Session R43: Normal State Properties of Unconventional Superconductors

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Strongly correlated electron materials exhibit an intimate relation between charge, spin and structural degrees of freedom, leading to new emergent phases which seemingly break the symmetries of the underlying crystal and result in often unexpected sensitivity to external stimuli. The members of the Ruddlesden-Popper-series Sr_n+1Ru_nO_3n+1 exhibit a wide range of properties attributed to such physics, including unconventional superconductivity, metamagnetic quantum criticality and ferromagnetism. We show in a detailed study of the surface electronic structure of Sr₂RuO₄, an unconventional superconductor, how tiny structural distortions lead to a significant reconstruction of the Fermi surface and the low energy electronic structure. We use ultra-low temperature Scanning tunnelling microscopy to establish the existence of four van Hove singularities within 5 mV of E_f, as well as checkerboard charge order and nematicity of the electronic states. Including these orders in a tight-binding model gives excellent agreement with the experiment. By applying a magnetic field up to 14 T, we observe one of the van Hove singularities to Zeeman split, with one branch extrapolated to reach E_f at ~32 T – providing a text-book example of tuning towards a magnetic field-driven Lifshitz transition.   

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Strain tuning Sr₂RuO₄ through the Lifshitz point, where the van Hove singularity of the electronic spectrum crosses the Fermi energy, causes a change in the temperature dependence of the resistivity [1]. This is rather surprising as usually a single, “hot” point on the Fermi surface does not influence the transport properties of a system. However there are exceptions to this rule [2]. In this talk we discuss a multi-band tight-binding model for strained Sr₂RuO₄ where the Fermi surface crosses the van Hove point. Following [2], we show that this van Hove singularity can cause a change in the temperature and frequency dependence of the conductivity of the system over a wide regime of temperatures and frequencies. For the resistivity the usual T² dependence becomes T²log(1/T), consistent with [1]. Interestingly, this behavior only extends down to lowest temperatures and frequencies if one includes all relevant bands that cross the Fermi energy. Put another way, the inclusion of additional “cold” states on the Fermi surface makes the anomalous temperature dependence more robust.

[1] M. E. Barber, A.S. Gibbs, Y. Maeno, A.P. Mackenzie, and C.W. Hicks, Phys. Rev. Lett. 120, 076602 (2018).

[2] C. H. Mousatov, E. Berg, and S. A. Hartnoll, Proc. Natl. Acad. Sci. 117, 2852 (2020).   

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The normal state of the unconventional superconductor Sr₂RuO₄ (T_c = 1.45 K) is a textbook Fermi Liquid (FL), with signatures of long-lived quasiparticles seen in resistivity, optical conductivity and quantum oscillations below T_FL∼30 K. However at higher temperatures, its resistivity increases unconstrained and eventually exceeds the Ioffe-Regel limit, indicative of strange metallic behavior. We present evidence from two experiments for the presence of nematic fluctuations (along [100]) in Sr₂RuO₄ above T_FL. From ultrasound experiments, we find a large (∼20%) anomalous softening in the B_1g shear modulus (c₁₁ - c₁₂)/2 between 300 K and 35 K, below which its behavior is standard. In contrast, the B_2g shear modulus c₆₆ shows standard behavior over the entire range. Motivated by this evidence of [100] nematicity, and to rule out a lattice origin of the effect, we then performed elastoresistivity measurements. We measure a diverging nematic susceptibility in the B_1g channel which saturates around 60 K, about the same temperature where (c₁₁ - c₁₂)/2 starts to show deviations from Curie-Weiss behavior. Our study suggests that nematic correlations might be the reason behind non-FL physics in Sr₂RuO₄, and hints towards Sr₂RuO₄ being close to a nematic quantum critical point.   

