Split superconducting and time-reversal symmetry-breaking transitions, and magnetic order in Sr$_2$RuO$_4$ under uniaxial stress
Vadim Grinenko, Shreenanda Ghosh, Rajib Sarkar, Jean-Christophe Orain, Artem Nikitin, Matthias Elender, Debarchan Das, Zurab Guguchia, Felix Brückner, Mark E. B… 展开作者
Vadim Grinenko, Shreenanda Ghosh, Rajib Sarkar, Jean-Christophe Orain, Artem Nikitin, Matthias Elender, Debarchan Das, Zurab Guguchia, Felix Brückner, Mark E. Barber, Joonbum Park, Naoki Kikugawa, Dmitry A. Sokolov, Jake S. Bobowski, Takuto Miyoshi, Yoshiteru Maeno, Andrew P. Mackenzie, Hubertus Luetkens, Clifford W. Hicks, Hans-Henning Klauss
Among unconventional superconductors, Sr$_2$RuO$_4$ has become a benchmark for experimentation and theoretical analysis because its normal-state electronic structure is known with exceptional precision, and because of experimental evidence that its superconductivity has, very unusually, a spontaneous angular momentum, i.e. a chiral state. This hypothesis of chirality is however difficult to reconcile with recent evidence on the spin part of the order parameter. Measurements under uniaxial stress offer an ideal way to test for chirality, because under uniaxial stress the superconducting and chiral transitions are predicted to split, allowing the empirical signatures of each to be identified separately. Here, we report zerofield muon spin relaxation (ZF-$μ$SR) measurements on crystals placed under uniaxial stresses of up to 1.05 GPa. We report a clear stress-induced splitting between the onset temperatures of superconductivity and time-reversal symmetry breaking, consistent with qualitative expectations for chiral superconductivity. We also report the appearance of unexpected bulk magnetic order under a uniaxial stress of ~ 1.0 GPa in clean Sr$_2$RuO$_4$.
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…
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…
Muon spin rotation/relaxation ($μ$SR) and polar Kerr effect measurements provide evidence for a time-reversal symmetry breaking (TRSB) superconducting state in Sr$_2$RuO$_4$. However, the absence of a cusp in the superconducting transition temperature ($T_{\rm c}$) vs. stress and the absence of a resolvable specific heat anomaly at TRSB transition temperature ($T_{\rm TRSB}$) under uniaxial stress challenge a hypothesis of TRSB superconductivity. Recent $μ$SR studies under pressure and with disorder indicate that the splitting between $T_{\rm c}$ and $T_{\rm TRSB}$ occurs only when the structu…
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…
Applying in-plane uniaxial pressure to strongly correlated low-dimensional systems has been shown to tune the electronic structure dramatically. For example, the unconventional superconductor Sr$_2$RuO$_4$ can be tuned through a single Van Hove singularity which results in a strong enhancement of both $T_\text{c}$ and $H_\text{c2}$. Out-of-plane ($c$ axis) uniaxial pressure is expected to tune the quasi-two-dimensional structure even more strongly, causing it to approach two Van Hove singularities simultaneously. Here we achieve a record value of $3.2$ GPa compression along the $c$ axis of Sr$…
We investigate pairing states realized at the (001) interface of a spin-triplet superconductor Sr$_2$RuO$_4$ on the basis of microscopic calculations. Because of a Rashba-type spin-orbit interaction induced at the interface, strong parity-mixing of Cooper pairs between a spin-singlet state and a spin-triplet state occurs in this system. There are also strong inter-band pair correlations between the spin-orbit split bands, in spite of the considerably large spin-orbit splitting. This is due to frustration between the spin-orbit interaction and pairing interactions. In this pairing state, time-r…
The internal structure of the superconducting state in Sr$_2$RuO$_4$ remains elusive at present, and exhibits evidence for time-reversal symmetry breaking. Recent muon spin relaxation measurements under uniaxial strain have revealed an increasing splitting between the superconducting critical temperature $T_c$ and the onset of time-reversal symmetry breaking $T_{\rm TRSB}$ with applied strain [Grinenko et al., arXiv:2001.08152]. In addition, static magnetic order is induced by the uniaxial strain beyond $\sim$1 GPa, indicating that unstrained Sr$_2$RuO$_4$ is close to a magnetic quantum critic…
