall coefficient RH undergoes a drastic change and sign reversal from negative to positive, which can be partially explained by the enhanced mobility of hole-type carriers. In addition, the results of quantum oscillations show that there are some very small Fermi surfaces with low effective mass, consistent with the existence of multiple highly dispersive Dirac band near the Fermi energy level.

Superconductivity and Normal-State Properties of Kagome Metal RbV$_{3}$Sb$_{5}$ Single Crystals

We report the discovery of superconductivity and detailed normal-state physical properties of RbV3Sb5 single crystals with V kagome lattice RbV3Sb5 single crystals show a superconducting transition at Tc ~ 092 K Meanwhile, resistivity, magnetization and heat capacity measurements indicate that it exhibits anomalies of properties at T* ~ 102 - 103 K, possibly related to the formation of charge ordering state When T is lower than T*, the Hall coefficient RH undergoes a drastic change and sign reversal from negative to positive, which can be partially explained by the enhanced mobility of hole-type carriers In addition, the results of quantum oscillations show that there are some very small Fermi surfaces with low effective mass, consistent with the existence of multiple highly dispersive Dirac band near the Fermi energy level

Superconductivity and normal-state properties of kagome metal RbV3Sb5 single crystals

Topological spin textures with versatile configurations exhibit fascinating physical behavior as high-efficiency information units. Recent observations of nontrivial spin textures in two-dimensional (2D) van der Waals (vdW) ferromagnets have shed light on their functionality as a paradigm for spintronic devices. Here, the spin configuration of single-crystal 2D vdW ${\mathrm{Fe}}_{5\text{\ensuremath{-}}x}\mathrm{Ge}{\mathrm{Te}}_{2}$ is investigated by Lorentz transmission electron microscopy, where the conversion from Bloch-type bubbles to N\'eel-type skyrmions can be observed by tuning sample thickness. Remarkably, high-density N\'eel-type skyrmions can be obtained via field-cooling manipulation. We further demonstrate the underlying mechanism by varying the sample thickness and Dzyaloshinskii-Moriya interaction (DMI) parameters in a series of micromagnetic simulations, manifesting the presence of DMI at the ${\mathrm{Fe}}_{5\text{\ensuremath{-}}x}\mathrm{Ge}{\mathrm{Te}}_{2}$ surface by first-principles calculation. Our findings disclose the rich variety of topological spin textures in 2D vdW ${\mathrm{Fe}}_{5\text{\ensuremath{-}}x}\mathrm{Ge}{\mathrm{Te}}_{2}$, possessing great promise for future nonvolatile memories based on spin topology. 

Manipulation of topological spin configuration via tailoring thickness in van der Waals ferromagnetic 
Fe5−xGeTe2

Moir\'e magnetism, parallel with moir\'e electronics that has led to novel correlated and topological electronic states, emerges as a new venue to design and control exotic magnetic phases in twisted magnetic two-dimensional(2D) crystals. Here, we report direct evidence of noncollinear spin texture in 2D twisted double bilayer (tDB) magnet chromium triiodide (CrI$_3$). Using magneto-optical spectroscopy in tDB CrI$_3$, we revealed the presence of a net magnetization, unexpected from the composing antiferromagnetic bilayers with compensated magnetizations, and the emergence of noncollinear spins, originated from the moir\'e exchange coupling-induced spin frustrations. Exploring the twist angle dependence, we demonstrated that both features are present in tDB CrI$_3$ with twist angles from 0.5$^o$ to 5$^o$, but are most prominent in the 1.1$^o$ tDB CrI$_3$. Focusing on the temperature dependence of the 1.1$^o$ tDB CrI$_3$, we resolved the dramatic suppression in the net magnetization onset temperature and the significant softening of noncollinear spins, as a result of the moir\'e induced frustration. Our results demonstrate the power of moir\'e superlattices in introducing novel magnetic phenomena that are absent in natural 2D magnets. 

/pdf/evidence-of-non-collinear-spin-texture-in-magnetic-moire-3agmz4gd.pdf

Evidence of non-collinear spin texture in magnetic moiré superlattices

Layered α-RuCl3 is a promising material to potentially realize the long-sought Kitaev quantum spin liquid with fractionalized excitations. While evidence of this state has been reported under a modest in-plane magnetic field, such behaviour is largely inconsistent with theoretical expectations of spin liquid phases emerging only in out-of-plane fields. These predicted field-induced states have been largely out of reach due to the strong easy-plane anisotropy of bulk crystals, however. We use a combination of tunnelling spectroscopy, magnetotransport, electron diffraction and ab initio calculations to study the layer-dependent magnons, magnetic anisotropy, structure and exchange coupling in atomically thin samples. Due to picoscale distortions, the sign of the average off-diagonal exchange changes in monolayer α-RuCl3, leading to a reversal of spin anisotropy to easy-axis anisotropy, while the Kitaev interaction is concomitantly enhanced. Our work opens the door to the possible exploration of Kitaev physics in the true two-dimensional limit. 

/pdf/magnetic-anisotropy-reversal-driven-by-structural-symmetry-3a7ufwo8.pdf

Shaohua Yan

Papers

Superconductivity and Normal-State Properties of Kagome Metal RbV$_{3}$Sb$_{5}$ Single Crystals

Superconductivity and normal-state properties of kagome metal RbV3Sb5 single crystals

Manipulation of topological spin configuration via tailoring thickness in van der Waals ferromagnetic Fe5−xGeTe2

Evidence of non-collinear spin texture in magnetic moiré superlattices

Magnetic anisotropy reversal driven by structural symmetry-breaking in monolayer α-RuCl_3