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We report measurements of the local temperature-dependent penetration depth, $\lambda(T)$, in the Kagome superconductors AV$_3$Sb$_5$ (A = Cs, K, Rb) using scanning superconducting quantum interference device (SQUID) microscopy. Our results suggest that the superconducting order in all three compounds is fully gapped, in contrast to reports of nodal superconductivity in KV$_3$Sb$_5$ and RbV$_3$Sb$_5$. Analysis of the temperature-dependent superfluid density, $\rho_s(T)$, shows deviations from the behavior expected for a single isotropic gap, but the data are well described by models incorporating either a single anisotropic gap or two isotropic gaps. Notably, the temperature dependences of $\lambda(T)$ and $\rho_s(T)$ in KV$_3$Sb$_5$ and RbV$_3$Sb$_5$ are qualitatively more similar to each other than to CsV$_3$Sb$_5$, consistent with the superconducting phase reflecting features of the normal-state band structure. Our findings provide a direct comparison of the superconducting properties across the AV$_3$Sb$_5$ family., Comment: 5 pages, 3 figures

Kagome superconductors AV$_{3}$Sb$_{5}$ provide a unique platform for studying the interplay between a variety of electronic orders, including superconductivity, charge density waves, nematic phases and more. Understanding the evolution of the electronic state from the charge density wave to the superconducting transition is essential for unraveling the interplay of charge, spin, and lattice degrees of freedom giving rise to the unusual magnetic properties of these nonmagnetic metals. Previous zero-field and high-field $\mu$SR studies revealed two anomalies in the muon spin relaxation rate, a first change at $T_{CDW} \sim 100$ K and a second steep increase at $T^{*}\sim 40$ K, further enhanced by an applied magnetic field, thus suggesting a contribution of magnetic origin. In this study, we use the avoided level crossing $\mu$SR technique to investigate charge order in near-zero applied field. By tracking the temperature dependence of quadrupolar level-crossing resonances, we examined the evolution of the electric field gradient at V nuclei in the kagome plane. Our results show a significant rearrangement of the charge density starting at $T^{*}$ indicating a transition in the charge distribution, likely electronic in origin, well below $T_{CDW}$. These findings, combined with previous $\mu$SR, STM, and NMR studies, emphasize the intertwined nature of proximate phases in these systems, with the charge rearrangement dominating the additional increase in $\mu$SR relaxation rate below $T^{*}$.

We present X-ray scattering studies resolving structural twinning and phase separation in the charge density wave (CDW) state of the kagome superconductor CsV$_3$Sb$_5$. The three-dimensional CDW state in CsV$_3$Sb$_5$ is reported to form a complex superposition of Star of David (SoD) or Tri-Hexagonal (TrH) patterns of distortion within its kagome planes, but the out-of-plane stacking is marked by metastability. In order to resolve the impact of this metastability, we present reciprocal space mapping and real-space images of CsV$_3$Sb$_5$ collected across multiple length scales using temperature-dependent high-dynamic range mapping (HDRM) and dark-field X-ray microscopy (DFXM). The experimental data provide evidence for a rich microstructure that forms in the CDW state. Data evidence metastability in the formation of $2\times 2\times 4$ and $2\times 2\times 2$ CDW supercells dependent on thermal history and mechanical deformation. We further directly resolve the real space phase segregation of both supercells as well as a real-space, structural twinning driven by the broken rotational symmetry of the CDW state. Our combined results provide insights into the role of microstructure and twinning in experiments probing the electronic properties of CsV$_3$Sb$_5$ where rotational symmetry is broken by the three-dimensional charge density wave order but locally preserved for any single kagome layer., Comment: 12 pages, 9 figures

We report the observation of two-dimensional superconductivity (2D SC) in exfoliated kagome metal CsV$_3$Sb$_5$ with a thickness far thicker than the atomic limit. By examining the critical current and upper critical magnetic fields ($H_{c2}$) of 40-60 nm thick films in the superconducting state, we identify a pronounced Berezinskii-Kosterlitz-Thouless (BKT) transition behavior, i.e. a drastic decrease of the superfluid stiffness near the transition, and a cusp-like feature of the angular dependent $H_{c2}$, both of which serve as direct evidence of 2D SC. In addition, an exceeding of the Pauli paramagnetic limit of the in-plane $H_{c2}$ is consistent with the 2D SC nature. The observed 2D SC occurs in thick films with the highest superconducting transition temperature $T_c$ and the lowest charge density wave transition temperature $T_{\rm {CDW}}$, which suggests that the charge density wave states are interrelated with the superconducting states. Our findings impose constraints in understanding the enhancement of SC in kagome superconductors, and illuminate pathways for achieving novel 2D superconducting states in more stable and much thicker systems., Comment: 6 pages and 4 figures for the main text; 10 pages and 9 figures for the Supplementary Materials

The kagome superconductor CsV$_3$Sb$_5$ hosts a variety of charge density wave (CDW) phases, which play a fundamental role in the formation of other exotic electronic instabilities. However, identifying the precise structure of these CDW phases and their intricate relationships remain the subject of intense debate, due to the lack of static probes that can distinguish the CDW phases with identical spatial periodicity. Here, we unveil the competition between two coexisting $2\times2\times2$ CDWs in CsV$_3$Sb$_5$ harnessing time-resolved X-ray diffraction. By analyzing the light-induced changes in the intensity of CDW superlattice peaks, we demonstrate the presence of both phases, each displaying a significantly different amount of melting upon excitation. The anomalous light-induced sharpening of peak width further shows that the phase that is more resistant to photo-excitation exhibits an increase in domain size at the expense of the other, thereby showcasing a hallmark of phase competition. Our results not only shed light on the interplay between the multiple CDW phases in CsV$_3$Sb$_5$, but also establish a non-equilibrium framework for comprehending complex phase relationships that are challenging to disentangle using static techniques., Comment: 10 pages, 4 figures with supplemental Material

Exotic quantum solids can host electronic states that spontaneously break rotational symmetry of the electronic structure, such as electronic nematic phases and unidirectional charge density waves (CDWs). When electrons couple to the lattice, uniaxial strain can be used to anchor and control this electronic directionality. Here we reveal an unusual impact of strain on unidirectional "smectic" CDW orders in kagome superconductors AV3Sb5 using spectroscopic-imaging scanning tunneling microscopy. We discover local decoupling between the smectic electronic director axis and the direction of anisotropic strain. While the two are generally aligned along the same direction in regions of small CDW gap, the two become misaligned in regions where CDW gap is the largest. This in turn suggests nanoscale variations in smectic susceptibility, which we attribute to a combination of local strain and electron correlation strength. Overall, we observe an unusually high decoupling rate between the smectic electronic director of the 3-state Potts order and anisotropic strain, revealing weak smecto-elastic coupling in the CDW phase of kagome superconductors. This is phenomenologically different from the extensively studied nemato-elastic coupling in the Ising nematic phase of Fe-based superconductors, providing a contrasting picture of how strain can control electronic unidirectionality in different families of quantum materials.