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Sr₂RuO₄ had an eventful past, lingering between an insulating, strongly correlated antiferromagnetic spin system and a low-temperature Fermi liquid superconductor. Moreover, the long-standing problem on the superconducting order parameter has been solved recently, demanding a reassessment of the intrinsic electronic structure of this material using well-defined specimens. Here, superconducting thin films of the low-temperature superconductor Sr₂RuO₄ were grown by molecular beam epitaxy. The highest superconducting transition temperature was 1.4 K and those films showed a residual-resistivity ratio (RRR) of 114. High magnetic field (up to 24 T) magneto-resistance measurements above 0.5 K show Shubnikov-de Haas oscillations thus allowing us to study the intrinsic electronic structure of this material along with the influence of in-plane epitaxial strain in comparison to bulk samples. We also assessed the temperature dependence of the Hall effect of these samples and confirmed that for superconducting samples with RRR > 50, the sign of the Hall coefficient changes twice (130 K and 30 K) and the sign change at 30 K is driven by impurity scattering. In contrast, samples with RRR< 50 show a negative Hall coefficient below 300 K.   

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We present elastoresistance measurements of the iron-based superconductors AFe₂As₂ (A = K, Rb, Cs) in the A_1g, B_1g and B_2g symmetry channels. These materials have strong electronic correlations and show a crossover between a low-temperature coherent heavy Fermi liquid and a high-temperature regime of reduced quasiparticle coherence [1,2]. Neutralizing the large thermal expansion of these materials by means of a piezoelectric strain cell is found to be essential to obtaining intrinsic results. All three materials have a significant in-plane symmetric A_1g response, consistent with the coherence-incoherence crossover.

[1] F. Hardy et al., Phys. Rev. B 94, 205113 (2016)
[2] F. Hardy et al., Phys. Rev. Lett. 111, 027002 (2013)
[3] P. Wiecki et al., Phys. Rev. Lett. accepted (2020)   

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Nematic phases in iron-based and cuprate superconductors are interesting exotic material phases. In these phases, electric quadrupole moments (EQMs) are candidates of the order parameter.
Quantum-mechanical formulation of multipole moments in materials with the C4 symmetry breaking has not been completed, in contrast to C4-preserving cases [1, 2]. Recently, the thermodynamic approach to the formulation of EQMs [3] has been proposed. These formulations are unit cell independent and gauge invariant. Thus, it is now possible to evaluate EQMs-related properties[3] and discuss their origin.
In this work, we analyze thermodynamic EQMs in three materials: LaFeAsO, FeSe, and La2CuO4 which show nematic phases, using a multiband tight-binding models constructed by a first-principles calculation. We discuss thermodynamic EQMs arising from an orbital order and/or bond order. Based on the results, we discuss the difference between iron-based superconductors and cuprate superconductors` EQMs.

[1] Wladimir A. Benalcazar, B. Andrei Bernevig, and Taylor L. Jughes, Science. 357 61 (2017)
[2] Wladimir A. Benalcazar, B. Andrei Bernevig, and Taylor L. Jughes, Phys. Rev. B. 96 245115 (2017)
[3] A. Daido, A. Shitade, and Y. Yanase, arXiv:2010.13999 (2020)   

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The pseudogap phase in cuprate compounds remains poorly understood. While a decades-old idea attributes it to an underlying fractionalization of electrons into spinons and chargons, recent work points to the existence of a fractionalized Fermi liquid (FL*), where deconfined spinons and chargons form a meson-like bound state. Here we report direct numerical evidence for this bound state and its internal rotational excitations in the 2D t-J model doped with a single hole. We propose a combined Raman-ARPES protocol which allows to spectroscopically resolve non-trivial rotational resonances which are invisible in traditional ARPES spectra. Experimentally, we propose to drive a d-wave symmetric B_1g phonon mode and study multi-photon resonances in the ARPES spectrum. In our state-of-the-art time-dependent DMRG calculations we reveal a pronounced new rotational quasiparticle peak at low energies, in a regime where the traditional ARPES spectra is featureless. We explain the observed peak, as well as its dependence on the super-exchange energy J/t, by a simplified toy model where spinons and chargons are connected by a geometric string of displaced spins.   

