Superconductivity in the Z 2 kagome metal KV 3 Sb 5
TL;DR: In this paper, the authors reported the observation of bulk superconductivity in single crystals of the two-dimensional kagome metal (KV, Rb, Cs) with magnetic susceptibility, resistivity, and heat capacity measurements.
Abstract: Here we report the observation of bulk superconductivity in single crystals of the two-dimensional kagome metal ${\mathrm{KV}}_{3}{\mathrm{Sb}}_{5}$. Magnetic susceptibility, resistivity, and heat capacity measurements reveal superconductivity below ${T}_{c}=0.93\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, and density functional theory (DFT) calculations further characterize the normal state as a ${\mathbb{Z}}_{2}$ topological metal. Our results demonstrate that the recent observation of superconductivity within the related kagome metal ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ is likely a common feature across the $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A$: K, Rb, Cs) family of compounds and establishes them as a rich arena for studying the interplay between bulk superconductivity, topological surface states, and likely electronic density wave order in an exfoliable kagome lattice.
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TL;DR: In this paper, the authors used high-resolution scanning tunnelling microscopy to discover an unconventional chiral charge order in a kagome material, KV3Sb5, with both a topological band structure and a superconducting ground state.
Abstract: Intertwining quantum order and non-trivial topology is at the frontier of condensed matter physics1–4. A charge-density-wave-like order with orbital currents has been proposed for achieving the quantum anomalous Hall effect5,6 in topological materials and for the hidden phase in cuprate high-temperature superconductors7,8. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy to discover an unconventional chiral charge order in a kagome material, KV3Sb5, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2 × 2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2 × 2 charge modulation exhibits an intensity reversal in real space, signalling charge ordering. At the impurity-pinning-free region, the strength of intrinsic charge modulations further exhibits chiral anisotropy with unusual magnetic field response. Theoretical analysis of our experiments suggests a tantalizing unconventional chiral charge density wave in the frustrated kagome lattice, which can not only lead to a large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity. An unconventional chiral charge order is observed in a kagome superconductor by scanning tunnelling microscopy. This charge order has unusual magnetic tunability and intertwines with electronic topology.
275 citations
TL;DR: In this paper, the interplay between CDW and superconductivity in a topological kagome metal has been studied using measurements of resistivity, dc and ac magnetic susceptibility under various pressures up to 6 GPa.
Abstract: ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ 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.
209 citations
TL;DR: In this article, the authors investigated the electronic and structural properties of charge density wave (CDW) by first-principles calculations and revealed an inverse Star of David deformation as the $2\ifmmode\times\else\texttimes\fi{}2
Abstract: 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.
199 citations
TL;DR: In this paper, the anomalous Hall effect (AHE) typically occurs in ferromagnetic materials but is not expected in conventional superconductors, and the authors find a giant AHE in the kagome superconductor CsV${}_{3}$Sb${}-5}$.
Abstract: 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
173 citations
TL;DR: In this paper, a temperature-dependent cascade of different symmetry-broken electronic states in a new kagome superconductor, CsV3Sb5, was discovered using spectroscopic imaging scanning tunnelling microscopy.
Abstract: The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology1–18, which continues to bear surprises. Here, using spectroscopic imaging scanning tunnelling microscopy, we discover a temperature-dependent cascade of different symmetry-broken electronic states in a new kagome superconductor, CsV3Sb5. We reveal, at a temperature far above the superconducting transition temperature Tc ~ 2.5 K, a tri-directional charge order with a 2a0 period that breaks the translation symmetry of the lattice. As the system is cooled down towards Tc, we observe a prominent V-shaped spectral gap opening at the Fermi level and an additional breaking of the six-fold rotational symmetry, which persists through the superconducting transition. This rotational symmetry breaking is observed as the emergence of an additional 4a0 unidirectional charge order and strongly anisotropic scattering in differential conductance maps. The latter can be directly attributed to the orbital-selective renormalization of the vanadium kagome bands. Our experiments reveal a complex landscape of electronic states that can coexist on a kagome lattice, and highlight intriguing parallels to high-Tc superconductors and twisted bilayer graphene. A study reveals a temperature-dependent cascade of different symmetry-broken electronic states in the kagome superconductor CsV3Sb5, and highlights intriguing parallels between vanadium-based kagome metals and materials exhibiting similar electronic phases.
168 citations
References
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TL;DR: A simple derivation of a simple GGA is presented, in which all parameters (other than those in LSD) are fundamental constants, and only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked.
Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif
146,533 citations
"Superconductivity in the Z 2 kagome..." refers methods in this paper
...In order to address potential orbital localization (particularly V d) and the van der Waals forces that play a role in c-layer stacking in this compound, we performed simulations using the SCAN functional [22] and D2/D3 [23, 24] dispersion corrections as well as the more standard PBE functional [25]....
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TL;DR: An efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set is presented and the application of Pulay's DIIS method to the iterative diagonalization of large matrices will be discussed.
Abstract: We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order ${\mathit{N}}_{\mathrm{atoms}}^{3}$ operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special ``metric'' and a special ``preconditioning'' optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order ${\mathit{N}}_{\mathrm{atoms}}^{2}$ scaling is found for systems containing up to 1000 electrons. If we take into account that the number of k points can be decreased linearly with the system size, the overall scaling can approach ${\mathit{N}}_{\mathrm{atoms}}$. We have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable. \textcopyright{} 1996 The American Physical Society.
81,985 citations
IBM1
TL;DR: An approach for electronic structure calculations is described that generalizes both the pseudopotential method and the linear augmented-plane-wave (LAPW) method in a natural way and can be used to treat first-row and transition-metal elements with affordable effort and provides access to the full wave function.
Abstract: An approach for electronic structure calculations is described that generalizes both the pseudopotential method and the linear augmented-plane-wave (LAPW) method in a natural way. The method allows high-quality first-principles molecular-dynamics calculations to be performed using the original fictitious Lagrangian approach of Car and Parrinello. Like the LAPW method it can be used to treat first-row and transition-metal elements with affordable effort and provides access to the full wave function. The augmentation procedure is generalized in that partial-wave expansions are not determined by the value and the derivative of the envelope function at some muffin-tin radius, but rather by the overlap with localized projector functions. The pseudopotential approach based on generalized separable pseudopotentials can be regained by a simple approximation.
61,450 citations
TL;DR: In this paper, the formal relationship between US Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived and the Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional.
Abstract: The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Bl\"ochl's projector augmented wave (PAW) method is derived. It is shown that the total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addition, critical tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed core all electron methods. These tests include small molecules $({\mathrm{H}}_{2}{,\mathrm{}\mathrm{H}}_{2}{\mathrm{O},\mathrm{}\mathrm{Li}}_{2}{,\mathrm{}\mathrm{N}}_{2}{,\mathrm{}\mathrm{F}}_{2}{,\mathrm{}\mathrm{BF}}_{3}{,\mathrm{}\mathrm{SiF}}_{4})$ and several bulk systems (diamond, Si, V, Li, Ca, ${\mathrm{CaF}}_{2},$ Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
57,691 citations
TL;DR: A detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set is presented in this article. But this is not a comparison of our algorithm with the one presented in this paper.
47,666 citations