The recent discovery of the AV$_3$Sb$_5$ (A=K, Rb, Cs) kagome superconductors launched a growing field of research investigating electronic instabilities in kagome metals. Specifically, the AV$_3$Sb$_5$ family naturally exhibits a Fermi level tuned to the Van Hove singularities associated with the saddle points formed from the prototypical kagome band structure. The charge density wave and superconducting states that form within the kagome networks of these compounds exhibit a number of anomalous properties reminiscent of theoretical predictions of exotic states in kagome metals tuned close to their Van Hove fillings. Here we provide an overview of the key structural and electronic features of AV$_3$Sb$_5$ compounds and review the status of investigations into their unconventional electronic phase transitions., Comment: 6 figures, 17 pages

A wide array of unusual phenomena has recently been uncovered in kagome solids. The charge density wave (CDW) state in the kagome superconductor AV3Sb5 in particular intrigued the community -- the CDW phase appears to break the time-reversal symmetry despite the absence of spin magnetism, which has been tied to exotic orbital loop currents possibly intertwined with magnetic field tunable crystal distortions. To test this connection, precise determination of the lattice response to applied magnetic field is crucial, but can be challenging at the atomic-scale. We establish a new scanning tunneling microscopy based method to study the evolution of the AV3Sb5 atomic structure as a function of magnetic field. The method substantially reduces the errors of typical STM measurements, which are at the order of 1% when measuring an in-plane lattice constant change. We find that the out-of-plane lattice constant of AV3Sb5 remains unchanged (within 10^-6) by the application of both in-plane and out-of-plane magnetic fields. We also reveal that the in-plane lattice response to magnetic field is at most at the order of 0.05%. Our experiments provide further constraints on time-reversal symmetry breaking in kagome metals, and establish a new tool for higher-resolution extraction of the field-lattice coupling at the nanoscale applicable to other quantum materials.

Here we study the effect of electron doping the kagome superconductor CsV$_3$Sb$_5$. Single crystals and powders of CsV$_3$Sb$_{5-x}$Te$_x$ are synthesized and characterized via magnetic susceptibility, nuclear quadrupole resonance, and x-ray diffraction measurements, where we observe a slight suppression of the charge density wave transition temperature and superconducting temperature with the introduction of electron dopants. In contrast to hole-doping, both transitions survive relatively unperturbed up to the solubility limit of Te within the lattice. A comparison is presented between the electronic phase diagrams of electron- and hole-tuned CsV$_3$Sb$_5$., Comment: 11 pages, 4 figures

Kagome materials have emerged as a setting for emergent electronic phenomena that encompass different aspects of symmetry and topology. It is debated whether the XV$_6$Sn$_6$ kagome family (where X is a rare earth element), a recently discovered family of bilayer kagome metals, hosts a topologically non-trivial ground state resulting from the opening of spin-orbit coupling gaps. These states would carry a finite spin-Berry curvature, and topological surface states. Here, we investigate the spin and electronic structure of the XV$_6$Sn$_6$ kagome family. We obtain evidence for a finite spin-Berry curvature contribution at the center of the Brillouin zone, where the nearly flat band detaches from the dispersing Dirac band because of spin-orbit coupling. In addition, the spin-Berry curvature is further investigated in the charge density wave regime of ScV$_6$Sn$_6$, and it is found to be robust against the onset of the temperature-driven ordered phase. Utilizing the sensitivity of angle resolved photoemission spectroscopy to the spin and orbital angular momentum, our work unveils the spin-Berry curvature of topological kagome metals, and helps to define its spectroscopic fingerprint., Comment: 21 pages, 4 figures

Kagome metals AV3Sb5 (A = K, Cs, Rb) provide a rich platform for intertwined orders, where evidence for time-reversal symmetry breaking, likely due to the long-sought loop currents, has emerged in STM and muon spin relaxation experiments. An isotropic component in the spontaneous optical rotation has also been reported, and it was interpreted as the magneto-optic Kerr effect arising from time-reversal symmetry breaking. Intriguingly, the observed rotations differ by five orders of magnitude between different wavelengths and samples, suggesting more intricate physics. Here we report optical rotation and polar Kerr measurements in CsV3Sb5 crystals at the same wavelength. We observe large isotropic components of 1 milliradian in the optical rotation that do not respond to applied magnetic fields but flip sign between samples, while the spontaneous Kerr signal is less than 20 nanoradian. Our results prove unambiguously that the reported isotropic rotation is not related to time-reversal symmetry breaking but instead indicates a new intertwined order that onsets at the same temperature., Comment: 15 pages, 8 figures, submitted version

The kagome superconductor family AV3Sb5 (A=Cs, K, Rb) emerged as an exciting platform to study exotic Fermi surface instabilities. Here we use spectroscopic-imaging scanning tunneling microscopy (SI-STM) and angle-resolved photoemission spectroscopy (ARPES) to reveal how the surprising cascade of higher and lower-dimensional density waves in CsV3Sb5 is intimately tied to a set of small reconstructed Fermi pockets. ARPES measurements visualize the formation of these pockets generated by a 3D charge density wave transition. The pockets are connected by dispersive q* wave vectors observed in Fourier transforms of STM differential conductance maps. As the additional 1D charge order emerges at a lower temperature, q* wave vectors become substantially renormalized, signaling further reconstruction of the Fermi pockets. Remarkably, in the superconducting state, the superconducting gap modulations give rise to an in-plane Cooper pair-density-wave at the same q* wave vectors. Our work demonstrates the intrinsic origin of the charge-stripes and the pair-density-wave in CsV3Sb5 and their relationship to the Fermi pockets. These experiments uncover a unique scenario of how Fermi pockets generated by a parent charge density wave state can provide a favorable platform for the emergence of additional density waves.

