Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session F57: Superconductivity: Unconventional Theories IRecordings Available

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Sponsoring Units: DCMP Chair: Benjamin Fregoso, Kent State University Room: Hyatt Regency Hotel Clark 
Tuesday, March 15, 2022 8:00AM  8:12AM 
F57.00001: Frequencydependent Interpseudospin Solutions of Superconducting Strontium Ruthenate Olivier Gingras, Michel Cote, A.M. S Tremblay Recent experimental improvements have shifted the discussion on superconducting Sr_{2}RuO_{4} away from the chiral pwave solution, yet experiments give seemingly different pictures that are challenging to reconcile. In this multiorbital system with important spinorbit coupling, pairing mediated by electronic correlations leads to superconducting order parameters with rich structures. Taking advantage of pseudospin and inversion symmetries, we investigate the possible superconducting instabilities mediated by these spin and charge fluctuations. We find that spinorbit coupling ubiquitously mixes even and odd contributions in orbital, spin and frequency spaces. We find two different leading interpseudospin symmetries: a B_{1g}^{+} and an A_{2g}^{} that have intraorbital components respectively even and odd in Matsubara frequencies. An accidental degeneracy between those could help unify experimental evidence. 
Tuesday, March 15, 2022 8:12AM  8:24AM 
F57.00002: Fractional fermionic Mott insulator and hightemperature superconductor in the doublonconserving Hubbard model Rohit Hegde The Hubbard model's doublonconserving (DC) series expansion most directly mimics the true Hamiltonian dynamic (which does not conserve doublon number) when interaction dominates over bandwidth and the series can be truncated at low order in t/u. This work explores lowtemperature electronic and superconducting orders driven by a renormalized particlehole symmetric DC Hubbard model at intermediate coupling crucially including correlated hopping, accompanied by strong, exotic threebody fluctuations at finite temperature. Fluctuations couple not only to spins and charges, but to their hoppings and currents, and include terms promoting chirality. HartreeFock calculations reveal a spontaneous metric fostering exoticism including unstable gauged ferromagnetism with undamped Higgs mode at halffilling, antiferromagnetism, a strongly insulating Wigner crystal of holons at fractional filling, and gapless striped states. BdG theory incorporates Hirsch's swave superconductor, but reveals a tendency to inhomogeneity and stripeyintertwining with charge and spin order. The harmony of Hubbard U, correlated hopping, and superexchange strongly prefers dwave pairing over swave. Including the DC current in a linear response calculation reveals distinctly nonBCS electrodynamics, including a vanishing of superfluid density approaching halffilling. The pivotal role of t' is explored alongside psuedogap candidatestates. 
Tuesday, March 15, 2022 8:24AM  8:36AM 
F57.00003: Orbital entanglement mechanism of unconventional supercondcutivity Sergei Urazhdin, Alexander Mitrofanov The widely held notion that the superconducting holes in cuprates reside in Cu d_{x2y2} orbitals is incorrect, because twohole correlations responsible for superconductivity are not described by the molecular orbital approximation. We utilize Hubbard model to show that insted, the nearestneighbor d_{2+} and d_{2} Cu orbitals become entangled due to orbitallyselective virtual hopping onto the p_{+}, p_{} orbitals of oxygens shared by Cu neighbors. Without doping, these correlations lead to the Mott state or orbital antiferromagnetism. Doping suppresses these states, and the ground state becomes orbitally entangled singletlike with a residual gauge symmetry. We provide thermodynamic arguments that the gauge symmetry becomes broken at sufficiently low temperature due to the collective correlation effects, resulting in the onset of superconductivity. We expect that the proposed orbital entanglement mechanism explains superconductivity in other unconventional superconductors, including SrTiO_{3}, iron pnictides and twisted multilayer graphene, and elucidates their direct connection with ferromagnetism, which can be described as condensation of orbitallyentangled spin triplets. Our analysis also provids specific guidance in the search for better hightemperature superconductors. 
Tuesday, March 15, 2022 8:36AM  8:48AM 
F57.00004: The Effect of Repulsion on Superconductivity at Low Density Dan Phan, Andrey V Chubukov We examine the effect of repulsion on superconductivity in a threedimensional system with a BardeenPineslike interaction in the lowdensity limit, where the chemical potential is much smaller than the phonon frequency. We parameterize the strength of the repulsion by a dimensionless parameter f. We find that the superconducting transition temperature T_{c} approaches a nonzero value in the limit of zero density as long as f is below a certain threshold f^{*}. We show that T_{c} goes to zero as a power of f^{*} f, in contrast to the high density limit, where T_{c} goes to zero exponentially quickly as f approaches f^{*}. At the same time as T_{c} goes to zero, the nodes of the gap function along the Matsubara axis approach zero also as a power of f^{*} f. 
