Uniaxial Pressure Studies of the Unconventional Superconductor Sr₂RuO₄

This thesis concentrates on the effect of Lifshitz transitions and associated Van Hove singularities on the superconducting state of Sr₂RuO₄. I will start by giving a short summary of the unconventional superconducting state of Sr₂RuO₄, and discuss how a Lifshitz transition can be accessed using uniaxial pressure. I will then discuss recent results of measurements under uniaxial stress, which have changed our view of the nature of the superconductivity of this material considerably

Evidence for even parity unconventional superconductivity in Sr2RuO4

Funding: A.C. is grateful for support from the Julian Schwinger Foundation for Physics Research. A.P. acknowledges support by the Alexander von Humboldt Foundation through the Feodor Lynen Fellowship. Work at Los Alamos was funded by Laboratory Directed Research and Development (LDRD) program, and A.P. acknowledges partial support through the LDRD. N.K. acknowledges the support by the Grants-in-Aid for Scientific Research (KAKENHI, Grant JP18K04715 and JP21H01033) from Japan Society for the Promotion of Science (JSPS). The work at Dresden was funded by the Deutsche Forschungsgemeinschaft - TRR 288 - 422213477 (projects A10 and B01). The work at University of California, Los Angeles, was supported by NSF Grants 1709304 and 2004553.Unambiguous identification of the superconducting order parameter symmetry in Sr2RuO4 has remained elusive for more than a quarter century. While a chiral p-wave ground state analogue to superfluid 3He-A was ruled out only very recently, other proposed triplet-pairing scenarios are still viable. Establishing the condensate magnetic susceptibility reveals a sharp distinction between even-parity (singlet) and odd-parity (triplet) pairing since the superconducting condensate is magnetically polarizable only in the latter case. Here field-dependent 17O Knight shift measurements, being sensitive to the spin polarization, are compared to previously reported specific heat measurements for the purpose of distinguishing the condensate contribution from that due to quasiparticles. We conclude that the shift results can be accounted for entirely by the expected field-induced quasiparticle response. An upper bound for the condensate magnetic response of < 10% of the normal state susceptibility is sufficient to exclude all purely odd-parity candidates. PostprintPeer reviewe

Strong peak in Tc of Sr2RuO4 under uniaxial pressure

Sr2RuO4 is an unconventional superconductor that has attracted widespread study because of its high purity and the possibility that its superconducting order parameter has odd parity. We study the dependence of its superconductivity on anisotropic strain. Applying uniaxial pressures of up to ~1 gigapascals along a 〈100〉 direction (a axis) of the crystal lattice results in the transition temperature (Tc) increasing from 1.5 kelvin in the unstrained material to 3.4 kelvin at compression by ≈0.6%, and then falling steeply. Calculations give evidence that the observed maximum Tc occurs at or near a Lifshitz transition when the Fermi level passes through a Van Hove singularity, and open the possibility that the highly strained, Tc = 3.4 K Sr2RuO4 has an even-parity, rather than an odd-parity, order parameter.PostprintPeer reviewe

Upper Critical Field of Sr2_2RuO4_4 under In-Plane Uniaxial Pressure

In-plane uniaxial pressure has been shown to strongly tune the superconducting state of Sr$_2$RuO$_4$ 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 achieved due to an improved sample preparation. We find that the in-plane upper critical field is mostly linear in $T_c$. On the other hand, the out-of-plane upper critical field varies with a higher power in $T_c$, and peaks strongly at the VHS. The strong increase in magnitude and the change in form of $H_\mathrm{c2||c}$ occur very close to the Van Hove strain, and points to a strong enhancement of both the density of states and the gap magnitude at the Lifshitz transition

Superconducting penetration depth through a Van Hove singularity: Sr₂RuO₄ under uniaxial stress

A plethora of experiments in Sr2⁢RuO4 have reached conflicting conclusions about the symmetry of the superconducting gap. To probe the gap's structure in k space, we use strain to continuously tune the band structure through a Van Hove singularity (VHS) while imaging the superconductivity with scanning superconducting quantum interference device microscopy. We find that the superfluid density peaks at the VHS and that the temperature dependence of the penetration depth is 2 quadratic over the entire measured range of strain ɛ. These results are consistent with a gap structure that has vertical line nodes, experimentally confirming that nonlocal effects in the Meissner screening can lead to 2 behavior and clarifying the nature of the low-energy excitations in Sr2⁢RuO4