The kagome superconductors KV$_3$Sb$_5$, RbV$_3$Sb$_5$, and CsV$_3$Sb$_5$ are known to display charge density wave (CDW) order which impacts the topological characteristics of their electronic structure. Details of their structural ground states and how they evolve with temperature are revealed here using single crystal X-ray crystallographic refinements as a function of temperature, carried out with synchrotron radiation. The compounds KV$_3$Sb$_5$ and RbV$_3$Sb$_5$ present 2$\times$2$\times$2 superstructures in the $Fmmm$ space group with a staggered tri-hexagonal deformation of vanadium layers. CsV$_3$Sb$_5$ displays more complex structural evolution, whose details have been unravelled by applying machine learning methods to the scattering data. Upon cooling through the CDW transition, CsV$_3$Sb$_5$ displays a staged progression of ordering from a 2$\times$2$\times$1 supercell and a 2$\times$2$\times$2 supercell into a final 2$\times$2$\times$4 supercell that persists to $T$ = 11 K and exhibits an average structure where vanadium layers display both tri-hexagonal and Star of David patterns of deformations. Diffraction from CsV$_3$Sb$_5$ under pulsed magnetic fields up to $\mu_0H$ = 28 T suggest the real component of the CDW state is insensitive to external magnetic fields., Comment: 9 pages, 6 figures

Layered crystalline materials that consist of transition metal atoms on a kagome network have emerged as a versatile platform to study unusual electronic phenomena. For example, in the vanadium-based kagome superconductors AV3Sb5 (where A can stand for K, Cs, or Rb) there is a parent charge density wave phase that appears to simultaneously break both the translational and the rotational symmetry of the lattice. Here, we show a contrasting situation where electronic nematic order - the breaking of rotational symmetry without the breaking of translational symmetry - can occur without a corresponding charge density wave. We use spectroscopic-imaging scanning tunneling microscopy to study the kagome metal CsTi3Bi5 that is isostructural to AV3Sb5 but with a titanium atom kagome network. CsTi3Bi5 does not exhibit any detectable charge density wave state, but comparison to density functional theory calculations reveals substantial electronic correlation effects at low energies. Comparing the amplitudes of scattering wave vectors along different directions, we discover an electronic anisotropy that breaks the six-fold symmetry of the lattice, arising from both in-plane and out-of-plane titanium-derived d orbitals. Our work uncovers the role of electronic orbitals in CsTi3Bi5, suggestive of a hexagonal analogue of the nematic bond order in Fe-based superconductors., Comment: This is the submitted version. Final manuscript will appear in Nature Physics

In this work we explore the chemical-property phase diagram of the AV$_3$Sb$_5$ family through A-site alloying. We demonstrate full miscibility of the alkali-site, highlighting that the three parent compounds are the terminal ends of a single solid-solution. Using both polycrystalline and single crystal methods, we map the dependence of the two primary electronic instabilities: (1) the onset of charge density wave (CDW) order ($T_\text{CDW}$) and (2) the onset of superconductivity ($T_\text{c}$) with alkali-site composition. We show continuous trends in both $T_\text{CDW}$ and $T_\text{c}$, including a region of enhanced CDW stability in K$_{1-x}$Cs$_{x}$V$_3$Sb$_5$ alloys. Together, our results open new routes for chemical perturbation and exploration of the chemical-property relationships in the class of AV$_3$Sb$_5$ kagome superconductors.

The recently discovered vanadium-based kagome metals AV$_3$Sb$_5$ (A = K, Rb, Cs) offer the possibility to study the interplay between competing electronic orderings, such as charge density order and superconductivity. We focus on the former and provide a comprehensive set of $^{51}$V, $^{87}$Rb, and $^{121}$Sb magnetic resonance measurements on an RbV$_3$Sb$_5$ single crystal. Elucidating the symmetries and properties of the CDW phase is essential to understanding the unconventional electronic orderings occurring in this material. We establish the structure of the $2\times 2 \times 2$ superlattice that describes the system below the charge density wave transition by combining both experimental and computational methods, with a methodology that can be readily applied to the remaining compounds of the same family. Our results give compelling evidence that the CDW structure occurring below 103 K for RbV$_3$Sb$_5$ is the so-called Inverse Start of David pattern $\pi$-shifted along the c axis (also known as staggered tri-hexagonal).

The kagom\'e metals RbTi$_3$Bi$_5$ and CsTi$_3$Bi$_5$ were synthesized both as polycrystalline powders by heating the elements an argon atmosphere and as single crystals grown using a self-flux method. The compounds crystallize in the hexagonal crystal system isotypically to KV$_3$Sb$_5$ (P6/mmm, Z = 1, CsTi3Bi5: a = 5.7873(1) {\AA}, c = 9.2062(1) {\AA}; RbTi3Bi5: a = 5.773(1) {\AA}, c = 9.065(1) {\AA}). Titanium atoms form a kagom\'e net with bismuth atoms in the hexagons as well as above and below the triangles. The alkali metal atoms are coordinated by 12 bismuth atoms and form AlB$_2$-like slabs between the kagom\'e layers. Magnetic susceptibility measurements with CsTi$_3$Bi$_5$ and RbTi$_3$Bi$_5$ single crystals reveal Pauli-paramagnetism and traces of superconductivity caused by CsBi$_2$/RbBi$_2$ impurities. Magnetotransport measurements reveal conventional Fermi liquid behavior and quantum oscillations indicative of a single dominant orbit at low temperature. DFT calculations show the characteristic metallic kagom\'e band structure similar to that of CsV$_3$Sb$_5$ with reduced band filling. A symmetry analysis of the band structure does not reveal an obvious and unique signature of a nontrivial topology., Comment: 20 pages, 5 Figures, submitted

