We investigated the Re-based kagome superconductor Re$_2$Zr through various measurements, including resistivity, magnetization, specific heat, and muon spin rotation and relaxation spectroscopy. These results suggest that Re$_2$Zr is a moderately coupled potential two-gap superconductor. Zero-field muon relaxation data indicate the possible presence of a time-reversal symmetry-breaking state in the superconducting ground state. Our investigation identifies Re$_{2}$Zr as a new unconventional superconductor with a potential complex order parameter that warrants considerable experimental and theoretical interest.
Since the discovery of a new family of vanadium-based kagome superconductor AV3Sb5 (A=K, Rb, and Cs) with topological band structures, extensive effort has been devoted to exploring the origin of superconducting states and the intertwined orders. Meanwhile, searching for new types of superconductors with novel physical properties and higher superconducting transition temperatures has always been a major thread in the history of superconductor research. Here we report a successful fabrication and the topological states of a Titanium-based kagome metal CsTi3Bi5 (CT3B5) crystal. The as-grown CT3B…
Recently the kagome compounds have inspired enormous interest and made some great progress such as in the field of superconductivity and topology. Here we predict a different kagome magnesium triboride (MgB3) superconductor with a calculated Tc ~12.2 K and Tc ~15.4 K by external stress, the potentially highest among the reported diverse kagome-type superconductors. We reveal its various exotic physical properties including the van Hove singularity, flat-band, multiple Dirac points, and nontrivial topology. The system can be described by a two-band model with highly anisotropic superconducting …
Time-Reversal Symmetry Breaking Superconducting State and Collective Modes in Kagome Superconductors
Capital Normal University（首都师范大学）；Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学理论科学研究所）；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）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
The superconducting gap structures in the transition-metal-based kagome metal AV$_3$Sb$_5$ (A=K,Rb,Cs), the first family of quasi-two-dimensional kagome superconductors, remain elusive as there is strong experimental evidence for both nodal and nodaless gap structures. Here we show that the dichotomy can be resolved because of the coexistence of time-reversal symmetry breaking with a conventional fully gapped superconductivity. The symmetry protects the edge states which arise on the domains of the lattice symmetry breaking order to remain gapless in proximity to a conventional pairing. We dem…
A recent Little-Parks experiment on Kagome-structured superconductor CsV_3Sb_5 demonstrated remarkable resistance oscillations with period \phi0/3=hc/6e. Here, we perform analysis based on a theory involving three 2e superconductivity (SC) order parameters associated with the three reciprocal lattice vectors which connect M points of the hexagonal Brillouin zone. In a ring geometry we unveil that, as a series of metastable states, phase of one SC order parameter winds 2πmore or less than the other two ones around the ring, which yields local free energy minima at integer multiples of \phi0/3. …
A Strongly Anisotropic Superconducting Gap in the Kagome Superconductor CsV$_3$Sb$_5$: A Study of Directional Point-Contact Andreev Reflection Spectroscopy
Arrays of Ni nanodots embedded in Nb superconducting films have been fabricated by sputtering and electron beam lithography techniques. The arrays are periodic triangular lattices of circular Ni dots arranged in a kagomé-like pattern with broken reflection symmetry. Relevant behaviors are found in the vortex lattice dynamics : i) At values lower than the first integer matching field, several fractional matching fields are present when the vortex lattice moves parallel or perpendicular to the reflection symmetry axis of the array showing a clear anisotropic character in the magnetoresistance cu…
We studied the effects of multiband electronic structure on the thermoelectric and electrical transport properties in the normal state of kagome superconductors $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs). In all three members, the multiband nature is manifested by sign changes in the temperature dependence of the Seebeck and Hall resistivity, together with sublinear response of the isothermal Nernst and Hall effects to external magnetic fields in the charge ordered state. Moreover, ambipolar transport effects appear ubiquitously in all three systems, giving rise to sizable Nernst signal. Finally, possib…