Quantum Oscillations of $\mathrm{Sr}_2\mathrm{RuO}_4$ under c-Axis Uniaxial Stress
Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, University of St Andrews（圣安德鲁斯大学物理与天文学学院苏格兰大学物理联盟）；National Institute for Materials Science（国立材料研究所）；Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）
We report a combined experimental and theoretical study of the dependence of the superconductivity of the unconventional superconductor Sr$_2$RuO$_4$ on anisotropic strain. Novel piezoelectric apparatus is used to apply uniaxial pressures of up to $\sim$1~GPa along a $\langle 100 \rangle$ direction ($a$-axis) of the crystal lattice. $T_c$ increases from 1.5~K in unstrained material to 3.4~K at compression by $\approx$0.6\%, then falls steeply. The $c$-axis upper critical field for the strained $T_c$ = 3.4~K material is a factor of twenty larger than that of the unstrained crystal, whereas the …
A key question regarding the unconventional superconductivity of Sr$_2$RuO$_4$ remains whether the order parameter is single- or two-component. Under a hypothesis of two-component superconductivity, uniaxial pressure is expected to lift their degeneracy, resulting in a split transition. The most direct and fundamental probe of a split transition is heat capacity. Here, we report development of new high-frequency methodology for measurement of heat capacity of samples subject to large and highly homogeneous uniaxial pressure. We place an upper limit on the heat capacity signature of any second …
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$10 K, consistent with an enhanced density of states associated with passing the Fermi energy thro…
Sr$_{2}$RuO$_{4}$ is one of the most promising candidates of a topological superconductor with broken time-reversal symmetry, because a number of experiments have revealed evidences for a spin-triplet chiral $p$-wave superconductivity. In order to clarify the time-reversal symmetry of Sr$_{2}$RuO$_{4}$, we introduce a novel test that examines the invariance of the Josephson critical current under the inversion of both the current and magnetic fields, in contrast to the detection of a spontaneous magnetic field employed in past experiments. Analyses of the transport properties of the planar and…
A key question regarding the unconventional superconductivity of Sr$_2$RuO$_4$ remains whether the order parameter is single- or two-component. Under a hypothesis of two-component superconductivity, uniaxial pressure is expected to lift their degeneracy, resulting in a split transition. The most direct and fundamental probe of a split transition is heat capacity. Here, we report measurement of heat capacity of samples subject to large and highly homogeneous uniaxial pressure. We place an upper limit on the heat-capacity signature of any second transition of a few per cent of that of the primar…
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…
In-plane uniaxial pressure has been shown to strongly tune the superconducting state of Sr2RuO4 by approaching a Lifshitz transition and associated Van Hove singularity (VHS) in the density of states. At the VHS, $T_c$ and the in- and out-of-plane upper critical fields are all strongly enhanced, and the latter has changed its curvature as a function of temperature from convex to concave. However, due to strain inhomogeneity it has not been possible so far to determine how the upper critical fields change with strain. Here, we show the strain dependence of both upper critical fields, which was …
We study the spin dynamics in a p-wave superconductor at the nesting vector associated with $α$ and $β$ bands in Sr$_2$RuO$_4$. We find a collective mode at the nesting vector in the superconducting phase identified as the odd-parity pairing state which breaks time reversal symmetry. This mode in the spin channel only exists in the p-wave superconductor, not in s- or d-wave superconductors. We propose that probing this mode would clarify the pairing symmetry in Sr$_2$RuO$_4$. The possibility of second superconducting phase transition is also discussed.