We report high resolution polar Kerr effect measurements on CsV${}_3$Sb${}_5$ single crystals in search for signatures of spontaneous time reversal symmetry breaking below the charge order transition at $T^* \approx 94$ K. Utilizing two different versions of zero-area loop Sagnac interferometers operating at 1550 nm wavelength, each with the fundamental attribute that without a time reversal symmetry breaking sample at its path, the interferometer is perfectly reciprocal, we find no observable Kerr effect to within the noise floor limit of the apparatus at 30 nanoradians. Simultaneous coherent reflection ratio measurements confirm the sharpness of the charge order transition in the same optical volume as the Kerr measurements. At finite magnetic field we observe a sharp onset of a diamagnetic shift in the Kerr signal at $T^*$, which persists down to the lowest temperature without change in trend. Since 1550 nm is an energy that was shown to capture all features of the optical properties of the material that interact with the charge order transition, we are led to conclude that it is highly unlikely that time reversal symmetry is broken in the charge ordered state in CsV${}_3$Sb${}_5$., Comment: 11 pages, 8 figures

High-pressure single-crystal x-ray diffraction experiments reveal that the superconducting kagome metal CsV$_3$Sb$_5$ transforms from hexagonal ($P6/mmm$) to monoclinic ($C2/m$) symmetry above 10 GPa if nonhydrostatic pressure conditions are created in a diamond anvil cell with silicon oil as pressure-transmitting medium. This is contrary to the behavior of CsV$_3$Sb$_5$ under quasi-hydrostatic conditions in neon, with the hexagonal symmetry retained up to at least 20 GPa. Monoclinic distortion leaves the kagome planes almost unchanged but deforms honeycomb nets of the Sb atoms. While the onset of the distortion almost coincides with the reentrance of superconductivity, our \textit{ab initio} density-functional calculations reveal only minor changes in the electronic structure compared to the quasi-hydrostatic case. In particular, Fermi surface reconstruction driven by the formation of interlayer Sb-Sb bonds is observed in both monoclinic and hexagonal CsV$_3$Sb$_5$ structures at high pressures and comes out as the likely cause for the reentrant behavior., Comment: published version: 5 pages + Supplemental Material, 4 figures, 2 tables

We track the evolution of charge correlations in the kagome superconductor CsV$_3$Sb$_5$ as its parent, long-ranged charge density order is destabilized. Upon hole-doping doping, interlayer charge correlations rapidly become short-ranged and their periodicity is reduced by half along the interlayer direction. Beyond the peak of the first superconducting dome, the parent charge density wave state vanishes and incommensurate, quasi-1D charge correlations are stabilized in its place. These competing, unidirectional charge correlations demonstrate an inherent electronic rotational symmetry breaking in CsV$_3$Sb$_5$, independent of the parent charge density wave state and reveal a complex landscape of charge correlations across the electronic phase diagram of this class of kagome superconductors. Our data suggest an inherent 2$k_f$ charge instability and the phenomenology of competing charge instabilities is reminiscent of what has been noted across several classes of unconventional superconductors., Comment: 6 pages, 4 figures

The family of AV$_3$Sb$_5$ (A = K, Rb, Cs) kagome metals exhibit charge density wave (CDW) order, proposed to be chiral, followed by a lower temperature superconducting state. Recent studies have proposed the importance of band structure saddle points proximal to the Fermi energy in governing these two transitions. Here we show the effects of hole-doping achieved via chemical substitution of Sn for Sb on the CDW and superconducting states in both KV$_3$Sb$_5$ and RbV$_3$Sb$_5$, and generate a phase diagram. Hole-doping lifts the $\Gamma$ pocket and van Hove singularities (vHs) toward $E_F$ causing the superconducting $T_C$ in both systems to increase to about 4.5 K, while rapidly suppressing the CDW state., Comment: 6 pages, 4 figures

Kagome metals AV3Sb5 (where the A can stand for K, Cs, or Rb) display a rich phase diagram of correlated electron states, including superconductivity and density waves. Within this landscape, recent experiments revealed signs of a transition below approximately 35 K attributed to an electronic nematic phase that spontaneously breaks rotational symmetry of the lattice. Here, we show that rotational symmetry breaking initiates universally at a high temperature in these materials, toward the 2 x 2 charge density wave transition temperature. We do this via spectroscopic-imaging scanning tunneling microscopy and study atomic-scale signatures of electronic symmetry breaking across several materials in the AV3Sb5 family: CsV3Sb5, KV3Sb5 and Sn-doped CsV3Sb5. Below a significantly lower temperature of about 30 K, we measure quantum interference of quasiparticles, a key signature for the formation of a coherent electronic state. These quasiparticles display a pronounced unidirectional feature in reciprocal space that strengthens as the superconducting state is approached. Our experiments reveal that high-temperature rotation symmetry breaking and the charge ordering states are separated from the superconducting ground state by an intermediate-temperature regime with coherent unidirectional quasiparticles. This picture is phenomenologically different compared to that in high-temperature superconductors, shedding light on the complex nature of rotation symmetry breaking in AV3Sb5 kagome superconductors.

In kagome metals AV3Sb5 (A = K, Rb, Cs), three-dimensional charge order (3D-CO) is the primary instability that sets the stage for other collective orders to emerge, including unidirectional stripe order, orbital flux order, electronic nematicity, and superconductivity. Here, we use high-resolution angle-resolved photoemission spectroscopy to determine the microscopic structure of three-dimensional charge order (3D-CO) in AV3Sb5 and its interplay with superconductivity. Our approach is based on identifying an unusual splitting of kagome bands induced by 3D-CO, which provides a sensitive way to refine the spatial charge patterns in neighboring kagome planes. We found a marked dependence of the 3D-CO structure on composition and doping. The observed difference between CsV3Sb5 and the other compounds potentially underpins the double-dome superconductivity in CsV3(Sb,Sn)5 and the suppression of Tc in KV3Sb5 and RbV3Sb5. Our results provide fresh insights into the rich phase diagram of AV3Sb5., Comment: 20 pages, 5 figures

The recently discovered layered kagome metals AV$_3$Sb$_5$(A=K, Rb, Cs) have attracted much attention because of their unique combination of superconductivity, charge density wave (CDW) order, and nontrivial band topology. The CDW order with an in-plane 2x2 reconstruction is found to exhibit exotic properties, such as time-reversal symmetry breaking and rotational symmetry breaking. However, the nature of the CDW, including its dimensionality, structural pattern, and effect on electronic structure, remains elusive despite intense research efforts. Here, using angle-resolved photoemission spectroscopy, we unveil for the first time characteristic double-band splittings and band reconstructions, as well as the band gap resulting from band folding, in the CDW phase. Supported by density functional theory calculations, we unambiguously show that the CDW in AV$_3$Sb$_5$ originates from the intrinsic coexistence of Star-of-David and Tri-Hexagonal distortions. The alternating stacking of these two distortions naturally leads to three-dimensional 2x2x2 or 2x2x4 CDW order. Our results provide crucial insights into the nature and distortion pattern of the CDW order, thereby laying down the basis for a substantiated understanding of the exotic properties in the family of AV$_3$Sb$_5$ kagome metals.