Superconducting penetration depth through a Van Hove singularity: Sr₂RuO₄ under uniaxial stress

A plethora of experiments in Sr2⁢RuO4 have reached conflicting conclusions about the symmetry of the superconducting gap. To probe the gap's structure in k space, we use strain to continuously tune the band structure through a Van Hove singularity (VHS) while imaging the superconductivity with scanning superconducting quantum interference device microscopy. We find that the superfluid density peaks at the VHS and that the temperature dependence of the penetration depth is 2 quadratic over the entire measured range of strain ɛ. These results are consistent with a gap structure that has vertical line nodes, experimentally confirming that nonlocal effects in the Meissner screening can lead to 2 behavior and clarifying the nature of the low-energy excitations in Sr2⁢RuO4

T_c and the elastocaloric effect of Sr₂RuO₄ under ⟨110⟩ uniaxial stress:No indications of transition splitting

There is considerable evidence that the superconductivity of Sr2RuO4 has two components. Among this evidence is a jump in the shear elastic modulus c66 at the critical temperature Tc, observed in ultrasound measurements. Such a jump is forbidden for homogeneous single-component order parameters, and it implies that Tc should develop as a cusp under the application of shear strain with ⟨110⟩ principal axes. This shear strain should split the onset temperatures of the two components, if they coexist, or select one component if they do not. Here, we report measurements of Tc and the elastocaloric effect of Sr2RuO4 under uniaxial stress applied along the [110] lattice direction. Within experimental resolution, we resolve neither a cusp in the stress dependence of Tc, nor any second transition in the elastocaloric effect data. We show that reconciling these null results with the observed jumps in c66 requires extraordinarily fine tuning to a triple point of the Ginzburg-Landau parameter space. In addition, our results are inconsistent with homogeneous time-reversal symmetry breaking at a temperature T2 ≤ Tc as identified in muon spin relaxation experiments

Dichotomous dynamics of magnetic monopole fluids

A recent advance in the study of emergent magnetic monopoles was the discovery that monopole motion is restricted to dynamical fractal trajectories [J. N. Hallén et al., Science 378, 1218 (2022)], thus explaining the characteristics of magnetic monopole noise spectra [R. Dusad et al., Nature 571, 234 (2019); A. M. Samarakoon et al., Proc. Natl. Acad. Sci. U.S.A. 119, e2117453119 (2022)]. Here, we apply this novel theory to explore the dynamics of field-driven monopole currents, finding them composed of two quite distinct transport processes: initially swift fractal rearrangements of local monopole configurations followed by conventional monopole diffusion. This theory also predicts a characteristic frequency dependence of the dissipative loss angle for AC field–driven currents. To explore these novel perspectives on monopole transport, we introduce simultaneous monopole current control and measurement techniques using SQUID-based monopole current sensors. For the canonical material Dy2Ti2O7, we measure Φ(t), the time dependence of magnetic flux threading the sample when a net monopole current J(t) = Φ̇ (t)∕0 is generated by applying an external magnetic field B0(t). These experiments find a sharp dichotomy of monopole currents, separated by their distinct relaxation time constants before and after t ~600 μs from monopole current initiation. Application of sinusoidal magnetic fields B0(t) = Bcos(t) generates oscillating monopole currents whose loss angle ( f ) exhibits a characteristic transition at frequency f ≈ 1.8 kHz over the same temperature range. Finally, the magnetic noise power is also dichotomic, diminishing sharply after t ~600 μs. This complex phenomenology represents an unprecedented form of dynamical heterogeneity generated by the interplay of fractionalization and local spin configurational symmetry

Elastocaloric determination of the phase diagram of Sr2_2RuO4_4

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 fascinating unconventional superconductor Sr$_2$RuO$_4$. Here we map out its phase diagram using high-precision measurements of the elastocaloric effect in what we believe to be the first such study including both the normal and the superconducting states. We observe a strong entropy quench on entering the superconducting state, in excellent agreement with a model calculation for pairing at the Van Hove point, and obtain a quantitative estimate of the entropy change associated with entry to a magnetic state that is observed in proximity to the superconductivity. The phase diagram is intriguing both for its similarity to those seen in other families of unconventional superconductors and for extra features unique, so far, to Sr$_2$RuO$_4$