Session S57: Superconductivity: Unconventional Theories-III

Unconventional superconductivity in systems with annular Fermi surfaces: Application to rhombohedral trilayer graphene

We show that in a two-dimensional electron gas with an annular Fermi surface, long-range Coulomb interactions can lead to unconventional superconductivity by the Kohn-Luttinger mechanism. Superconductivity is strongly enhanced when the inner and outer Fermi surfaces are close to each other. The most prevalent state has chiral p-wave symmetry, but d-wave and extended s-wave pairing are also possible. We discuss these results in the context of rhombohedral trilayer graphene, where superconductivity was recently discovered in  regimes where the normal state has an annular Fermi surface. Using realistic parameters, our mechanism can account for the order of magnitude of $T_c$, as well as its trends as a function of electron density and perpendicular displacement field. Moreover, it naturally explains some of the outstanding puzzles in this material, that include the weak temperature dependence of the resistivity above $T_c$, and the proximity of spin singlet superconductivity to the ferromagnetic phase.   

Polaron-Plasmon Superconductivity in Strontium Titanate

Strontium titanate (STO) is a bulk insulator that becomes a semiconducting superconductor at remarkably low carrier densities - below 10¹⁷ cm^-3 - with a characteristic superconducting dome as a function of doping which peaks at T_c~300mK, all in very close proximity to a ferroelectric quantum critical point. We investigate a scenario of superconductivity mediated by coupling to a strongly anti-adiabatic longitudinal optic phonon, by extending a Fröhlich electron-phonon Hamiltonian to include the effects of electronic Coulomb interactions. For the carrier densities of interest, there is a "cavity enhancement" of superconductivity by the material's own plasmons, which hybridize strongly with LO mode. Working within the cumulant expansion, we calculate the spectral signatures of this unusual regime to compare to photoemission[1] and tunneling[2] experiments, as well as the superconducting phase diagram.

    

[1]Wang et al. Nat Mater 15, 835 (2016)

[2]Swartz et al. PNAS 115, 1475 (2018)   

Lifetime of Scattering of Quasiparticles by Dipolons for Muon Spin Relaxation Rates in High Temperature Superconductors via Dipolon Theory

Ram R. Sharma,

 

University of Illinois at Chicago.

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Category: Superconductivity (Theoretical)

Presentation: Oral

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 ABSTRACT

ABSTRACT

We have investigated the mean lifetime of scattering of quasiparticles (QPs) by dipolons required to explain the muon spin relaxation rate (MSRR)

[1] in $YBa_2Cu_3O_{7-\delta}$  utilizing the dipolon theory

[2-5].Previously, we predicted first of all two new high energy kinks which were  observed later on. 

The theory uses the four momenta space diagrams in the dressed particle picture involvingthe QP Green's function, the dipolon propagator and screened electron-dipolon vertexThe evaluation of the self-energy reveals three processes are important:

(1)A QP  is annihilated and a dipolon   and a QP  are created.

 (2)A QP   and a dipolon are annihilated and a QP  is createdand

 (3)Two QPs  are annihilatedand a dipolon  

is created.

(1) R. R. Sharma, "Theory of Dipolon 

...",  

Physipoetics Press,Lake Barrington, IL, 2021.

(2)  R. R. Sharma, Phy. Rev. {\bf B 63}, 054506 (2001).

(3) R. R. Sharma, Physica {\bf C 439}, 47 (2006).

(4) R. R. Sharma, Physica {\bf C 468}, 190 (2008).

(5) R. R. Sharma, "Dipolon Theory of Kink Structure

...",  in "Superconducting ...", Ed. K. N. Courtlandt,

 P. 81-100, Nova Sc, Pub., Inc., New York, 2009.

\end{document}   

Ground State Phase Diagram of the $t$-$t'$-$J$ Model

We report results of large scale ground state density matrix renormalization group(DMRG) calculations on $t$-$t'$-$J$ cylinders with circumferences 6 and 8.  We determine a rough phase diagram which appears to approximate the 2D system. While for many properties, positive and negative $t'$ values ($t'/t = \pm 0.2$) appear to correspond to electron and hole doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The $t'<0$ (hole doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi-surface of the hole doped cuprates. However, we find $t'<0$ strongly suppresses superconductivity. The $t'>0$ (electron doped) region shows the expected circular Fermi pocket of holes around the $(\pi,\pi)$ point and a broad low-doped region of coexisting antiferromagnetism and $d$-wave pairing with a triplet $p$ component at wave-vector $(\pi,\pi)$ induced by the antiferromagnetism and $d$-wave pairing. The pairing for the electron low-doped system with $t'>0$ is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker $d$-wave pairing and striped $p$-wave pairing appears.  In a small doping region near $x=0.08$  for $t'\sim-0.2$, we find a new type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in  two-leg Heisenberg ladders.   

Robustness of superconductivity in the two-orbital Hubbard chain

Motivated by recent findings of both spin-singlet and spin-triplet pairing in one-dimensional multiorbital Hubbard models at intermediate interaction strengths [N. Patel et al., npj Quantum Mater. 5, 27 (2020)], we study the robustness of the superconducting phases in the two-orbital Hubbard chain. At half-filling, the model maps to the Haldane spin-1 chain in the limit of large Hubbard U and Hund's coupling J_H, whereas superconductivity emerges upon hole doping. Here we consider the system away from the ideal limit of unit hopping and  degenerate orbitals. Using DMRG calculations we explore the effects of interorbital hopping, detuned intraorbital hopping, and crystal fields expected to be present in real materials. We find that while these effects are all detrimental to the emergence of superconductivity, the presence of on-site easy-plane anisotropy tends to promote hole pairing. We discuss their impact on the pairing symmetry and phase diagram.   