The recently reported \textit{A}V$_3$Sb$_5$ (\textit{A} = K, Rb, Cs) family of kagome metals are candidates for unconventional superconductivity and chiral charge density wave (CDW) order; both potentially arise from nested saddle points in their band structures close to the Fermi energy. Here we use chemical substitution to introduce holes into CsV$_3$Sb$_{5}$ and unveil an unconventionalcoupling of the CDW and superconducting states. Specifically, we generate a phase diagram for CsV$_3$Sb$_{5-x}$Sn$_{x}$ that illustrates the impact of hole-doping the system and lifting the nearest vHs toward and above $E_F$. Superconductivity exhibits a non-monotonic evolution with the introduction of holes, resulting in two "domes" peaked at 3.6\,K and 4.1\,K and the rapid suppression of three-dimensional CDW order. The evolution of CDW and superconducting order is compared with the evolution of the electronic band structure of CsV$_3$Sb$_{5-x}$Sn$_x$, where the complete suppression of superconductivity seemingly coincides with an electron-like band comprised of Sb $p_z$ orbitals pushed above E$_F$., Comment: 6 pages, 4 figures

The interplay of superconductivity with electronic and structural instabilities on the kagome lattice provides a fertile ground for the emergence of unusual phenomena. The vanadium-based kagome metals $A$V$_3$Sb$_5$ ($A=$ K, Rb, Cs) exhibit superconductivity on an almost ideal kagome lattice, with the superconducting transition temperature $T_{\rm c}$ forming two domes upon pressure-tuning. The first dome arises from the competition between superconductivity and a charge-density-wave, whereas the origin for the second dome remains unclear. Herein, we show that the appearance of the second superconducting dome in KV$_3$Sb$_5$ and RbV$_3$Sb$_5$ is associated with transitions from hexagonal $P6$/$mmm$ to monoclinic $P2$/$m$ structures, evidenced by splitting of structural peaks from synchrotron powder X-ray diffraction experiments and imaginary phonon frequencies in first-principles calculations. In KV$_3$Sb$_5$, transition to an orthorhombic $Pmmm$ structure is further observed for pressure $p\gtrsim20$ GPa, and is correlated with the strong suppression of $T_{\rm c}$ in the second superconducting dome. Our findings indicate distortions of the crystal structure modulates superconductivity in $A$V$_3$Sb$_5$ under pressure, providing a platform to study the emergence of superconductivity in the presence of multiple structural instabilities.

The quasi two-dimensional (quasi-2D) kagome materials AV$_3$Sb$_5$ (A=K, Rb, Cs) were found to be a prime example of kagome superconductors, a new quantum platform to investigate the interplay between electron correlation effects, topology and geometric frustration. In this review, we report recent progress on the experimental and theoretical studies of AV$_3$Sb$_5$ and provide a broad picture of this fast-developing field in order to stimulate an expanded search for unconventional kagome superconductors. We review the electronic properties of AV$_3$Sb$_5$, the experimental measurements of the charge density wave state, evidence of time-reversal symmetry breaking, and other potential hidden symmetry breaking in these materials. A variety of theoretical proposals and models that address the nature of the time-reversal symmetry breaking are discussed. Finally, we review the superconducting properties of AV$_3$Sb$_5$, especially the potential pairing symmetries and the interplay between superconductivity and the charge density wave state., Comment: A review on kagome superconductors AV$_3$Sb$_5$, including 14 pages and 9 figures

The kagome metals $A$V$_3$Sb$_5$ ($A=$ K, Rb, Cs) under ambient pressure exhibit an unusual charge order, from which superconductivity emerges. In this work, by applying hydrostatic pressure using a liquid pressure medium and carrying out electrical resistance measurements for RbV$_3$Sb$_5$, we find the charge order becomes suppressed under a modest pressure $p_{\rm c}$ ($1.4

The kagome lattice is host to flat bands, topological electronic structures, Van Hove singularities and diverse electronic instabilities, providing an ideal platform for realizing highly tunable electronic states. Here, we report soft- and mechanical- point-contact spectroscopy (SPCS and MPCS) studies of the kagome superconductors KV$_3$Sb$_5$ and CsV$_3$Sb$_5$. Compared to the superconducting transition temperature $T_{\rm c}$ from specific heat measurements (2.8~K for CsV$_3$Sb$_5$ and 1.0~K for KV$_3$Sb$_5$), significantly enhanced values of $T_{\rm c}$ are observed via the zero-bias conductance of SPCS ($\sim$4.2~K for CsV$_3$Sb$_5$ and $\sim$1.8~K for KV$_3$Sb$_5$), which become further enhanced in MPCS measurements ($\sim$5.0~K for CsV$_3$Sb$_5$ and $\sim$3.1~K for KV$_3$Sb$_5$). While the differential conductance curves from SPCS are described by a two-gap $s$-wave model, a single $s$-wave gap reasonably captures the MPCS data, likely due to a diminishing spectral weight of the other gap. The enhanced superconductivity probably arises from local strain caused by the point-contact, which also leads to the evolution from two-gap to single-gap behaviors in different point-contacts. Our results demonstrate highly strain-sensitive superconductivity in kagome metals CsV$_3$Sb$_5$ and KV$_3$Sb$_5$, which may be harnessed in the manipulation of possible Majorana zero modes.