The newly discovered Kagome superconductors $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs) exhibit superconductivity, charge order, and band topology simultaneously. To explore the intricate interplay between the superconducting and charge orders, we investigate the doping evolution of superconductivity, charge-density-wave (CDW) order, and band topology in doped topological kagome superconductors Cs(V$_{1-x}$Ti$_x$)$_3$Sb$_5$ where the Ti-dopant introduces hole-like charge carriers. Despite the absence of the CDW phase transition in doped compounds even for the lowest doping level of $x=0.047$, the superco…
The superconductivity of a kagome superconductor CsV3Sb5 is studied by scanning tunneling microscopy / spectroscopy at an ultralow temperature with high resolution. Two kinds of superconducting gaps with multiple sets of coherent peaks and residual zero-energy density of states are observed on both half-Cs and Sb surfaces, implying multiband superconductivity with gap nodes. Sixfold star-shaped magnetic vortex is observed with conventional Caroli-de Gennes-Matricon bound states inside. Magnetic impurities suppress the superconductivity, while nonmagnetic impurities do not, suggesting the absen…
CsV3Sb5 is a newly discovered Z2 topological kagome metal showing the coexistence of a charge density wave (CDW)-like order at T* = 94 K and superconductivity (SC) at Tc = 2.5 K at ambient pressure. Here we study the interplay between CDW and SC in CsV3Sb5 via measurements of resistivity and magnetic susceptibility under hydrostatic pressures. We find that the CDW transition decreases with pressure and experience a subtle modification at Pc1 = 0.6-0.9 GPa before it vanishes completely at Pc2 = 2 GPa. Correspondingly, Tc(P) displays an unusual M-shaped double dome character with two maxima arou…
Materials with a kagome lattice provide a platform for searching for new electronic phases and investigating the interplay between correlation and topology. Various probes have recently shown that the kagome lattice can host diverse quantum phases with intertwined orders, including charge density wave states, bond density wave states, chiral charge order, and, rarely, superconductivity. However, reports of the coexistence of superconductivity and magnetic order in kagome materials remain elusive. Here we revisit a magnetic superconductor CeRu$_2$ with a kagome network formed by Ru atoms. Our f…
Layered kagome metals AV3Sb5 (A=K, Rb, Cs) exhibit diverse correlated electron phenomena. It includes charge density wave formation and superconductivity the pairing symmetry of which, however, is controversial due to contradictory experimental evidence. Through calculations based on real-space lattice models at the mean-field level, we investigate the vortex and surface spectra of all competitive pairing propensities suggested for AV3Sb5 from a weak coupling analysis of unconventional superconductivity. Chiral p-wave pairing emerges as the only option to host Majorana bound states in the vort…
The vanadium-based kagome superconductor CsV3Sb5 has attracted tremendous attention due to its unexcepted anomalous Hall effect (AHE), charge density waves (CDWs), nematicity, and a pseudogap pair density wave (PDW) coexisting with unconventional strong-coupling superconductivity (SC). The origins of CDWs, unconventional SC, and their correlation with different electronic states in this kagome system are of great significance, but so far, are still under debate. Chemical doping in the kagome layer provides one of the most direct ways to reveal the intrinsic physics, but remains unexplored. Her…
Owing to its inherent non-trivial geometry, the unique structural motif of the recently discovered Kagome topological superconductor AV3Sb5 is an ideal host of diverse topologically non-trivial phenomena, including giant anomalous Hall conductivity, topological charge order, charge density wave, and unconventional superconductivity. Despite possessing a normal-state CDW order in the form of topological chiral charge order and diverse superconducting gaps structures, it remains unclear how fundamental atomic-level properties and many-body effects including Fermi surface nesting, electron-phonon…
A kagome lattice naturally features Dirac fermions, flat bands and van Hove singularities in its electronic structure. The Dirac fermions encode topology, flat bands favour correlated phenomena such as magnetism, and van Hove singularities can lead to instabilities towards long-range many-body orders, altogether allowing for the realization and discovery of a series of topological kagome magnets and superconductors with exotic properties. Recent progress in exploring kagome materials has revealed rich emergent phenomena resulting from the quantum interactions between geometry, topology, spin a…
