Motivated by recent angle-resolved photoemission spectroscopy (ARPES) experiments, we analyze the temperature, frequency, and momentum dependence of the single-particle scattering rate in a model of the $γ$-band of Sr$_2$RuO$_4$ under strain, with particular emphasis on the behavior near the Lifshitz transition where the Fermi energy crosses a single Van Hove point. While the scattering rate is only moderately anisotropic at zero strain, we find that it becomes strongly anisotropic at the Lifshitz point. At the lowest energies, we recover the expected universal behavior: the scattering rate varies (ignoring logarithmic corrections) as $τ^{-1}\sim ω$ at the Van Hove point and as $τ^{-1}\sim ω^{3/2}$ away from it. At higher energies, however, corrections of order $ω^2$ become important in both regimes. We show that the experimentally observed behavior $τ^{-1} \sim ω^α$ with $α\approx 1.4(2)$ at the Van Hove point can be quantitatively explained by a superposition of linear and quadratic contributions to the scattering rate, which are comparable in magnitude at the intermediate energies probed by experiment, rather than in terms of a new universal power law. We further predict a distinctive anisotropy, strain dependence, and a non-monotonic frequency dependence of the scattering rate at a Lifshitz transition, all of which may be directly tested in experiments.
Shortly after the discovery of superconductivity in Sr$_2$RuO$_4$, spin-triplet pairing was proposed and further corroborated by a constant Knight shift ($K$) across the transition temperature (T$_c$). However, a recent experiment observed a drop in $K$ at T$_c$ which becomes larger under uniaxial strain, ruling out several spin-triplet scenarios. Here we show that inter-orbital spin-triplet pairing features a d-vector that rotates when uniaxial strain is applied, leading to a larger drop in the spin polarization perpendicular to the strain direction, distinct from spin-singlet pairing. We pro…
Motivated by the success of experimental manipulation of the band structure through biaxial strain in Sr$_2$RuO$_4$ thin film grown on a mismatched substrate, we investigate theoretically the effects of biaxial strain on the electronic instabilities, such as superconductivity (SC) and spin density wave (SDW), by functional renormalization group. According to the experiment, the positive strain (from lattice expansion) causes charge transfer to the $γ$-band and consequently Lifshitz reconstruction of the Fermi surface. Our theoretical calculations show that within a limited range of positive st…
We report the synthesis of Ca$_2$RuO$_4$ thin films on NdCaAlO$_{4}$ (110), LaAlO$_3$ (100) and LaSrAlO$_4$ (001) substrates and show that epitaxial strain induces a transition from the Mott-insulating phase of bulk Ca$_2$RuO$_4$ into a metallic phase. Magnetometry and spin-polarized neutron reflectometry reveal a low-temperature, small-moment ferromagnetic state in metallic Ca$_2$RuO$_4$ films.
In its ground state, RuO2 was long thought to be an ordinary metallic paramagnet. Recent neutron and x-ray diffraction revealed that bulk RuO2 is an antiferromagnet (AFM) with TN above 300 K. Furthermore, epitaxial strain induces novel superconductivity in thin films of RuO2 below 2 K. Here, we present a resonant elastic x-ray scattering (REXS) study at the Ru L2 edge of the strained RuO2 films exhibiting the strain-induced superconductivity. We observe an azimuthal modulation of the 100 Bragg peak consistent with canted AFM found in bulk. Most notably, in the strained films displaying novel s…
We analyze the spin anisotropy of the magnetic susceptibility of Sr$_2$RuO$4$ in presence of spin-orbit coupling and anisotropic strain using quasi-two-dimensional tight-binding parametrization fitted to the ARPES results. Similar to the previous observations we find the in-plane polarization of the low ${\bf q}$ magnetic fluctuations and the out-of-plane polarization of the incommensurate magnetic fluctuation at the nesting wave vector ${\bf Q}_1 = (2/3 π,2/3 π)$ but also nearly isotropic fluctuations near ${\bf Q}_2=(π/6,π/6)$. Furthermore, one finds that apart from the high-symmetry directi…
Combining first principle density functional calculations and Moriya's self-consistent renormalization theory, we explain the recently reported counterintuitive appearance of an ordered magnetic state in uniaxially strained Sr$_2$RuO$_4$ beyond the Lifshits transition. We show that strain weakens the quantum spin fluctuations, which destroy the static order, more strongly than the tendency to magnetism. A different rate of decrease of the spin fluctuations vs. magnetic stabilization energy promotes the onset of a static magnetic order beyond a critical strain.