The interplay of different electronic phases underlies the physics of unconventional superconductors. One of the most intriguing examples is a high-Tc superconductor FeTe1-xSex: it undergoes both a topological transition, linked to the electronic band inversion, and an electronic nematic phase transition, associated with rotation symmetry breaking, around the same critical composition xc where superconducting Tc peaks. At this regime, nematic fluctuations and symmetry-breaking strain could have an enormous impact, but this is yet to be fully explored. Using spectroscopic-imaging scanning tunneling microscopy, we study the electronic nematic transition in FeTe1-xSex as a function of composition. Near xc, we reveal the emergence of electronic nematicity in nanoscale regions. Interestingly, we discover that superconductivity is drastically suppressed in areas where static nematic order is the strongest. By analyzing atomic displacement in STM topographs, we find that small anisotropic strain can give rise to these strongly nematic localized regions. Our experiments reveal a tendency of FeTe1-xSex near x~0.45 to form puddles hosting static nematic order, suggestive of nematic fluctuations pinned by structural inhomogeneity, and demonstrate a pronounced effect of anisotropic strain on superconductivity in this regime., Comment: This is the original submitted version. The final version will appear in Nature Physics

The new two-dimensional (2D) kagome superconductor CsV$_3$Sb$_5$ has attracted much recent attention due to the coexistence of superconductivity, charge order, topology and kagome physics. A key issue in this field is to unveil the unique reconstructed electronic structure, which successfully accommodates different orders and interactions to form a fertile ground for emergent phenomena. Here, we report angle-resolved photoemission spectroscopy (ARPES) evidence for two distinct band reconstructions in CsV$_3$Sb$_5$. The first one is characterized by the appearance of new electron energy band at low temperature. The new band is theoretically reproduced when the three dimensionality of the charge order is considered for a band-folding along the out-of-plane direction. The second reconstruction is identified as a surface induced orbital-selective shift of the electron energy band. Our results provide the first evidence for the three dimensionality of the charge order in single-particle spectral function, highlighting the importance of long-range out-of-plane electronic correlations in this layered kagome superconductor. They also point to the feasibility of orbital-selective control of the band structure via surface modification, which would open a new avenue for manipulating exotic phenomena in this system, including superconductivity.

The layered vanadium antimonides AV3Sb5 (A = K, Rb, Cs) are a recently discovered family of topological kagome metals with a rich phenomenology of strongly correlated electronic phases including charge order and superconductivity. Understanding how the singularities inherent to the kagome electronic structure are linked to the observed many-body phases is a topic of great interest and relevance. Here, we combine angle-resolved photoemission spectroscopy and density functional theory to reveal multiple kagome-derived van Hove singularities (vHs) coexisting near the Fermi level of CsV3Sb5 and analyze their contribution to electronic symmetry breaking. Intriguingly, the vHs in CsV3Sb5 have two distinct flavors - p-type and m-type - which originate from their pure and mixed sublattice characters, respectively. This twofold vHs is unique property of the kagome lattice, and its flavor critically determines the pairing symmetry and ground states emerging in AV3Sb5 series. We establish that, among the multiple vHs in CsV3Sb5, the m-type vHs of the dxz/dyz kagome band and the p-type vHs of the dxy/dx2-y2 kagome band cross the Fermi level to set the stage for electronic symmetry breaking. The former band exhibits pronounced Fermi surface nesting, while the latter contributes via higher-order vHs. Our work reveals the essential role of kagome-derived vHs for the collective phenomena realized in the AV3Sb5 family, paving the way to a deeper understanding of strongly correlated topological kagome systems., Comment: Submitted to Nature Physics on May 28th, 2021. A revised version will appear in Nature Physics

Pressure evolution of the superconducting kagome metal CsV$_3$Sb$_5$ is studied with single-crystal x-ray diffraction and density-functional band-structure calculations. A highly anisotropic compression observed up to 5 GPa is ascribed to the fast shrinkage of the Cs-Sb distances and suppression of Cs rattling motion. This prevents Sb displacements required to stabilize the three-dimensional charge-density-wave (CDW) order and elucidates the disappearance of the CDW already at 2 GPa despite only minor changes in the electronic structure of the normal state. At higher pressures, vanadium bands still change only marginally, whereas antimony bands undergo a major reconstruction caused by the gradual formation of the interlayer Sb-Sb bonds. Our results exclude pressure tuning of vanadium kagome bands as the main mechanism for the non-trivial evolution of superconductivity in real-world kagome metals. Concurrently, we establish the central role of Sb atoms in the stabilization of a three-dimensional CDW and Fermi surface reconstruction., Comment: published version

The diversity of emergent phenomena in quantum materials often arises from the interplay between different physical energy scales or broken symmetries. Cooperative interactions among them are rare; however, when they do occur, they often stabilize fundamentally new ground states or phase behaviors. For instance, a pair density wave can form when the superconducting order parameter borrows spatial periodical variation from charge order; a topological superconductor can arise when topologically nontrivial electronic states proximitize with or participate in the formation of the superconducting condensate. Here, we report spectroscopic evidence for a unique synergy of topology and correlation effects in the kagome superconductor CsV$_3$Sb$_5$ - one where topologically nontrivial surface states are pushed below the Fermi energy (E$_F$) by charge order, making the topological physics active near E$_F$ upon entering the superconducting state. Flat bands are observed, indicating that electron correlation effects are also at play in this system. Our results reveal the peculiar electronic structure of CsV$_3$Sb$_5$, which holds the potential for realizing Majorana zero modes and anomalous superconducting states in kagome lattices. They also establish CsV$_3$Sb$_5$ as a unique platform for exploring the cooperation between the charge order, topology, correlation effects and superconductivity.

The iron-based superconductor FeTe$_{1-x}$Se$_{x}$ has attracted considerable attention as a candidate topological superconductor owing to a unique combination of topological surface states and bulk high-temperature superconductivity. The superconducting properties of as-grown single crystals, however, are highly variable and synthesis dependent due to excess interstitial iron impurities incorporated during growth. Here we report a novel physicochemical process for pumping this interstitial iron out of the FeTe$_{1-x}$Se$_{x}$ matrix and achieving bulk superconductivity. Our method should have significant value for the synthesis of high-quality single crystals of FeTe$_{1-x}$Se$_{x}$ with large superconducting volume fractions.

