Search

Symmetry plays an important role in determining the physical properties in condensed matter physics, as the symmetry operations of any physical property must include the symmetry operations of the point group of the crystal. As a consequence, crystallographic polarity and chirality are expected to have an impact on the Cooper pairing in a superconductor. While superconductivity with crystallographic polarity and chirality have both been found in a few crystalline phases separately; however, their coexistence and material realizations have not been studied. Here, by utilizing transport, Raman scattering, and transmission electron microscopy, we unveil a unique realization of superconductivity in single-crystalline Mo3Al2C (superconducting Tc=8K) with a polar charge-density-wave phase and well-defined crystallographic chirality. We show that the intriguing charge density wave order leads to a noncentrosymmetric-nonpolar to polar transition below T*=155K via breaking both the translational and rotational symmetries. Superconductivity emerges in this polar and chiral crystal structure below Tc=8K. Our results establish that Mo3Al2C is a superconductor with crystallographic polarity and chirality simultaneously, and motivate future studies of unconventional superconductivity in this category., Comment: 20 pages, 3 figures, journal version

Kagome vanadates {\it A}V$_3$Sb$_5$ display unusual low-temperature electronic properties including charge density waves (CDW), whose microscopic origin remains unsettled. Recently, CDW order has been discovered in a new material ScV$_6$Sn$_6$, providing an opportunity to explore whether the onset of CDW leads to unusual electronic properties. Here, we study this question using angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). The ARPES measurements show minimal changes to the electronic structure after the onset of CDW. However, STM quasiparticle interference (QPI) measurements show strong dispersing features related to the CDW ordering vectors. A plausible explanation is the presence of a strong momentum-dependent scattering potential peaked at the CDW wavevector, associated with the existence of competing CDW instabilities. Our STM results further indicate that the bands most affected by the CDW are near vHS, analogous to the case of {\it A}V$_3$Sb$_5$ despite very different CDW wavevectors., Comment: 33 pages, 4 figures

Spontaneous symmetry breaking-the phenomenon where an infinitesimal perturbation can cause the system to break the underlying symmetry-is a cornerstone concept in the understanding of interacting solid-state systems. In a typical series of temperature-driven phase transitions, higher temperature phases are more symmetric due to the stabilizing effect of entropy that becomes dominant as the temperature is increased. However, the opposite is rare but possible when there are multiple degrees of freedom in the system. Here, we present such an example of a symmetry-ascending phenomenon in a magnetic kagome metal FeGe by utilizing neutron Larmor diffraction and Raman spectroscopy. In the paramagnetic state at 460K, we confirm that the crystal structure is indeed hexagonal kagome lattice. On cooling to TN, the crystal structure changes from hexagonal to monoclinic with in-plane lattice distortions on the order of 10^(-4) and the associated splitting of the double degenerate phonon mode of the pristine kagome lattice. Upon further cooling to TCDW, the kagome lattice shows a small negative thermal expansion, and the crystal structure becomes more symmetric gradually upon further cooling. Increasing the crystalline symmetry upon cooling is unusual, it originates from an extremely weak structural instability that coexists and competes with the CDW and magnetic orders. These observations are against the expectations for a simple model with a single order parameter, hence can only be explained by a Landau free energy expansion that takes into account multiple lattice, charge, and spin degrees of freedom. Thus, the determination of the crystalline lattice symmetry as well as the unusual spin-lattice coupling is a first step towards understanding the rich electronic and magnetic properties of the system and sheds new light on intertwined orders where the lattice degree of freedom is no longer dominant., Comment: 20 pages with 10 figures, replaced with journal version

Broken time-reversal symmetry in the absence of spin order indicates the presence of unusual phases such as orbital magnetism and loop currents. The recently discovered family of kagome superconductors AV$_3$Sb$_5$ (A = K, Rb, or Cs), hosting an exotic charge-density wave (CDW) state, has emerged as a strong candidate for this phase. While initial experiments suggested that the CDW phase breaks time-reversal symmetry, this idea is being intensely debated due to conflicting experimental data. In this work we use laser-coupled scanning tunneling microscopy (STM) to study RbV$_3$Sb$_5$. STM data shows that the Fourier intensities of all three CDW peaks are different, implying that the CDW breaks rotational and mirror symmetries. By applying linearly polarized light along high-symmetry directions, we show that the relative intensities of the CDW peaks can be reversibly switched, implying a substantial electro-striction response, indicative of strong non-linear electron-phonon coupling. A similar CDW intensity switching is observed with perpendicular magnetic fields, which implies an unusual piezo-magnetic response that, in turn, requires time-reversal symmetry-breaking. We show that the simplest CDW that satisfies these constraints and reconciles previous seemingly contradictory experimental data is an out-of-phase combination of bond charge order and loop currents that we dub congruent CDW flux phase. Our laser-STM data opens the door to the possibility of dynamic optical control of complex quantum phenomenon in correlated materials., Comment: main text: 21 pages, 5 figures // Methods and Extended Data: 25 pages, 14 figures