Due to the presence of a nontrivial three-dimensional spin-orbital entanglement, Sr$_2$RuO$_4$ may be a time-reversal invariant nematic $p$-wave superconductor with coexisting in-plane and out-of-plane pairings. Here we discuss various signatures of such a state if the out-of-plane pairing component is dominant. First, the enhancement of the superconducting $T_c$ under in-plane uniaxial strains is nearly a quadratic function of the strain, because the out-of-plane pairing lacks a linear-order coupling to the strain. Second, when the strain applies along a certain in-plane direction, the nemati…
Pressure represents a clean tuning parameter for traversing the complex phase diagrams of interacting electron systems and as such has proved of key importance in the study of quantum materials. Application of controlled uniaxial pressure has recently been shown to more than double the transition temperature of the unconventional superconductor Sr$_{2}$RuO$_{4}$ for example, leading to a pronounced peak in $T_\mathrm{c}$ vs. strain whose origin is still under active debate. Here, we develop a simple and compact method to apply large uniaxial pressures passively in restricted sample environment…
Strain engineering vanadium dioxide thin films is one way to alter this material's characteristic first order transition from semiconductor to metal. In this study we extend the exploitable strain regime by utilizing the very large lattice mismatch of 8.78 % occurring in the VO$_2$/RuO$_2$ system along the c axis of the rutile structure. We have grown VO$_2$ thin films on single domain RuO$_2$ islands of two distinct surface orientations by atomic oxygen-supported reactive MBE. These films were examined by spatially resolved photoelectron and x-ray absorption spectroscopy, confirming the corre…
We report the evolution of the $k$-space electronic structure of lightly doped bulk Ca$_{2}$RuO$_{4}$ with uniaxial strain. Using ultrathin plate-like crystals, we achieve strain levels up to $-4.1\%$, sufficient to suppress the Mott phase and access the previously unexplored metallic state at low temperature. Angle-resolved photoemission experiments performed while tuning the uniaxial strain reveal that metallicity emerges from a marked redistribution of charge within the Ru $t_{2g}$ shell, accompanied by a sudden collapse of the spectral weight in the lower Hubbard band and the emergence of …
We present an implementation of the rotationally invariant slave boson technique as an impurity solver for density functional theory plus dynamical mean field theory (DFT+DMFT). Our approach provides explicit relations between quantities in the local correlated subspace treated with DMFT and the Bloch basis used to solve the DFT equations. In particular, we present an expression for the mass enhancement of the quasiparticle states in reciprocal space. We apply the method to the study of the electronic correlations in Sr$_2$RuO$_4$ under anisotropic strain. We find that the spin-orbit coupling …
Strain tuning Sr$_{2}$RuO$_{4}$ through the Lifshitz point, where the Van Hove singularity of the electronic spectrum crosses the Fermi energy, is expected to cause a change in the temperature dependence of the electrical resistivity from its Fermi liquid behavior $ρ\sim T^{2}$ to $ρ\sim T^{2}{\rm log}\left(1/T\right)$, a behavior consistent with experiments by Barber et al. [Phys. Rev. Lett. 120, 076601 (2018)]. This expectation originates from the same multi-band scattering processes with large momentum transfer that were recently shown to account for the linear in $T$ resistivity of the str…
Uniaxial pressure applied along an Ru-Ru bond direction induces an elliptical distortion of the largest Fermi surface of Sr$_2$RuO$_4$, eventually causing a Fermi surface topological transition, also known as a Lifshitz transition, into an open Fermi surface. There are various anomalies in low-temperature properties associated with this transition, including maxima in the superconducting critical temperature and in resistivity. In the present paper, we report new measurements, employing new uniaxial stress apparatus and new measurements of the low-temperature elastic moduli, of the strain at w…
We perform nuclear magnetic resonance (NMR) measurements of the oxygen-17 Knight shifts for Sr$_2$RuO$_4$, while subjected to uniaxial stress applied along [100] direction. The resulting strain is associated with a strong variation of the temperature and magnetic field dependence of the inferred magnetic response. A quasi-particle description based on density-functional theory calculations, supplemented by many-body renormalizations, is found to reproduce our experimental results, and highlights the key role of a van-Hove singularity. The Fermi liquid coherence scale is shown to be tunable by …
We report the evolution of the electronic structure at the surface of the layered perovskite Sr$_2$RuO$_4$ under large in-plane uniaxial compression, leading to anisotropic $B_{1g}$ strains of ${\varepsilon_{xx}-\varepsilon_{yy}=-0.9\pm0.1\%}$. From angle-resolved photoemission, we show how this drives a sequence of Lifshitz transitions, reshaping the low-energy electronic structure and the rich spectrum of van Hove singularities that the surface layer of Sr$_2$RuO$_4$ hosts. From comparison to tight-binding modelling, we find that the strain is accommodated predominantly by bond-length change…