Superconducting pairing correlations in the 2D Hubbard model with next nearest hoping.

We study the superconducting pairing correlations in the ground state of the two-dimensional doped Hubbard models --- with nearest hoping t and next nearest hoping t'. Following the previous work on the pure Hubbard model, we again employ two computational methods, auxiliary field quantum Monte Carlo (AFQMC) and density matrix renormalization group (DMRG). These methods complement each other, and provide a powerful combination to tackle this challenging problem, where the results are sensitive to numerical details and finite size effects. We deploy our latest algorithmic advances, including a more  robust procedure for self consistent constraint in AFQMC and the use of twist average boundary conditions. As a result, we achieve much higher accuracy than previously possible. We present detailed and systematic studies of the superconducting order parameter in the ground state for a number of parameter sets (t', U/t, doping), and discuss its interplay with magnetic and charge orders.   

Emergent Supersymmetry at the Boundaries in 1D Charge Conserving Superconductor Coupled to Magnetic Impurities

Interaction induced symmetry protected topological phases exhibit distinct properties which do not exist in the non interacting limit. The topological properties emerge due to strong correlations in the bulk. A well known example is a 1D charge conserving superconductor in the spin triplet phase (STS) with open boundary conditions which features a topological phase with protected Majorana zero modes at the edges. Here we consider a superconductor in the spin singlet phase (SSS) which is considered to be topologically trivial.   However  upon coupling  it  to magnetic impurities at the two edges  a topological phase will emerge  induced by the interplay between the bulk and impurity fluctuations.  This phase also  exhibits an emergent supersymmetry at the edges in a particular regime of the boundary parameters.  We discuss the effect of external fields at the edges that break the supersymmetry and reduces the topological structure to that exhibited by the STS phase   

Intertwined spin, charge and pair correlations in the two-dimensional Hubbard model in the thermodynamic limit

The high-temperature superconducting cuprates are governed by intertwined spin, charge, and superconducting orders. While various state-of-the-art numerical methods have demonstrated that these phases also manifest themselves in doped Hubbard models, they differ on which is the actual ground state. Finite cluster methods typically indicate that stripe order dominates while embedded quantum cluster methods, which access the thermodynamic limit by treating long-range correlations with a dynamical mean field, conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in the doped single-band Hubbard model using a quantum Monte Carlo dynamical cluster approximation (DCA) method. By resolving both the fluctuating spin and charge orders using DCA, we demonstrate that they survive in the doped Hubbard model in the thermodynamic limit. This discovery also provides a new opportunity to study the influence of fluctuating stripe correlations on the model's pairing correlations within a unified numerical framework. Using this approach, we also find evidence for pair-density-wave correlations whose strength is correlated with that of the stripes.   

Higher angular momentum pairings in interorbital shadowed-triplet superconductors: Application to Sr2RuO4

In multiorbital systems with significant Hund’s and spin-orbit coupling, even-parity interorbital spin-triplet pairing emerges as a relevant instability. Spin-orbit coupling generates an intraband pseudospin-singlet component of pairing, resulting in both singlet and triplet character and can also influence the pairing symmetry [1]. A natural question is whether higher angular momentum pairing symmetries such as d- and g-wave, proposed in candidate systems, can be realized from local spin-triplet pairing. We examine the interplay between spin-orbit coupling and the electronic dispersions in correlated metals such as Sr₂RuO₄ to demonstrate how they can be realized. The competition among pairing states is determined as multiple spin-orbit coupling parameters are tuned, and the presence of both d- and g-wave pairings, including a d+ig state, are found when the spin-orbit coupling with d-wave character is increased [2].   

Superconducting pairing from repulsive interactions of fermions in a flat band system

Many-body quantum systems of fermions with flat bands at the Fermi level are intensely studied for their potential to boost superconductivity by enhancement of the density of states. We use quasiexact numerical methods to show that repulsive interactions between spinless fermions in a model one-dimensional flat band system, the Creutz ladder, lead to a finite pairing energy that increases with repulsion. Pure repulsion however leaves charge-order as the dominant quasi-order over the superconductivity. Adding an additional attractive component to the interaction shifts the balance fully in favor of superconductivity. In this regime we find that the interactions of two flat bands further yields a remarkable enhancement to superconductivity far above and outside the known paradigms for one-dimensional fermions.   

Correcting the fatal flaw in BCS theory

Cooper pair is formed by two electrons outside E_F due to the phonon and the screened Coulomb fields[1]. The screened Coulomb field is very weak, which makes the electron density n_N outside E_F small. Thus, the Cooper pair density, n_Cooper, becomes very small, the pair coherence length ξ becomes very large, the double potential structure is made. We assert the weak screened Coulomb field is the fatal flaw in BCS theory not explaining superconductivity[2]. To correct the flaw, we apply the on-site Coulomb interaction U in the Brinkman-Rice(BR) picture[3]. When U increases, discontinuity[=m/m*=1-(U/U_c)²)] at E_F decreases, then n_N rapidly increases, n_Cooper becomes much larger, ξ becomes much smaller, a single potential well structure is generated. Thus T_{c_BR_BCS}[2] can explain the superconductivity. [1]PRL 104(1956)1189. [2]ScientificReport 11(2021)10329. [3]PRB 2(1970)4302.