Session M37: Recent Developments in the Theory of Superconductivity

Quantum Geometry and superconductivity in flat bands

We have found that superconductivity and superfluidity have a connection to quantum geometry [1,2]. Namely, the superfluid weight in a multiband system has a previously unnoticed component which we call the geometric contribution. It is proportional to the minimal quantum metric of the band. Quantum metric is connected to the Berry curvature, and this allows to relate superconductivity with the topological properties of the band. Using this theory, we have shown that superconductivity is possible also in a flat band where individual electrons would not move. Recently, we and other groups have shown [3,4] that these results may be essential in explaining the observation of superconductivity in bilayer graphene and may eventually help realize superconductors at elevated temperatures. In addition to the promise of high critical temperatures and strong correlation effects, also the quantum transport in flat band shows unique behavior [5]. In the normal state above the superconducting critical temperature, a new type of insulator can be found [6]. We have also explored the effect of quantum geometry on Bose-Einstein condensation and shown that the quantum distance and quantum metric determine the stability of the condensate, and quantum fluctuations dominate over mean-field effects [7]. Light-matter interactions become strongly enhanced by quantum geometry in flat bands [8].

[1] S. Peotta, P. Törmä, Nature Commun. 6, 8944 (2015); A. Julku, S. Peotta, T.I. Vanhala, D.-H. Kim, P. Törmä, Phys. Rev. Lett. 117, 045303 (2016); P. Törmä, L. Liang, S. Peotta, Phys. Rev. B 98, 220511(R) (2018)

[2] K.-E. Huhtinen, J. Herzog-Arbeitman, A. Chew, B.A. Bernevig, P. Törmä, Phys. Rev. B 106 , 014518 (2022); J. Herzog-Arbeitman, A. Chew, K.-E. Huhtinen, P. Törmä, B.A. Bernevig, arXiv:2209.00007 (2022)

[3] A. Julku, T.J. Peltonen, L. Liang, T.T. Heikkilä, P. Törmä, Phys. Rev. B 101, 060505(R) (2020)

[4] P. Törmä, S. Peotta, B.A. Bernevig, Nat. Rev. Phys.  4, 528 (2022)

[5] V.A.J. Pyykkönen, S. Peotta, P. Fabritius, J. Mohan, T. Esslinger, P. Törmä, Phys. Rev. B 103, 44519 (2021)

[6] K.-E. Huhtinen, P. Törmä, Phys. Rev. B 103, L220502 (2021)

[7] A. Julku, G.M. Bruun, P. Törmä, Phys. Rev. Lett., 127, 170404 (2021), ibid Phys. Rev. B 104, 144507 (2021)

[8] G.E. Topp, C.J. Eckhardt, D.M. Kennes, M.A. Sentef, P. Törmä, Phys. Rev. B 104, 064306 (2021)

    

Ab-initio theory of phonon-driven superconductivity

A prominent challenge of condensed-matter theory is to reliably predict material-specific properties of superconductors, such as the critical temperature. The superconducting version of density functional theory (SCDFT) meets this challenge for phonon-driven superconductors. The central quantity of SCDFT is a universal exchange-correlation functional which depends both on the electronic density and on the superconducting order parameter [1]. With the best available approximations for this functional, SCDFT is a genuine ab-initio theory with no adjustable parameters, allowing the prediction of the critical temperatures of phonon-driven superconductors within a few percent of experiment [2]. Examples of intermetallic compounds as well as hydrogen-rich materials under pressure will be presented. Apart from Tc, other quantities, such as the order parameter in real space, and the excitation gap are directly accessible in SCDFT. Highly complex materials such as NbSe2, featuring a competition between superconductivity and a charge density wave at low temperature, can be fully understood [3] with this approach. Furthermore, for a variety of materials, we analyze how the order parameter in real space is related to the chemical bonding structure [4]. Regions in the unit cell that provide an attractive coupling can be beautifully distinguished from those that contribute via Coulomb renormalization and those that are not coupled at all. By controlling the local bonding structure, SCDFT offers a route to locally tailor the order parameter in superconducting nanostructures [5].

 

[1]  L.N. Oliveira, E.K.U. Gross, W. Kohn, Phys.Rev.Lett. 60, 2430 (1988).

[2]  A. Sanna, C. Pellegrini, E.K.U. Gross, Phys. Rev. Lett. 125, 057001 (2020).

[3]  A. Sanna, C. Pellegrini, E. Liebhaber, K. Rossnagel, K.J. Franke, E.K.U. Gross, npj Quantum Materials (2022)7:6.

[4]  A. Linscheid, A. Sanna, A. Floris, E.K.U. Gross, Phys. Rev. Lett. 115, (2015).