There is considerable evidence that the superconducting state of Sr$_2$RuO$_4$ breaks time reversal symmetry. In the experiments showing time reversal symmetry breaking its onset temperature, $T_\text{TRSB}$, is generally found to match the critical temperature, $T_\text{c}$, within resolution. In combination with evidence for even parity, this result has led to consideration of a $d_{xz} \pm id_{yz}$ order parameter. The degeneracy of the two components of this order parameter is protected by symmetry, yielding $T_\text{TRSB} = T_\text{c}$, but it has a hard-to-explain horizontal line node at…
It has been shown [1] that many seemingly contradictory experimental findings concerning the superconducting state in Sr$_2$RuO$_4$ can be accounted for as resulting from the existence of an assumed tetra-critical point at near ambient pressure at which $d_{x^2-y^2}$ and $g_{xy(x^2-y^2)}$ superconducting states are degenerate. We perform both a Landau-Ginzburg and a microscopic mean-field analysis of the effect of spatially varying strain on such a state. In the presence of finite $xy$ shear strain, the superconducting state consists of two possible symmetry-related time-reversal symmetry (TRS…
The London penetration depth for the unconventional superconductor Sr$_2$RuO$_4$ is analyzed assuming an order parameter which breaks time reversal symmetry and parity simultaneously. Such a superconducting state possesses chiral quasiparticle states with subgap energies at the surface. We show that these subgap states can give a significant contribution to the low-temperature behavior of the London penetration depth yielding a $ T^2 $ power-law even though bulk quasiparticle spectrum is gapped. The presence of several electron bands gives rise to interband transition among the subgap surface …
It is widely believed that the perovskite Sr$_2$RuO$_4$ is an unconventional superconductor with broken time reversal symmetry. It has been predicted that superconductors with broken time reversal symmetry should have spontaneously generated supercurrents at edges and domain walls. We have done careful imaging of the magnetic fields above Sr$_2$RuO$_4$ single crystals using scanning Hall bar and SQUID microscopies, and see no evidence for such spontaneously generated supercurrents. We use the results from our magnetic imaging to place upper limits on the spontaneously generated supercurrents a…
Entropy mapping under uniaxial pressure utilizing the elastocaloric effect
Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Scottish Universities Physics Alliance, School of Physics and Astronomy, University of St Andrews（圣安德鲁斯大学物理与天文学学院苏格兰大学物理联盟）；Department of Physics, National Taiwan University（台湾大学物理学系）；National Institute for Materials Science（国立材料研究所）
The superconducting symmetry of Sr$_2$RuO$_4$ remains a puzzle. Time-reversal symmetry breaking $d_{x^2-y^2} + ig_{xy(x^2-y^2)}$ pairing has been proposed for reconciling multiple key experiments. However, its stability remains unclear. In this work, we theoretically study the superconducting instabilities in Sr$_2$RuO$_4$, including the effects of spin-orbit coupling (SOC), in the presence of both local and longer-range interactions within a random phase approximation. We show that the inclusion of second nearest neighbor repulsions, together with non-local SOC in the $B_{2g}$ channel or orbi…
Differential resistance measurements are conducted for point contacts (PCs) between tungsten tip approaching along the $c$ axis direction and the $ab$ plane of Sr$_{2}$RuO$_{4}$ single crystal. Three key features are found. Firstly, within 0.2 mV there is a dome like conductance enhancement due to Andreev reflection at the normal-superconducting interface. By pushing the W tip further, the conductance enhancement increases from 3\% to more than 20\%, much larger than that was previously reported, probably due to the pressure exerted by the tip. Secondly, there are also superconducting like fea…
Uniaxial strain experiments have become a powerful tool to unveil the character of unconventional phases of electronic matter. Here we propose a combination of the superconducting fitness analysis and density functional theory (DFT) calculations in order to dissect the effects of strain in complex multi-orbital quantum materials from a microscopic perspective. We apply this framework to the superconducting state of Sr$_2$RuO$_4$, and argue that the recently proposed orbitally anti-symmetric spin-triplet (OAST) order parameter candidate has unique signatures under strain which are in agreement …