Kagome metals are widely recognized as versatile platforms for exploring novel topological properties, unconventional electronic correlations, magnetic frustration, and superconductivity. In the $R$V$_6$Sn$_6$ family of materials ($R$ = Sc, Y, Lu), ScV$_6$Sn$_6$ hosts an unusual charge density wave ground state as well as structural similarities with the $A$V$_3$Sb$_5$ system ($A$ = K, Cs, Rb). In this work, we combine Raman scattering spectroscopy with first-principles lattice dynamics calculations to reveal the charge density wave state in ScV$_6$Sn$_6$. In the low temperature phase, we find a five-fold splitting of the V-containing totally symmetric mode near 240 cm$^{-1}$ suggesting that the density wave acts to mix modes of $P$6/$mmm$ and $R$$\bar{3}$$m$ symmetry - an effect that we quantify by projecting phonons of the high symmetry state onto those of the lower symmetry structure. We also test the stability of the density wave state under compression and find that both physical and chemical pressure act to quench the effect. We discuss these findings in terms of symmetry and the structure-property trends that can be unraveled in this system.

Recent experiments have shown that the phase diagrams of the kagome superconductors $A\mathrm{V}_3\mathrm{Sb}_5$ are strongly impacted by changes in the $c$-axis lattice parameter. Here, we show that $c$-axis deformations impact primarily the Sb apical bonds and thus the overlap between their $p_z$ orbitals. Changes in the latter, in turn, substantially affect low-energy electronic states with significant Sb character, most notably the central electron pocket and the van Hove singularities located above the Fermi level. Based on the orbital-selective character of $c$-axis strain, we argue that these electronic states experience a non-negligible attractive electron-phonon pairing interaction mediated by fluctuations in the apical Sb bonds. We thus propose a multi-band model for superconductivity in $A\mathrm{V}_3\mathrm{Sb}_5$ that includes both the Sb pocket and the V-derived van Hove singularities. Upon comparing the theoretical phase diagram with the experimentally observed vanishing of the $T_c$ dome across a Lifshitz transition of the Sb pocket, we propose that either an $s^{+-}$ or an $s^{++}$ state is realized in $A\mathrm{V}_3\mathrm{Sb}_5$., Comment: 7+5 pages, 2+4 figures. Accepted in Phys. Rev. B

Elucidating the microscopic mechanisms responsible for the charge density wave (CDW) instability of the AV$_3$Sb$_5$ (A=Cs, K, Rb) family of kagome metals is critical for understanding their unique properties, including superconductivity. In these compounds, distinct CDW phases with wave-vectors at the $M$ and $L$ points are energetically favorable, opening the possibility of tuning the type of CDW order by appropriate external parameters. Here, we shed light on the CDW landscape of CsV$_3$Sb$_5$ via a combination of first-principles calculations and phenomenology, which consists of extracting the coefficients of the CDW Landau free-energy expansion from density functional theory. We find that while the main structural distortions of the kagome lattice in the staggered tri-hexagonal CDW phase are along the nearest-neighbor V-V bonds, distortions associated with the Sb ions play a defining role in the energy gain in this and all other CDW states. Moreover, the coupling between ionic displacements from different unit cells is small, thus explaining the existence of multiple CDW instabilities with different modulations along the c-axis. We also investigate how pressure and temperature impact the CDW phase of CsV$_3$Sb$_5$. Increasing pressure does not change the staggered tri-hexagonal CDW ground state, even though the $M$-point CDW instability disappears before the $L$-point one, a behavior that we attribute to the large nonlinear coupling between the order parameters. Upon changing the temperature, we find a narrow regime in which another transition can take place, toward a tri-hexagonal Star-of-David CDW phase. We discuss the implications of our results by comparing them with experiments on this compound.

The recently discovered vanadium-based kagome metals $A$V$_{3}$Sb$_{5}$ ($A$~=~K,~Rb,~Cs) exhibit superconductivity at low-temperatures and charge density wave (CDW) order at high-temperatures. A prominent feature of the charge ordered state in this family is that it breaks time-reversal symmetry (TRSB), which is connected to the underlying topological nature of the band structure. In this work, a powerful combination of zero-field and high-field muon-spin rotation/relaxation is used to study the signatures of TRSB of the charge order in CsV$_3$Sb$_5$, as well as its anisotropic character. By tracking the temperature evolution of the in-plane and out-of-plane components of the muon-spin polarization, an enhancement of the internal field width sensed by the muon-spin ensemble was observed below $T_{\rm TRSB}=T_{\rm CDW}\simeq95$~K. Additional increase of the internal field width, accompanied by a change of the local field direction at the muon site from the $ab$-plane to the $c$-axis, was detected below $T^\ast\simeq30$~K. Remarkably, this two-step feature becomes well pronounced when a magnetic field of 8~T is applied along the crystallographic $c-$axis, thus indicating a field-induced enhancement of the electronic response at the CDW transition. These results point to a TRSB in CsV$_3$Sb$_5$ by charge order with an onset of ${\simeq}~95$~K, followed by an enhanced electronic response below ${\simeq}~30$~K. The observed two-step transition is discussed within the framework of different charge-order instabilities, which, in accordance with density functional theory calculations, are nearly degenerate in energy., Comment: 10 pages, 4 figures