[5]  M.Schackert, T. Märkl, J. Jandke, M. Hölzer, S. Ostanin, E.K.U. Gross, A. Ernst, W. Wulfhekel,  Phys. Rev. Lett. 114, 047002 (2015).

    

Superconductivity without quasiparticles: Quantum critical Eliashberg theory and its holographic dual

Superconductivity is abundant near quantum-critical points, where fluctuations suppress the formation of Fermi liquid quasiparticles and the Bardeen-Cooper-Schrieffer theory no longer applies. Two very distinct approaches have been developed to address this issue: quantum-critical Eliashberg theory and holographic superconductivity. The former includes a strongly retarded pairing interaction of ill-defined fermions, the latter is rooted in the duality of quantum field theory and gravity theory. We demonstrate that both are different perspectives of the same theory. We derive holographic superconductivity in form of a gravity theory with emergent space-time from a quantum many-body Hamiltonian - the Yukawa SYK model and finite-dimensional generalizations thereof - where the Eliashberg formalism is exact. Exploiting the power of holography, we then determine the phase diagram, dynamic pairing susceptibility , and electromagnetic properties of the model. Finally, the theory can be used to study the crossover from non Fermi liquid to Fermi liquid superconductivity.   

Quantum Critical Metals: From Loss of Quasiparticles to High-Tc Superconductivity

Strange metals develop near quantum critical points in a variety of correlated systems. Some of the key issues include how the quantum critical state loses quasiparticles, how it drives superconductivity, and to what extent the strange-metal physics in different classes of correlated systems is connected with each other.

In this talk, I will confront some of these issues from the vantage point of heavy fermion metals, which represent a prototype family for quantum critical metals and strange-metal phenomena. I will describe the notion of Kondo destruction [1] and how it leads to a change of the Fermi surface from “large” to “small” across the quantum critical point, a loss of quasiparticles everywhere on the Fermi surface at the quantum critical point, and a dynamical Planckian scaling in various properties including the charge responses [2]. I will then present results showing that such a strange-metal state drives unconventional superconductivity with high-Tc: the transition temperature Tc reaches a few percent of the effective Fermi temperature [3].

Connections with other correlated systems – including the cuprates, moir structures and in particular frustrated bulk systems with topological “flat bands” [4] -- will be briefly discussed.

In collaboration with A. Cai, L. Chen, L. Y. Chen, K. Grube, H. Hu, K. Ingersent, A. Kandala, S. Kirchner, J. Kono, X. Li, C.-C. Liu, D. Natelson, E. M. Nica, J. Pixley, S. Paschen, L. Prochaska, C. Setty, F. Steglich, S. Sur, J. D. Thompson, H. von Lhneysen, Y. Wang,  S. Wirth, F. Xie, R. Yu and J.-X. Zhu.   

Triplet pairing mechanisms from Hund's-Kondo models - applications to heavy fermion superconductors

The family of heavy fermion materials, with active f-electrons, hosts a large variety of candidate-triplet superconductors, with upper critical fields often exceeding the Pauli limit by an order of magnitude. Some, like UTe₂ remain superconducting in fields over 60T indicating tightly bound pairs with coherence lengths shorter than 2nm. Notably, almost every triplet heavy fermion superconductor shares a common structural motif – two or more f-shell atoms in the primitive unit cell related to each other by inversion, with only two exceptions UAu₂ and YbRh₂Si₂. I will present a triplet pairing mechanism driven by Hund’s and Kondo coupling and enabled by this structural motif. In essence, Hund's coupling leads to pre-formed triplet pairs between the electrons trapped inside local moments. Kondo hybridization imbues these triplet correlations onto the conduction electron cloud that screens the moment. As these heavy electron pairs delocalize on a lattice of such moments, they remember the triplet entanglement of their parent configuration. In heavy fermion superconductors as diverse as UPt₃, UBe₁₃, UTe₂, CeRh₂As₂, UGe₂, U(Co,Rh)Ge, CeSb₂ as well as PrTi₂Al₂₀ and analogues, the moments are situated away from the inversion center, so that their pre-formed triplet pairs can be odd under inversion. As they delocalize, these heavy fermion pairs then have finite overlap with odd-parity triplet pairs on the same Fermi surface, leading to a triplet pairing instability. This pairing mechanism is demonstrated by a two-channel Kondo model, in which Hund’s coupling modifies the Kondo interaction into a triplet superexchange between local moment and conduction spins. This unifies the triplet superconductivity and the local moment physics in a coherent framework, and we discuss experimental consequences and existing support for this pairing mechanism. The near-universal correlation with the structural motif suggests a common origin of heavy fermion triplet superconductivity in Hund’s-coupled local moments.