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The Kadowaki-Woods ratio can be used to probe the electron correlations in metals that can be described by Fermi liquid theory [1]. It is possible to formulate this ratio in terms of the quasiparticle renormalization Z_k and the Fermi liquid cutoff frequency ω_c [2]. Here, we use the two-particle self-consistent approach to study theoretically the effect of antiferromagnetic fluctuations on the Fermi liquid in the electron-doped cuprate NCCO. More precisely, we show the effect of electron correlations on the cutoff frequency and the Kadowaki-Woods-like ratio between Z_k and ω_c. We also investigate the effect of antiferromagnetic fluctuations at two dopings right above and below the antiferromagnetic quantum critical point, as well as in the strongly overdoped region, where we recover the expected Fermi liquid behaviour. We find a gradual and anisotropic breakdown of the quasiparticles along the Fermi surface, analogous to what was observed previously in LSCO [3].

[1] Jacko et al, Nature Physics (2009)
[2] Horio et al, arXiv:2006.13119 (2020)
[3] Chang et al, Nature Communications (2013)   

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We present a combined theoretical and experimental study of the still mysterious pseudogap phase in the lightly hole-doped high-T_c superconductor Na_xCa_2-xCuO₂Cl₂ (Na-CCOC), which has a simple I4/mmm crystal structure stable at all doping levels and temperatures. The CuO₂ layers are nearly independent from each other, suggesting a 2D square lattice for which we consider a single-band Hubbard model solved within Cluster Dynamical Mean-Field Theory (C-DMFT) with a continuous-time quantum Monte Carlo solver. The calculations are compared to ARPES data carried out on the undoped parent compound and on lightly doped Na-CCOC samples. We find good agreement of the spectral functions, which show characteristic features of the pseudogap phase such as a well-defined quasi-particle in the nodal point (π/2,π/2) and the opening of a pseudogap in the anti-nodal region (π,0). Moreover, we observe a magnon-like excitation in the C-DMFT data, which we analyze in the light of fluctuation diagnostics and recent RIXS measurements.   

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Nonlocal Coulomb interactions can significantly affect the electronic correlations in (quasi-)two-dimensional materials. Based on a variational principle, we derive effective Hubbard model descriptions to capture electronic correlations even in the presence of nonlocal Coulomb interactions. For square lattice systems like the cuprate superconductors, we calculate the effective on-site repulsion U* using the Dynamical Cluster Approximation (DCA) as function of doping, interaction strength and temperature. We find a pronouced reduction of U* in the doped regime compared to the half-filled case. In other words, Hubbard based modelling of cuprate superconductors should involve doping-dependent effective interactions U*.   

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In cuprate superconductors, the nature of the pseudogap phase and its interplay with superconductivity are still unclear. Its onset at a doping p* is characterized by a drop in carrier density n from n=1+p above p* to n=p below p* [1]. In Nd_0.4La_1.6-xSr_xCuO₄ (Nd-LSCO), this shows up as a low-temperature upturn in the resistivity ρ and Hall coefficient R_H at dopings below p*=0.23 [2]. Here we present thermoelectric measurements in Nd-LSCO across p*, in magnetic fields large enough to suppress superconductivity. For a heat current in the CuO₂ planes, the Seebeck coefficient S shows a large increase at low temperature below p*, confirming the loss of carrier density. Alon the c-axis, we find that S is isotropic for p > p*, i.e. S_c/T and S_a/T are equal (and positive) in the T=0 limit. In sharp contrast, S_c becomes negative at low temperature when p < p*, revealing a profound change in the Fermi surface topology across p*. Using a Boltzmann transport model, which is shown to calculate accurately resistivity with a k-dependent scattering rate [3], we find that one needs an energy dependent scattering to get the correct sign and temperature dependence of S_a and S_c.
[1] Badoux et al, Nature 531, 210 (2016)
[2] Collignon et al, PRB 95, 224517 (2017)
[3] Fang et al, arXiv:2004.01725   