Strontium ruthenate (Sr$_2$RuO$_4$) has long been thought to host a spin-triplet chiral $p$-wave superconducting state. However, the singletlike response observed in recent spin-susceptibility measurements casts serious doubts on this pairing state. Together with the evidence for broken time-reversal symmetry and a jump in the shear modulus $c_{66}$ at the superconducting transition temperature, the available experiments point towards an even-parity chiral superconductor with $k_z(k_x\pm ik_y)$-like $E_g$ symmetry, which has consistently been dismissed based on the quasi-two-dimensional electr…
We report the development of a technique to measure heat capacity at large uniaxial pressure using a piezoelectric-driven device generating compressive and tensile strain in the sample. Our setup is optimized for temperatures ranging from 8 K down to millikelvin. Using an AC heat-capacity technique we are able to achieve an extremely high resolution and to probe a homogeneously strained part of the sample. We demonstrate the capabilities of our setup on the unconventional superconductor Sr$_2$RuO$_4$. By replacing thermometer and adjusting the remaining setup accordingly the temperature regime…
Origins of spontaneous magnetic fields in Sr$_2$RuO$_4$
PSI Center for Neutron and Muon Sciences CNM（瑞士保罗谢尔研究所中子与μ子科学中心）；STFC-ISIS Facility, Rutherford Appleton Laboratory（英国科学与技术设施委员会- ISIS设施，鲁瑟福阿普尔顿实验室）；National Institute for Materials Science（日本国立材料研究所）；Toyota Riken - Kyoto-Univ. Research Center (TRiKUC)（丰田理研-京都大学研究中心）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）
We study the pairing symmetry of Sr$_2$RuO$_4$ through the group-theoretical approach. We emphasize the role of pairing interaction between the quasi-one-dimensional(Q1D) $d_{xz/yz}$ and quasi-two-dimensional(Q2D) $d_{xy}$ orbitals. It is found that two degenerate inter-orbital time-reversal-invariant(TRI) p-wave pairings, one is spin-singlet and the other spin-triplet with out-of-plane $\bm{d}$-vector, could be the most promising candidates. Several important physical quantities are presented, including the near-nodal gap structure, the unchanged out-of-plane Knight shift, and no split transi…
In conventional and high transition temperature copper oxide and iron pnictide superconductors, the Cooper pairs all have even parity. As a rare exception, Sr$_2$RuO$_4$ is the first prime candidate for topological chiral p-wave superconductivity, which has time-reversal breaking odd-parity Cooper pairs known to exist before only in the neutral superfluid $^3$He. However, there are several key unresolved issues hampering the microscopic description of the unconventional superconductivity. Spin fluctuations at both large and small wavevectors are present in experiments, but how they arise and d…
We study theoretically the mixed state properties of a strong uniaxially-anisotropic type II superconductor with the Pauli paramagnetic effect, focusing on their behaviors when the magnetic field orientation is tilted from the conduction layer ab plane. On the basis of Eilenberger theory, we quantitatively estimate significant contributions of the Pauli paramagnetic effects on a variety of physical observables, including transverse and longitudinal components of the flux line lattice form factors, magnetization curves, Sommerfeld coefficient, field distributions and magnetic torques. We apply …
The superconducting pairing in Sr$_2$RuO$_4$ is widely considered to be chiral $p$-wave with $\vec{d}_{\boldsymbol k} \sim (k_x + ik_y)\hat{z}$, which belongs to the $E_u$ representation of the crystalline $D_{4h}$ group. However, this superconducting order appears hard to reconcile with a number of key experiments. In this paper, based on symmetry analysis we discuss the possibility of odd-parity pairing with inherent three-dimensional (3D) character enforced by the inter-orbital interlayer coupling and the sizable spin-orbit coupling (SOC) in the material. We focus on a yet unexplored $E_u$ …
Recent experiments suggest that the superconducting order parameter of Sr$_2$RuO$_4$ has two components. A two-component order parameter has multiple degrees of freedom in the superconducting state that can result in low-energy collective modes or the formation of domain walls -- a possibility that would explain a number of experimental observations including the smallness of the time reversal symmetry breaking signal at T$_\mathrm{c}$ and telegraph noise in critical current experiments. We perform ultrasound attenuation measurements across the superconducting transition of Sr$_2$RuO$_4$ using…
We propose to realize second-order topological superconductivity in bilayer spin-polarized Fermi gas superfluids. We focus on systems with intralayer chiral $p$-wave pairing and with tunable interlayer hopping and interlayer interactions. Under appropriate circumstances, an interlayer even-parity $s$- or $d$-wave pairing may coexist with the intralayer $p$-wave. Our model supports localized Majorana zero modes not only at the corners of the system geometry, but also at the terminations of certain one-dimensional defects, such as lattice line defects and superfluid domain walls. We show how suc…