Tuesday, March 15, 2022 8:48AM  9:00AM 
F57.00005: On the possibility of mixed helical pwave pairings in Sr$_2$RuO$_4$ Zhiqiang Wang, Wen Huang The exact nature of the 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 results. Given the situation, we propose alternative possibilities with complex mixtures of distinct helical pwave order parameters, namely, $A_{1u}+iA_{2u}$ and $B_{1u}+iB_{2u}$ in the group theory nomenclature. We show that these states can explain the Kerr data and exhibit salient features that may explain several other key observations in this material, including the absence of spontaneous edge current, a substantial Knight shift drop, and possibly signatures in uniaxial strain and ultrasound measurements. 
Tuesday, March 15, 2022 9:00AM  9:12AM 
F57.00006: Straininduced time reversal breaking and half quantum vortices near a putative superconducting tetracritical point in Sr_{2}RuO_{4} Andrew C Yuan, Steven A Kivelson, Erez Berg It has been shown 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 tetracritical point at near ambient pressure at which $d_{x^2y^2}$ and $g_{xy(x^2y^2)}$ superconducting states are degenerate. We perform both a LandauGinzburg and a microscopic meanfield 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 symmetryrelated timereversal symmetry (TRS) preserving states: $d \pm g$. However, at domain walls between two such regions, TRS can be broken, resulting in a $d+ig$ state. More generally, we find that various natural patterns of spatially varying strain induce a rich variety of superconducting textures, including halfquantum fluxoids. These results may resolve some of the apparent inconsistencies between the theoretical proposal and various experimental observations, including the suggestive evidence of halfquantum vortices. 
Tuesday, March 15, 2022 9:12AM  9:24AM 
F57.00007: Effects of longerrange interaction on superconductivity in Sr_{2}RuO_{4} Xin Wang, Zhiqiang Wang, Catherine Kallin The superconducting symmetry of Sr_{2}RuO_{4} (SRO) remains a puzzle. Currently, none of the proposed order parameters (OP) can account for all the key experiments, highlighting the importance of exploring different alternatives. Recently, among others, d_{x2y2} + ig_{xy(x2y2) }and s+id_{xy} pairings have been proposed as OP candidates. However, their stability remains unclear. In this work, with effects of the sizable spinorbit coupling accounted for, we theoretically study the superconducting instabilities in SRO in the presence of both local and longerrange interactions. We show that inclusion of a second nearest neighbor repulsion or orbitalanisotropy of the longerrange interaction can have a significant impact on the stability of the gwave pairing. Different pairing states, including d_{x2y2} + ig, s+id_{xy}, mixed helical, and d_{x2y2} + ip, are found to be stabilized in different regimes of the interaction parameter space. We further investigate their properties such as Knight shift and spontaneous edge current. Lastly, we make a connection to the orbitalbasis classification of superconducting states that has been actively discussed recently. 
Tuesday, March 15, 2022 9:24AM  9:36AM 
F57.00008: Superconducting gaps for Sr_{2}RuO_{4} and their manifestations on observables MarcAntoine Gauthier, Olivier Gingras, A.M. S Tremblay The superconducting gap of the Sr2RuO4 is still unknown [1]. The most recent striking inconsistency is observed under uniaxial pressure. While highsensitivity specific heat measurements detect only one transition temperature [2], muon spin relaxation experiments suggest two [3]. Because the minimal effective model of Sr2RuO4 involves multiple orbitals coupled by spinorbit interaction, the possible gap functions are extremely intricate and possess oddfrequency contributions [4]. Starting from a model Hamiltonian, we compute the specific heat, the spectral weight and the band diagram expected for various superconducting order parameters. We inspect the effect of interorbital pairing on those quantities and we generalize the formalism to account for frequency dependent gap functions. 
Tuesday, March 15, 2022 9:36AM  9:48AM 
F57.00009: Spin triplet superconductivity driven by finite momentum spin fluctuations Andreas Kreisel, Peter J Hirschfeld, Yundi Quan A small number of superconductors are believed to exhibit intrinsic spin triplet pairing, 
Tuesday, March 15, 2022 9:48AM  10:00AM 
F57.00010: Thermodynamic properties of superconductors in the extended BCSBose crossover theory Luis Abraham García Hernández, Marcela Dolores Grether González, Manuel de Llano Superconductivity in a generalized BoseEinstein condensation theory (GBEC) is addressed. This theory contains three coupled transcendental equations for all temperatures: two gaplike equations and a particle number density equation that guarantees charge conservation. Here we explore the special case of an extended BCSBose crossover picture where twohole Cooper pairs are explicitly included. We solved these three associated coupled equations yielding two pure BoseEinsteincondensation phases of twoelectron Cooper pairs and/or of twohole Cooper pairs plus a mixed phase with varying proportions of both kinds of pairs. We found that the mere inclusion of twohole Cooper pairs can lead to critical temperatures enhanced by several orders of magnitude compared with BCS theory. We also found a weakintermediate and strongcoupling regime. Within the BCSBose crossover theory, we calculated the entropy and from that we analysed the rest of the wellknown thermodynamic quantities that can be compared with experimental data. Results fit better for elemental superconductors, suggesting that twohole Cooper pairs might be indispensable to describe this kind of materials. 