The kagome metals of the family $A$V$_3$Sb$_5$, featuring a unique structural motif, harbor an array of intriguing phenomena such as chiral charge order and superconductivity. CsV$_3$Sb$_5$ is of particular interest because it displays a double superconducting dome in the region of the temperature-pressure phase diagram where charge order is still present. However, the microscopic origin of such an unusual behavior remains an unsolved issue. Here, to address it, we combine high-pressure, low-temperature muon spin relaxation with first-principles calculations. We observe a pressure-induced threefold enhancement of the superfluid density, which also displays a double peak feature, similar to the superconducting critical temperature. This leads to three distinct regions in the phase diagram, each of which features distinct slopes of the linear relation between superfluid density and the critical temperature. These results are attributed to a possible evolution of the charge order pattern from the superimposed tri-hexagonal Star-of-David phase at low pressures (within the first dome) to the staggered tri-hexagonal phase at intermediate pressures (between the first and second domes). Our findings suggest a change in the nature of the charge ordered state across the phase diagram of CsV$_3$Sb$_5$, with varying degrees of competition with superconductivity., Comment: 9 pages, 4 figures

The thermal properties of materials are critically important to various technologies and are increasingly the target of materials design efforts. However, it is only relatively recent advances in first-principles computational techniques that have enabled researchers to explore the microscopic mechanisms of thermal properties, such as thermal expansion. We use the Gr\"{u}neisen theory of thermal expansion in combination with density functional calculations and the quasiharmonic approximation to uncover mechanisms of thermal expansion in PbTiO$_3$ thin-films in terms of elastic and vibrational contributions to the free energy. Surprisingly, we find that although the structural parameters of PbTiO$_3$ thin-films evolve with temperature as if they are dominated by linear elasticity, PbTiO$_3$ thin-films are strongly anharmonic, with large changes in the elastic constants and Gr\"{u}neisen parameters with both misfit strain and temperature. We show that a fortuitous near-cancellation between different types of anharmonicity gives rise to this behavior. Our results illustrate the importance of high-order phonon-strain anharmonicity in determining the temperature-dependent structural parameters of PbTiO$_3$ thin-films, and highlight the complex manner in which thermal expansion, misfit strain and elastic and vibrational properties are intertwined.

The sensitivity of materials properties, particularly those of perovskite oxides, to epitaxial strain has been exploited to great advantage to create materials with new or enhanced properties. Although it has certainly been recognized that mismatch in the thermal expansion coefficients of the bulk and substrate material will contribute to the misfit strain, the significance of this contribution for ferroelectric perovskite thin-films has not been systematically explored. We use first-principles density functional theory and the example of ferroelectric PbTiO$_3$ thin-films on various substrates to show that ignoring the thermal expansion of the substrate (that is, assuming that the in-plane lattice parameter of the film remains roughly constant as a function of temperature) results in ferroelectric transition temperatures and structural trends that are completely qualitatively different from calculations in which thermal expansion mismatch is properly taken into account. Our work suggests that the concept of a misfit strain defined as a single number is particularly ill-defined for PbTiO$_3$ and invites further study of the interplay between thermal expansion mismatch and structural and functional properties in other thin-film materials.

In this Tutorial, we describe the use of the quasiharmonic approximation and first-principles density functional theory (DFT) to calculate and analyze the thermal expansion of insulating solids. We discuss the theory underlying the quasiharmonic approximation, and demonstrate its practical use within two common frameworks for calculating thermal expansion: the Helmholtz free energy framework and Gr\"{u}neisen theory. Using the example of silicon, we provide a guide for predicting how the lattice parameter changes as a function of temperature using DFT, including the calculation of phonon modes and phonon density of states, elastic constants, and specific heat. We also describe the calculation and interpretation of Gr\"{u}neisen parameters, as well as how they relate to coefficients of thermal expansion. The limitations of the quasiharmonic approximation are briefly touched on, as well as the comparison of theoretical results with experimental data. Finally, we use the example of ferroelectric PbTiO$_3$ to illustrate how the methods used can be adapted to study anisotropic systems.

We use first-principles theory to show that the ingredients assumed to be essential to the occurrence of negative thermal expansion (NTE) -- rigid unit phonon modes with negative Gr\"{u}neisen parameters -- are neither sufficient nor necessary for a material to undergo NTE. Instead, we find that NTE in PbTiO$_3$ involves a delicate interplay between the phonon properties of a material (Gr\"{u}neisen parameters) and its anisotropic elasticity. These unique insights open new avenues in our fundamental understanding of the thermal properties of materials, and in the search for NTE in new materials classes.