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The recent discovery of a nonsaturating linear magnetoresistance in several correlated electron systems near a quantum critical point has revealed an interesting interplay between the linear magnetoresistance and the zero-field linear-in-temperature resistivity. These studies suggest a possible role of quantum criticality on the observed linear magnetoresistance. In this presentation, I will present our discovery of a nonsaturating, linear magnetoresistance in Mo₈Ga₄₁, a nearly isotropic strong electron-phonon coupling superconductor with a linear-in-temperature resistivity from the transition temperature to ∼55 K. The growth of the resistivity in field is comparable to that in temperature, provided that both quantities are measured in the energy unit. Our datasets are remarkably similar to magnetoresistance data of the optimally doped La_2−xSr_xCuO₄, despite the clearly different crystal and electronic structures, and the apparent absence of quantum critical physics in Mo₈Ga₄₁. A new empirical scaling formula is developed, which is able to capture the key features of the low-temperature magnetoresistance data of Mo₈Ga₄₁, as well as the data of La_2−xSr_xCuO₄.   

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Application of in-plane uniaxial stress to the quasi-2D correlated material Sr₂RuO₄ results in pronounced changes to the physical properties; most widely recognized is a factor 2.5 increase in superconducting transition temperature. The normal state is also significantly impacted. Reported here are ¹⁷O NMR hyperfine shifts over a wide range of stress, field, and temperature. Results are compared to renormalized 3-band Wannier models constructed from DFT calculations. The crossover temperature to standard Fermi Liquid properties is observed to be tuned continuously from T_FL=30 K to 0 K with applied stress. Furthermore, the combination of correlations and the stress-controlled proximity of E_F to a van Hove singularity are the main factors in determining the normal state properties for temperatures of order 300 K and below.   

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Recently, Grissonnanche et al. observed a giant thermal Hall effect in several cuprate compounds below the critical doping p*. [1] A large, negative thermal Hall coefficient was measured independent of the direction of the applied heat current, making phonons the most likely heat carriers. [2] There is, however, no compelling explanation for why phonons become “chiral” in these cuprates. Here, we use pulse echo ultrasound to probe whether phonons couple to chiral order in the parent compound La2CuO4.
In the absence of mirror symmetry the phase velocity of sound can be sensitive to whether the sound wave-vector is parallel or antiparallel to an applied magnetic field. [3] Detection of such a phonon magnetochiral effect (MCE) suggests coupling to chiral order. By depositing thin-film transducers on opposing faces of an LCO sample, we measure the relative change in the speed of sound of an ultrasonic wave traveling with versus against an applied magnetic field. We discuss the phonon MCE as a symmetry-sensitive measurement of cuprates.

1. Grissonnanche G., et al. Nature 571, 376–380 (2019).
2. Grissonnanche G., et al. Nat. Phys. (2020).
3. Nomura T., et al. Phys. Rev. Lett. 122, 145901 (2019).   

On Demand

High-temperature non-saturating resistivity (so-called “bad metal” behavior), and low-temperature T-linear resistivity (so-called “strange metal” behavior) are well-known puzzles that signifies the non-Fermi liquid nature of the normal-state of cuprates. Here we investigate the temperature-dependent dynamical conductivity of an emergent Bose liquid and found that it reproduces most key features of the observed optical conductivity of cuprates, including the puzzling featureless continuum and the mid-infrared peak. Amazingly, the corresponding resistivity demonstrates both bad metal and strange metal behavior, with simple physical explanations. The results even display similar doping dependence to the experimental data. Our results not only support the notion that the low-energy physics of cuprates are dominant by an emergent Bose liquid, but also suggest a new paradigm to the non-Fermi liquid transport properties of a class of strongly correlated materials.