We will extend the concept of electron band Berry curvatures to superconducting materials. We show that this can be defined for the Bogoliubov-de Gennes equation describing the superconducting state in a periodic crystal. In addition, the concept is exploited to understand the driving mechanism for the optical Kerr effect in time reversal symmetry breaking superconductors. Finally, we establish a sum rule analogue to the normal state Hall sum rule making quantitative contact between the imaginary part of the optical conductivity and the Berry curvature. The general theory will be applied and t…
Strontium ruthenate (Sr$_2$RuO$_4$) is a multiband superconductor that displays evidence of topological superconductivity, although a model of the order parameter that is consistent with all experiments remains elusive. We integrated a piezoelectric-based strain apparatus with a scanning superconducting quantum interference device (SQUID) microscope to map the diamagnetic response of single-crystal Sr$_2$RuO$_4$ as a function of temperature, uniaxial pressure, and position with micron-scale spatial resolution. We thereby obtained local measurements of the superconducting transition temperature…
The superconducting state in the quasi-two-dimensional and strongly correlated Sr$_2$RuO$_4$ is uniquely held up as a solid state analog to superfluid $^3$He-$A$, with an odd-parity order parameter that also breaks time reversal symmetry, and for which the vector order parameter has the same direction in spin space for all electron momenta. The recent discovery that uniaxial pressure causes a steep rise and maximum in transition temperature ($T_c$) in strained samples motivated the study of $^{17}$O nuclear magnetic resonance (NMR) that we describe in this article. A reduction of Knight shifts…
Although correlated electronic-structure calculations explain very well the normal state of Sr$_2$RuO$_4$, its superconducting symmetry is still unknown. Here we construct the spin and charge fluctuation pairing interactions based on its correlated normal state. Correlations significantly reduce ferromagnetic in favor of antiferromagnetic fluctuations and increase inter-orbital pairing. From the normal-state Eliashberg equations, we find spin-singlet $d$-wave pairing close to magnetic instabilities. Away from these instabilities, where charge fluctuations increase, we find two time-reversal sy…
The vortex lattice structures of Sr$_2$RuO$_4$ for the odd parity representations of the superconducting state are examined for the magnetic field along the crystallographic directions. Particular emphasis is placed upon the two dimensional representation which is believed to be relevant to this material. It is shown that when the zero-field state breaks time reversal symmetry, there must exist two superconducting transitions when there is a finite field along a high symmetry direction in the basal plane. Also it is shown that a square vortex lattice is expected when the field is along the $c$…
A comprehensive theory of superconductivity in Sr$_2$RuO$_4$ must explain experiments that suggest even parity superconducting order and others that suggest broken time reversal symmetry. Completeness further requires that the theory applies to Ca$_2$RuO$_4$, a Mott-Hubbard semiconductor that exhibits an unprecedented insulator-to-metal transition driven by very small electric field, and also by doping with very small concentration of electrons, leading to a metallic state proximate to ferromagnetism. A valence transition model, previously proposed for superconducting cuprates [Phys. Rev. B {\…
In this work, after reviewing the theory of the elastic properties of Strontium ruthenate, an extension suitable to explain the sound speed experiments of Lupien et. al. \protect\cite{lup2} and Clifford et. al. \protect\cite{clif1} is carried out. It is found that the discontinuity in the elastic constant C$_{66}$ gives unambiguous experimental evidence that the \sr superconducting order parameter $Ψ$ has two components and shows a broken time-reversal symmetry state. A detailed study of the elastic behavior is performed by means of a phenomenological theory employing the Ginzburg-Landau forma…
We present an analysis of the Hall conductivity $σ_{xy}(ω, T)$ in time reversal symmetry breaking states of exotic superconductors. We find that the dichroic signal is non-zero in systems with inter-band order parameters. This new intrinsic mechanism may explain the Kerr effect observed in strontium ruthenate and possibly other superconductors. We predict coherence factor effects in the temperature dependence of the imaginary part of the ac Hall conductivity $ Imσ_{xy}(ω, T)$, which can be tested experimentally.