Recently discovered kagome superconductors AV3Sb5 (A=K, Rb, Cs) provide a fresh opportunity to realize and study correlation-driven electronic phenomena on a kagome lattice. The observation of a 2a0 by 2a0 charge density wave (CDW) in the normal state of all members of AV3Sb5 kagome family has generated an enormous amount of interest, in an effort to uncover the nature of this CDW state, and identify any "hidden" broken symmetries. We use spectroscopic-imaging scanning tunneling microscopy to reveal a pronounced intensity anisotropy between different 2a0 CDW directions in KV3Sb5. In particular, by examining the strength of ordering wave vectors as a function of energy in Fourier transforms of differential conductance maps, we find that one of the CDW directions is distinctly different compared to the other two. This observation points towards an intrinsic rotation symmetry broken electronic ground state, where the symmetry is reduced from C6 to C2. Furthermore, in contrast to previous reports, we find that the CDW phase is insensitive to magnetic field direction, regardless of the presence or absence of atomic defects. Our experiments, combined with earlier observations of a stripe 4a0 charge ordering in CsV3Sb5, establish correlation-driven rotation symmetry breaking as a unifying feature of AV3Sb5 kagome superconductors.

The recently discovered family of AV$_3$Sb$_5$ (A: K, Rb Cs) kagome metals possess a unique combination of nontrivial band topology, superconducting ground states, and signatures of electron correlations manifest via competing charge density wave order. Little is understood regarding the nature of the charge density wave (CDW) instability inherent to these compounds and the potential correlation with the accompanying onset of a large anomalous Hall response. To understand the impact of the CDW order on the electronic structure in these systems, we present quantum oscillation measurements on single crystals of CsV$_3$Sb$_5$. Our data provides direct evidence that the CDW invokes a substantial reconstruction of the Fermi surface pockets associated with the vanadium orbitals and the kagome lattice framework. In conjunction with density functional theory modeling, we are able to identify split oscillation frequencies originating from reconstructed pockets built from vanadium orbitals and Dirac-like bands. Complementary diffraction measurements are further able to demonstrate that the CDW instability has a correlated phasing between neighboring V$_3$Sb$_5$ planes. These results provide critical insights into the underlying CDW instability in AV$_3$Sb$_5$ kagome metals and support minimal models of CDW order arising from within the vanadium-based kagome lattice., Comment: 12 pages, 9 figures

The recently discovered kagome metal series $A$V$_3$Sb$_5$ ($A$=K, Rb, Cs) exhibits topologically nontrivial band structures, chiral charge order and superconductivity, presenting a unique platform for realizing exotic electronic states. The nature of the superconducting state and the corresponding pairing symmetry are key questions that demand experimental clarification. Here, using a technique based on the tunneling diode oscillator, the magnetic penetration depth $\Delta\lambda(T)$ of CsV$_3$Sb$_5$ was measured down to 0.07 K. A clear exponential behavior in $\Delta\lambda(T)$ with marked deviations from a $T$ or $T^2$ temperature dependence is observed at low temperatures, indicating a deficiency of nodal quasiparticles. Temperature dependence of the superfluid density and electronic specific heat can be described by two-gap $s$-wave superconductivity, consistent with the presence of multiple Fermi surfaces in CsV$_3$Sb$_5$. These results evidence nodeless superconductivity in CsV$_3$Sb$_5$ under ambient pressure, and constrain the allowed pairing symmetry.

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 lattice. As the system is cooled down towards Tc, we observe a prominent V-shape spectral gap opening at the Fermi level and an additional breaking of the six-fold rotation symmetry, which persists through the superconducting transition. This rotation 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 V kagome bands. Our experiments reveal a complex landscape of electronic states that can co-exist on a kagome lattice, and provide intriguing parallels to high-Tc superconductors and twisted bilayer graphene.

The kagome metal KV$_3$Sb$_5$ hosts charge order, topologically nontrivial Dirac band crossings, and a superconducting ground state with unconventional characteristics, providing an ideal platform to investigate the interplay between different electronic states on the kagome lattice. Here we study the evolution of charge order and superconductivity in KV$_3$Sb$_5$ under hydrostatic pressure using electrical resistivity measurements. With the application of pressure, the superconducting transition temperature $T_{\rm c}=0.9$ K under ambient pressure quickly increases to 3.1 K at $p=0.4$ GPa, as charge order progressively weakens. Upon further increasing pressure, signatures of charge order disappears at $p_{\rm c1}\approx0.5$ GPa and $T_{\rm c}$ is gradually suppressed, forming a superconducting dome that terminates at $p\approx10$ GPa. Beyond $p\approx10$ GPa, a second superconducting dome emerges with maximum $T_{\rm c}\approx1.0$ K at $p_{\rm c2}\approx22$ GPa, which becomes fully suppressed at $p\approx28$ GPa. The suppression of superconductivity for the second superconducting dome is associated with the appearance of a unique high-pressure phase , possibly a distinct charge order., Comment: expanded to include new data

Intertwining quantum order and nontrivial topology is at the frontier of condensed matter physics. A charge density wave (CDW) like order with orbital currents has been proposed as a powerful resource for achieving the quantum anomalous Hall effect in topological materials and for the hidden phase in cuprate high-temperature superconductors. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy (STM) to discover an unconventional 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 2x2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2x2 charge modulation exhibits an intensity reversal in real-space, signaling charge ordering. At 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 CDW in the frustrated kagome lattice, which can not only lead to large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity., Comment: Orbital magnetism calculation added

Here we report the observation of bulk superconductivity in single crystals of the two-dimensional kagome metal KV$_3$Sb$_5$. Magnetic susceptibility, resistivity, and heat capacity measurements reveal superconductivity below $T_c = 0.93$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 CsV$_3$Sb$_5$ is likely a common feature across the AV$_3$Sb$_5$ (A: K, Rb, Cs) family of compounds and establish 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.

Materials with transition metals in triangular lattices are of great interest for their potential combination of strong correlation, exotic magnetism and electronic topology. Kagome nets are of particular importance since the discovery of geometrically frustrated magnetism and topological band structures in crystals like Herbertsmithite and Fe3Sn2, respectively. KV3Sb5 was discovered to be a layered topological metal with a Kagome net of vanadium. Here, we fabricated Josephson Junctions (JJ) of K1-xV3Sb5 and induced superconductivity over long junction lengths. Through magnetoresistance and current vs. phase measurements, we observed magnetic field sweeping direction dependent magnetoresistance, and an anisotropic interference pattern with a Fraunhofer pattern for in-plane magnetic field, but a suppression of critical current for out-of-plane magnetic field. These results indicate an anisotropic internal magnetic field in K1-xV3Sb5 which influences the superconducting coupling in the junction, possibly giving rise to spin-triplet superconductivity. In addition, the observation of long-lived fast oscillations shows evidence of spatially localized conducting channels arising from edge states. These observations pave the way for studying unconventional superconductivity and Josephson device based on Kagome metals with electron correlation and topology.