The kagome lattice, the most prominent structural motif in quantum physics, benefits from inherent nontrivial geometry to host diverse quantum phases, ranging from spin-liquid phases, topological matter to intertwined orders, and most rarely unconventional superconductivity. Recently, charge sensitive probes have suggested that the kagome superconductors AV_3Sb_5 (A = K, Rb, Cs) (A = K, Rb, Cs) exhibit unconventional chiral charge order, which is analogous to the long-sought-after quantum order in the Haldane model or Varma model. However, direct evidence for the time-reversal symmetry-breakin…
Josephson spectroscopy study of kagome superconductors toward the deep point-contact regime
Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；State Key Laboratory of Quantum Functional Materials, Department of Physics, and Guangdong Basic Research Center of Excellence for Quantum Science, Southern University of Science and Technology（南方科技大学）
Nonreciprocal charge transport phenomena are widely studied in two-dimensional superconductors, which demonstrate unidirectional-anisotropy magnetoresistances as a result of symmetry breaking. Here, we report a strong nonreciprocal transport phenomenon in superconducting CsV$_{3}$Sb$_{5}$ thin flakes. The second harmonic voltages, mainly originating from the rectification effect of vortex motion, are unambiguously developed with in-plane and out-of-plane magnetic fields, and their magnitudes are comparable to those in noncentrosymmetric superconductors. The second harmonic magnetoresistances s…
Motivated by recent experimental evidences signalling the chiral charge order in the vanadium-based kagome superconductors, we theoretically investigate the impact of the chiral flux charge order over the experimental outcomes for the normal and the SC properties. It is revealed that the spectral weight on the Fermi surface (FS) is partially gaped by the chiral flux charge order with the reservation of the spectral weight on the $M$ points and the midpoint between the two adjacent $M$ points, resulting in the momentum-dependent energy gap being consistent with the recent experimental observati…
Topological pair density waves in kagome superconductors
Southern University of Science and Technology（南方科技大学）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Zurich（苏黎世大学）；The University of Tokyo（东京大学）
Topological superconductors are gapped superconductors with protected Majorana surface/edge states on the boundary. In this paper, we study the Josephson coupling between time-reversal invariant topological superconductors and s-wave superconductors. The Majorana edge/surface states of time-reversal invariant topological superconductors in all physical dimensions 1, 2, 3 have a generic topological property which we named as time-reversal anomaly. Due to the time-reversal anomaly, the Josephson coupling prefers a nonzero phase difference between topological and trivial superconductors. The nont…
Phase-sensitive evidence for pair density waves in a kagome superconductor
Southern University of Science and Technology（南方科技大学）；High Magnetic Field Laboratory of Chinese Academy of Sciences（中国科学院合肥物质科学研究院强磁场科学中心）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Johns Hopkins University（约翰斯·霍普金斯大学）；The University of Tokyo（东京大学）；Peking University（北京大学）；Paul Scherrer Institute（保罗谢尔研究所）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Nanjing University（南京大学）；University of Wurzburg（维尔茨堡大学）；ETH Zürich（苏黎世联邦理工学院）
Linear nonsaturating magnetoresistance (LMR) represents a class of anomalous resistivity response to external magnetic field that has been observed in a variety of materials including but not limited to topological semi-metals, high-Tc superconductors and materials with charge/spin density wave (CDW/SDW) orders. Here we report the observation of LMR in layered kagome superconductor and CDW material CsV3Sb5 thin flakes, as well as the dimensional crossover and temperature (T) crossover of such LMR. Specifically, in ultrathin CsV3Sb5 crystals, the magnetoresistance (MR) exhibits a crossover from…
In a first-order topological phase with sublattice degrees of freedom, a change in the boundary sublattice termination has no effect on the existence of gapless boundary states in dimensions higher than one. However, such a change may strongly affect the physical properties of those boundary states. Motivated by this observation, we perform a systematic study of the impact of sublattice terminations on the boundary physics on the two-dimensional kagome lattice. We find that the energies of the Dirac points of helical edge states in two-dimensional first-order topological kagome insulators sens…
We report muon spin rotation ($μ$SR) experiments on the microscopic properties of superconductivity and magnetism in the kagome superconductor CeRu$_{2}$ with $T_{\rm c}$~${\simeq}$~5~K. From the measurements of the temperature-dependent magnetic penetration depth $λ$, the superconducting order parameter exhibits nodeless pairing, which fits best to an anisotropic $s$-wave gap symmetry. We further show that the $T_{\rm c}$/$λ^{-2}$ ratio is comparable to that of unconventional superconductors. Furthermore, the powerful combination of zero-field (ZF)-$μ$SR and high-field $μ$SR has been used to …