Here we demonstrate how the Fermi surface topology and quantum many-body interactions can be manipulated via epitaxial strain in the spin-triplet superconductor Sr$_2$RuO$_4$ and its isoelectronic counterpart Ba$_2$RuO$_4$ using oxide molecular beam epitaxy (MBE), \emph{in situ} angle-resolved photoemission spectroscopy (ARPES), and transport measurements. Near the topological transition of the $γ$ Fermi surface sheet, we observe clear signatures of critical fluctuations, while the quasiparticle mass enhancement is found to increase rapidly and monotonically with increasing Ru-O bond distance.…
The effects of uniaxial compressive stress on the normal state $^{17}$O nuclear magnetic resonance properties of the unconventional superconductor Sr$_{2}$RuO$_{4}$ are reported. The paramagnetic shifts of both planar and apical oxygen sites show pronounced anomalies near the nominal $\mathbf{a}$-axis strain $\varepsilon_{aa}\equiv\varepsilon_v$, that maximizes the superconducting transition temperature, $T_{c}$. The spin susceptibility weakly increases on lowering the temperature below $T$$\simeq$10 K, consistent with an enhanced density of states associated with passing the Fermi energy thro…
Influence of Fermi Surface Geometry and Van Hove Singularities on the Optical Response of Sr$_2$RuO$_4$
Bu-Ali Sina University（布阿利·西纳大学）；University of Toronto（多伦多大学）；DelQuanTech Inc.（DelQuanTech公司）；Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京应用数学与物理研究所）
We report the results of a combined study of the normal state resistivity and superconducting transition temperature $T_c$ of the unconventional superconductor Sr$_2$RuO$_4$ under uniaxial pressure. There is strong evidence that as well as driving $T_c$ through a maximum at $\sim$3.5 K, compressive strains $\varepsilon$ of nearly 1 % along the crystallographic [100] axis drive the $γ$ Fermi surface sheet through a Van Hove singularity, changing the temperature dependence of the resistivity from $T^2$ above and below the transition region to $T^{1.5}$ within it. This occurs in extremely pure si…
Recent experiments revealed non-Fermi-liquid resistivity in the unconventional superconductor Sr$_{2}$RuO$_{4}$ when strain pushes one of the Fermi surfaces close to a van Hove singularity. The origin of this behavior and whether it can be understood from a picture of well defined quasiparticles is unclear. We employ a Boltzmann transport analysis beyond the single relaxation-time approximation based on a single band which undergoes a Lifshitz transition, where the Fermi surface crosses a van Hove singularity, either due to uni-axial or epitaxial strain. First analytically investigating impuri…
Strain-Tuned Nodal Superconductivity in the Charge-Ordered Kagome Metal CsV$_3$Sb$_5$
Okayama University（冈山大学）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Beijing National Laboratory for Condensed Matter Physics（北京凝聚态物理国家实验室）；Fujian Provincial Collaborative Innovation Center for Advanced High-Field Superconducting Materials and Engineering（福建省先进高场超导材料与工程协同创新中心）；College of Physics and Energy, Fujian Normal University（福建师范大学物理与能源学院）；Guang’an Institute of Technology
A phase transition between topologically distinct insulating phases involves closing and reopening of the bandgap. Close to this topological phase transition, the bulk energy spectrum is characterized by a massive Dirac dispersion, where the mass plays the role of bandgap. Here we report the observation of a non-monotonic strain dependence of resistivity and negative longitudinal magnetoresistance in ZrTe5, which is known to host massive Dirac Fermions in the bulk. This non-monotonic strain dependence is consistent with the closing and reopening of the bandgap at the Brillouin-zone center, ind…
Strain-Tuned Incommensurate Kekulé Spiral Order in Twisted Bilayer Graphene: a Quantum Many-Body Study
The University of Hong Kong（香港大学）；University of Texas at Dallas（德克萨斯大学达拉斯分校）；Princeton University（普林斯顿大学）；Universität Würzburg（维尔茨堡大学）；Max Planck Institute for Solid State Reserach（马克斯·普朗克固体研究所）；Technische Universität München（慕尼黑工业大学）
Materials with strong electronic correlations host remarkable -- and technologically relevant -- phenomena such as magnetism, superconductivity and metal-insulator transitions. Harnessing and controlling these effects is a major challenge, on which key advances are being made through lattice and strain engineering in thin films and heterostructures, leveraging the complex interplay between electronic and structural degrees of freedom. Here we show that the electronic structure of LaNiO3 can be tuned by means of lattice engineering. We use different substrates to induce compressive and tensile …
Recent experiments have discovered multipolar orders in a variety of $d$-orbital Mott insulators. Motivated by uncovering the exchange interactions which underlie octupolar order proposed in the osmate double perovskites, we study a two-site model using exact diagonalization on a five-orbital Hamiltonian, incorporating spin-orbit coupling (SOC) and interactions, and including both intra-orbital and inter-orbital hopping. Using an exact Schrieffer-Wolff transformation, we then extract an effective pseudospin Hamiltonian for the non-Kramers doublets, uncovering dominant ferrooctupolar coupling d…