Tuesday, March 15, 2022 10:00AM  10:12AM 
F57.00011: Superconducting Instability From Spin Fluctuations in Sr_{2}RuO_{4} Astrid T Rømer, Peter J Hirschfeld, Brian M Andersen, Andreas Kreisel, Thomas A Maier The symmetry of the superconducting condensate in Sr_{2}RuO_{4} remains controversial after recent experiments overturned the dominant chiral pwave paradigm: NMR leaves almost no room for a triplet component and ultrasound experiments put very stringent constraints on the superconducting order parameter which is deemed to comprise two components[1,2,3]. At the same time, specific heat finds no evidence for a split transition under uniaxial strain [4] in sharp contrast to the findings of muon spin rotation[5]. We explore which superconducting order parameters are favorable from the perspective of spinfluctuation mediated pairing, taking into account the three Ru orbitals, a sizable spinorbit coupling, longer range Coulomb interaction as well as threedimensional effects. A full selfconsistent solution of the gap sheds light on the propensity to timereversal breaking superconducting order based on the neardegeneracy of symmetrydistinct pairing states and we will discuss effects due to strain and impurities. [1] A. Pustogow et al., Nature 574, 72 (2019) [2] S. Ghosh et al., Nat. Phys. 17, 199 (2021) [3] S. Benhabib et al., Nat. Phys. 17, 194 (2021) [4] Y.S. Li et al, PNAS 118, 10 (2021) [5] V. Grinenko et al, Nat. Phys. 17, 748 (2021) 
Tuesday, March 15, 2022 10:12AM  10:24AM 
F57.00012: Emergence of multiple Higgs modes in a superconductor due to spontaneous breakdown of a Z_{2} symmetry Shunji Tsuchiya Higgs modes and NambuGoldstone (NG) modes are ubiquitous collective excitations that arise in systems with spontaneous symmetry breaking. Although Higgs modes are believed to emerge with NG modes when continuous symmetries are spontaneously broken, Higgs modes do not necessarily appear in systems exhibiting spontaneous breakdown of continuous symmetries. We study the Higgs mode in a BardeenCooperSchrieffer (BCS) superconductor. Motivated by the observation that U(1) symmetry of the BCS Hamiltonian is not essential for the Higgs mode, we study the Isinglike Hamiltonian in the pseudospin representation. We show that the Higgs mode emerges as the lowest excited state of the Isinglike Hamiltonian due to spontaneous breakdown of Z_{2} symmetry under the timereversal operation T in the pseudospin space. We further predict the existence of multiple Higgs modes that have quantized energy 2(n+1)∆_{0} (0 ≤ n ≤ N_{kF} ), where ∆_{0 }is the superconducting gap, n is an integer, and N_{kF }is the number of states on the Fermi surface. 
Tuesday, March 15, 2022 10:24AM  10:36AM 
F57.00013: Study of vorticesPDW mixed state predicted by the tJ model via renormalized meanfield theory YiHsuan Liu, GiaWei Chern, TingKuo Lee

Tuesday, March 15, 2022 10:36AM  10:48AM Withdrawn 
F57.00014: Quantum Phase Fluctuations Dominate Unconventional Superconductivity Anthony C Hegg, Wei Ku, Ruoshi Jiang, Yucel Yildirim Unconventional superconductivity has remained one of the most important mysteries in condensed matter physics since its discovery several decades ago. In contrast to conventional gapped swave BCS theory, early experiments indicated Tlinear superfluid density at low temperature and more recent experiments with everhigher accuracy frequently find superlinear dependence at low temperature, casting doubt on conventional theory categorically. We examine many wellknown prototypical unconventional superconductors from several families and discover systematic T^{3} depletion of the 3D superfluid density at low temperature. To explain this novel behavior, we study the manybody currentcurrent response of bosons in a lattice and find generic T^{3} depletion of the superfluid density. In contrast to the universality found in the vicinity of phase transitions, such stable lowtemperature behavior is highly sensitive to the underlying quantum manybody theory and can be used to distinguish between possible theories. The success of our bosonic model at low temperature implies that phasefluctuation dominated superfluidity underlies the quantum nature of the superconductivity in many of these materials. 
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