The exact nature of unconventional superconductivity in Sr$_2$RuO$_4$ remains a mystery. At the phenomenological level, no superconducting order parameter proposed thus far seems able to coherently account for all essential experimental signatures. Among the latter is the prominent polar Kerr effect, which implies a nonzero ac anomalous Hall conductivity. Assuming the Kerr effect is intrinsic, it can be accounted for by a bulk chiral Cooper pairing with nonzero orbital angular momentum, such as $p+ip$ or $d+id$, which, however, has difficulties in being reconciled with other experimental resul…
The search for broken time reversal symmetry (TRSB) in unconventional superconductors intensified in the past year as more systems have been predicted to possess such a state. Following our pioneering study of TRSB states in Sr$_2$RuO$_4$ using magneto-optic probes, we embarked on a systematic study of several other of these candidate systems. The primary instrument for our studies is the Sagnac magneto-optic interferometer, which we recently developed. This instrument can measure magneto-optic Faraday or Kerr effects with an unprecedented sensitivity of 10 nanoradians at temperatures as low a…
Using an asymptotically exact weak coupling analysis of a multi-orbital Hubbard model of the electronic structure of \SRO, we show that the interplay between spin and charge fluctuations leads unequivocally to triplet pairing which originates in the quasi-one dimensional bands. The resulting superconducting state spontaneously breaks time-reversal symmetry and is of the form $Δ\sim p_x + i p_y \hat{z}$ with sharp gap minima and a d-vector that is only {\it weakly} pinned. The supercondutor is topologically {\it trivial} and hence lacks robust chiral Majorana fermion modes along the boundary. T…
One of the main developments in unconventional superconductivity in the past two decades has been the discovery that most unconventional superconductors form phase diagrams that also contain other strongly correlated states. Many systems of interest are therefore close to more than one instability, and tuning between the resultant ordered phases is the subject of intense research1. In recent years, uniaxial pressure applied using piezoelectric-based devices has been shown to be a particularly versatile new method of tuning, leading to experiments that have advanced our understanding of the fas…
The symmetry of the superconducting condensate in Sr$_2$RuO$_4$ remains controversial after nuclear magnetic resonance (NMR) experiments recently overturned the dominant chiral $p$-wave paradigm. Several theoretical proposals have been put forward to account for existing experiments, including a $d+ig$-wave admixture, conjectured to be stabilized by longer-range Coulomb interactions. We perform a material-specific microscopic theoretical study of pairing by spin- and charge-fluctuations in Sr$_2$RuO$_4$, including the effects of spin-orbit coupling, and both local and longer-range Coulomb repu…
Starting from the orthorhombic magnetically ordered phase, we investigate the effects of uniaxial tensile and compressive stresses along a, b, and the diagonal a+b directions in BaFe2As2 and CaFe2As2 in the framework of ab initio density functional theory (DFT) and a phenomonological Ginzburg-Landau model. While -contrary to the application of hydrostatic or c-axis uniaxial pressure- both systems remain in the orthorhombic phase with a pressure-dependent nonzero magnetic moment, we observe a sign-changing jump in the orthorhombicity at a critical uniaxial pressure, accompanied by a reversal of…
We present scanning SQUID microscopy data on the superconductors Sr2RuO4 (Tc = 1.5 K) and PrOs$_4$Sb$_{12}$ (Tc = 1.8 K). In both of these materials, superconductivity-related time-reversal symmetry-breaking fields have been observed by muon spin rotation; our aim was to visualize the structure of these fields. However in neither Sr$_2$RuO$_4$ nor PrOs$_4$Sb$_{12}$ do we observe spontaneous superconductivity-related magnetization. In Sr$_2$RuO$_4$, many experimental results have been interpreted on the basis of a $px \pm ipy$ superconducting order parameter. This order parameter is expected to…
Standard superconductors display a ubiquitous discontinuous jump in the electronic specific heat at the critical superconducting transition temperature. In a growing class of unconventional superconductors, however, a second order parameter component may get stabilized and produce a second heat capacity jump at a lower temperature, typically associated with the spontaneous breaking of time-reversal symmetry. The splitting of the two specific heat discontinuities can be controlled by external perturbations such as chemical substitution, hydrostatic pressure, or uniaxial strain. We develop a the…