The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology, which continues to bear surprises. In this work, using spectroscopic imaging scanning tunneling microscopy, we discover a cascade of different symmetry-broken electronic states as a function of temperature in a new kagome superconductor, CsV3Sb5. At a temperature far above the superconducting transition Tc ~ 2.5 K, we reveal a tri-directional charge order with a 2a0 period that breaks the translation symmetry of the l…
Classification of Lifshitz invariant in multiband superconductors: an application to Leggett modes in the linear response regime in Kagome lattice models
New materials based on Kagome lattices, predicted to host exotic quantum physics because they can display flat electronic bands, Dirac cones and topologically nontrivial surface states, are strongly desired. Here we report the crystal structure and superconducting properties of LaIr3Ga2, a previously unreported material that is based on a Kagome lattice of the heavy atom Ir. LaIr3Ga2 is a type II superconductor with Tc ~ 5.2 K, mu0Hc1 (0) ~ 7.1 mT and mu0Hc2 (0) ~ 4.7 T. The normalized heat capacity jump at the superconducting transition, (deltaC/gammaTc), 1.41, is within error of the value ex…
We show that under certain conditions multiband superconductors with broken time-reversal symmetry have a new vortex viscosity-generating mechanism which is different from that in conventional superconductors. It appears due to the existence of mixed superfluid phase-density mode inside vortex core. This new contribution is dominant near the time reversal symmetry breaking phase transition. The results could be relevant for three band superconductor $Ba_{1-x}K_{x}Fe_2As_2$.
The topological invariants of gapped time reversal invariant lattice superconductors are studied by mapping the superconducting mean field Hamiltonian to a Bloch Hamiltonian. There is a single $Z_2 $ invariant in two dimensions and four such invariants in three dimensions. We briefly discuss the properties of states with non-trivial topological invariants.
We argue that the topological charge density wave phase in the quasi-2D Kagome superconductor AV$_3$Sb$_5$ is a chiral flux phase. Considering the symmetry of the Kagome lattice, we show that the chiral flux phase has the lowest energy among those states which exhibit $2\times2$ charge orders observed experimentally. This state breaks the time-reversal symmetry and displays anomalous Hall effect. The explicit pattern of the density of this state in real space is calculated. These results are supported by recent experiments and suggest that these materials are a new platform to investigate the …
In this paper we study the order parameter and density of states near a grain boundary between two $d_{x^2-y^2}$ superconductors. We examine broken time reversal symmetry near the interface. In particular we show that, under suitable circumstances, time reversal symmetry must be broken even when the order parameter is purely $d_{x^2-y^2}$ everywhere in space.
A novel time-reversal symmetry breaking state is found theoretically in the Josephson junction between the two-gap superconductor and the conventional s-wave superconductor. This occurs due to the frustration between the three order parameters analogous to the two antiferromagnetically coupled XY-spins put under a magnetic field. This leads to the interface states with the energies inside the superconducting gap. Possible experimental observations of this state with broken time-reversal symmetry are discussed.
The kagome metal CsV$_{3}$Sb$_{5}$ features an unusual competition between the charge-density-wave (CDW) order and superconductivity. Evidence for time-reversal symmetry breaking (TRSB) inside the CDW phase has been accumulating. Hence, the superconductivity in CsV$_{3}$Sb$_{5}$ emerges from a TRSB normal state, potentially resulting in an exotic superconducting state. To reveal the pairing symmetry, we first investigate the effect of nonmagnetic impurity. Our results show that the superconducting critical temperature is insensitive to disorder, pointing to conventional $s$-wave superconductiv…
Recently synthesized Kagome compounds AV$_3$Sb$_5$ attract great attention due to the unusual coexistence of the topology, charge density wave and superconductivity. In this {\it Letter}, based on the band structures for CsV$_3$Sb$_5$ in pristine phase, we fit an effective 6-band model for the low-energy processes; utilizing the random phase approximation (RPA) on the effective minimal model, we obtain the momentum-resolved static spin susceptibility attributing the spin-fluctuation pairing mechanism, we find that the superconducting pairing strengths increase with the lift of the Coulomb corr…