Recently discovered alongside its sister compounds KV$_3$Sb$_5$ and RbV$_3$Sb$_5$, CsV$_3$Sb$_5$ crystallizes with an ideal kagome network of vanadium and antimonene layers separated by alkali metal ions. This work presents the electronic properties of CsV$_3$Sb$_5$, demonstrating bulk superconductivity in single crystals with a T$_{c} = 2.5$K. The normal state electronic structure is studied via angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), which categorize CsV$_3$Sb$_5$ as a $\mathbb{Z}_2$ topological metal. Multiple protected Dirac crossings are predicted in close proximity to the Fermi level ($E_F$), and signatures of normal state correlation effects are also suggested by a high temperature charge density wave-like instability. The implications for the formation of unconventional superconductivity in this material are discussed., Comment: 6 pages, 4 figures

A complete structural solution of the bilayer iridate compound Sr3Ir2O7 presently remains outstanding. Previously reported structures for this compound vary and all fail to explain weak structural violations observed in neutron scattering measurements as well as the presence of a net ferromagnetic moment in the basal plane. In this paper, we present single crystal neutron diffraction and rotational anisotropy second harmonic generation measurements unveiling a lower, monoclinic symmetry inherent to Sr3Ir2O7 . Combined with density functional theory, our measurements identify the correct structural space group as No. 15 (C2/c) and provide clarity regarding the local symmetry of Ir 4+ cations within this spin-orbit Mott material., Comment: 7 pages, 3 figures

High-resolution single crystal neutron diffraction measurements are presented probing the magnetostructural response to uniaxial pressure in the iron pnictide parent system BaFe2As2. Scattering data reveal a strain-activated, anisotropic broadening of nuclear Bragg reflections, which increases upon cooling below the resolvable onset of global orthorhombicity. This anisotropy in lattice coherence continues to diverge until a lower temperature scale---the first-order onset of antiferromagnetism---is reached. Our data suggest that antiferromagnetism and strong magnetoelastic coupling drive the strain-activated lattice response in this material and that the development of anisotropic lattice coherence under strain is the physical origin for the anomalous nematic anisotropy in this compound., Comment: 5 pages, 4 figures

The evolution of the electronic properties of electron-doped (Sr{1-x}La{x})2IrO4 is experimentally explored as the doping limit of La is approached. As electrons are introduced, the electronic ground state transitions from a spin-orbit Mott phase into an electronically phase separated state, where long-range magnetic order vanishes beyond x = 0.02 and charge transport remains percolative up to the limit of La substitution (x~0.06). In particular, the electronic ground state remains inhomogeneous even beyond the collapse of the parent state's long-range antiferromagnetic order, while persistent short-range magnetism survives up to the highest La-substitution levels. Furthermore, as electrons are doped into Sr2IrO4, we observe the appearance of a low temperature magnetic glass-like state intermediate to the complete suppression of antiferromagnetic order. Universalities and differences in the electron-doped phase diagrams of single layer and bilayer Ruddlesden-Popper strontium iridates are discussed., Comment: 12 pages, 12 figures. New version has revised text, added references, and updated figures

The electronic phase diagram of the weak spin-orbit Mott insulator (Sr(1-x)Lax)3Ir2O7 is determined via an exhaustive experimental study. Upon doping electrons via La substitution, an immediate collapse in resistivity occurs along with a narrow regime of nanoscale phase separation comprised of antiferromagnetic, insulating regions and paramagnetic, metallic puddles persisting until x~0.04. Continued electron doping results in an abrupt, first-order phase boundary where the Neel state is suppressed and a homogenous, correlated, metallic state appears with an enhanced spin susceptibility and local moments. As the metallic state is stabilized, a weak structural distortion develops and suggests a competing instability with the parent spin-orbit Mott state., Comment: 5 pages, 4 figures

Neutron diffraction measurements are presented measuring the responses of both magnetic and structural order parameters of parent and lightly Co-doped Ba(Fe{1-x}Co{x})2As2 under the application of uniaxial pressure. We find that the uniaxial pressure induces a thermal shift in the onset of antiferromagnetic order that grows as a percentage of T_N as Co-doping is increased and the superconducting phase is approached. Additionally, as uniaxial pressure is increased within parent and lightly-doped Ba(Fe{1-x}Co{x})2As2 on the first order side of the tricritical point, we observe a decoupling between the onsets of the orthorhombic structural distortion and antiferromagnetism. Our findings place needed constraints on models exploring the nematic susceptibility of the bilayer pnictides in the tetragonal, paramagnetic regime., Comment: 10 pages, 7 figures

The interplay between magnetism and crystal structures in three CaFe$_{2}$As$_{2}$ samples is studied. For the nonmagnetic quenched crystals, different crystalline domains with varying lattice parameters are found, and three phases (orthorhombic, tetragonal, and collapsed tetragonal) coexist between T$_{S}$ = 95 K and 45 K. Annealing of the quenched crystals at 350{\deg}C leads to a strain relief through a large (~1.3 %) expansion of the c-parameter and a small (~0.2 %) contraction of the a-parameter, and to local ~0.2 {\AA} displacements at the atomic-level. This annealing procedure results in the most homogeneous crystals for which the antiferromagnetic and orthorhombic phase transitions occur at T$_{N}$/T$_{S}$ = 168(1) K. In the 700{\deg}C-annealed crystal, an intermediate strain regime takes place, with tetragonal and orthorhombic structural phases coexisting between 80 to 120 K. The origin of such strong shifts in the transition temperatures are tied to structural parameters. Importantly, with annealing, an increase in the Fe-As length leads to more localized Fe electrons and higher local magnetic moments on Fe ions. Synergistic contribution of other structural parameters, including a decrease in the Fe-Fe distance, and a dramatic increase of the c-parameter, which enhances the Fermi surface nesting in CaFe$_{2}$As$_{2}$, are also discussed., Comment: 5 pages main text, 5 figures and 6 pages Supporting Information