Session M16: Microscopic Theories of Superconductors I

p-wave superconductivity in Rashba electron systems

We introduce a novel mechanism that triggers superconducting instabilities in electron systems with Rashba spin-orbit interaction (SOI). Electron pairing results from the interplay of the pair SOI, induced by the mutual Coulomb fields among itinerant electrons, and the screened Coulomb interactions, without reliance on phonons or other attraction mediators. This gives rise to a p-wave superconductivity in both 3D and 2D electron systems. Notably, a strong Rashba effect isn't mandatory; the superconducting instability arises even for an arbitrarily weak pair SOI. In sufficiently clean materials it results in a particular p-wave order, where spin up/down electrons form triplet pairs with m = ±1 projection of the angular momentum on a spontaneously chosen direction. In 3D such order parameter has two nodes along the chosen direction, while in 2D this direction is the normal one and the state is fully gaped. The pair-SOI-induced p-wave superconductor exhibits several unique features such as spin-polarized supercurrents and the spin-valve effect as well as peculiar structure of the magnetic vortexes.   

van Hove, Rashba, and Hubbard meet to form first-order and higher-order topological superconductors

We investigate topological superconductivity in the Rashba-Hubbard model, describing heavy-atom superlattice and van der Waals materials with broken inversion. We focus in particular on fillings close to the van Hove singularities, where a large density of states enhances the superconducting transition temperature. To determine the topology of the superconducting gaps and to analyze the stability of their surface states in the presence of disorder and residual interactions, we develop an fRG+MFT approach, which combines the unbiased functional renormalization group (fRG) with a real-space mean-field theory (MFT). Our approach uncovers a cascade of topological superconducting states, including A1 and B1 pairings, whose wave functions are of dominant p- and d-wave character, respectively, as well as a time-reversal breaking A1+iB1 pairing. While the A1 and B1 states have first order topology with helical and flat-band Majorana states, respectively, the A1+iB1 pairing exhibits second-order topology with Majorana corner modes.   

Chiral Electron-Hole Condensation: A New Non-BCS Superconductivity Mechanism

A novel chiral electron-hole (CEH) pairing mechanism [1] is proposed to account for non-BCS superconductivity. In contrast to BCS Cooper pairs, CEH pairs exhibit a pronounced affinity to antiferromagnetism for superconductivity. The gap equations derived from this new microscopic mechanism are analyzed for both s- and d-wave superconductivity, revealing marked departures from the BCS theory. Unsurprisingly, CEH naturally describes superconductivity in strongly-correlated systems, necessitating an exceedingly large coupling parameter (λ>1 for s-wave and λ>π/2 for d-wave) to be efficacious. The new mechanism provides a better understanding of various non-BCS features, especially in cuprate and iron-based superconductors. In particular, CEH, through quantitative comparison with experimental data, shows promise in solving long-standing puzzles such as the unexpectedly large gap-to-critical-temperature ratio Δ₀/T_c, the lack of gap closure at T_c, superconducting phase diagrams, and a non-zero heat-capacity-to-temperature ratio C/T at T=0 (i.e., the "anomalous linear term"), along with its quadratic behavior near T=0 for d-wave cuprates.

[1] https://osf.io/xauqn/   

Pair density wave superconductivity: a microscopic model in two dimensions

Pair-density-wave (PDW) superconductivity is a long-sought exotic state with oscillating superconducting order parameter without the need of applying magnetic field. So far it has been rare in establishing a two-dimensional (2D) microscopic model with such exotic long-range order in its ground state. Here we propose to study PDW superconductivity in a minimal model of spinless fermions on the honeycomb lattice with nearest-neighbor (NN) and next-nearest-neighbor (NNN) interaction V₁ and V₂, respectively. By performing a state-of-the-art density-matrix renormalization group (DMRG) study of this V₁-V₂ model at finite doping on six-leg and eight-leg honeycomb cylinders, we showed that the ground state exhibits PDW ordering (namely quasi-long-range order with a divergent PDW susceptibility). Remarkably this PDW state persists on the wider cylinder with 2D-like Fermi surfaces (FS). To the best of our knowledge, this is probably the first controlled numerical evidence of PDW in systems with 2D-like FS.   

Odd-parity superconductivity from dipolar fluctuations in doped Bi2Se3

Doped Bi₂Se₃ is an unconventional superconductor with a nematic two-component order parameter, most likely of the p-wave symmetry. Yet the absence any nearby instabilities has made explaining the pairing mechanism difficult. Here we propose dipolar fluctuations as the pairing glue. We show that strong spin-orbit coupling mixes orbitals of opposite parities in doped Bi₂Se₃, inducing a finite dipolar density on the Fermi surface. The k_z-dependence of this mixing, which is closely related to the topological insulator state of the undoped compound, makes p-wave the preferred pairing channel under very natural assumptions.   

Robust d-wave superconductivity from the Su-Schrieffer-Heeger-Hubbard model: possible route to high-temperature superconductivity

Increasing numerical studies showed that the simplest Hubbard model on the square lattice with strong repulsion may not exhibit high-temperature superconductivity (SC). It is desired to look for other possible microscopic mechanism of realizing high-temperature SC. Here, we explore the interplay between the Su-Schrieffer-Heeger (SSH) electron-phonon coupling (EPC) and the Hubbard repulsion by density-matrix-renormalization-group (DMRG) simulations. Our state-of-the-art DMRG study showed convincingly that the interplay between strong Hubbard $U$ and moderate Su-Schrieffer-Heeger EPC $lambda$ can induce robust $d$-wave SC. The SSH-type EPC can generates effective antiferromagnetic spin-exchange interactions between neighboring sites, which plays a crucial role in the interplay of inducing robust $d$-wave SC. Specifically, for $U=8t$, we find that $d$-wave SC emerges when $lambda>lambda_c$ with a moderate critical value $lambda_c=0.1sim 0.2$. Our results might shed new light to understanding high-temperature SC in cuprates as well as pave a possible new route in looking for high-temperature SC in other quantum materials with both strong $U$ and moderate $lambda$.   

Kohn-Luttinger superconductivity in the presence of feedback effects

The Kohn-Luttinger scheme is a well known theoretical mechanism for deriving superconductivity from repulsive interactions. This has been shown to give rise to attractive Cooper pairing correlations through screening effects, arising from various mechanisms including Kohn anomalies, van Hove electronic structures, and Umklapp scattering effects.

In such instances where the pairing is known to be driven by repulsive interactions (in particular in superfluid He-3), it has been argued that the screening response should incorporate a feedback effect in which the existence of a pairing gap modifies the response functions which are themselves responsible for the pairing attraction. The feedback effects will manifest in strong-pairing superconductors whenever there are substantial preformed Cooper pairs in the normal state.

In this talk we address the question of whether these feedback effects are harmful or helpful for Kohn-Luttinger type of superconductivity. What can be

anticipated is that the presence of a normal state gap may substantially alter the effects of van Hove contributions and Kohn anomalies in Kohn-Luttinger superconductivity.   

Order by Projection in fermionic Hubbard model with finite on-site interaction

In a repulsive Fermi system near or at half-filling, a superconducting pairing channel, not explicitly present in the Hamiltonian, can be enhanced by suppressing another channel with uncertainty principle inequality, such as the extended s-wave pairing can be enhanced by suppressing the s-wave pairing. This phenomenon is referred to as 'Order by Projection' [1], with an exact solution having been obtained for the case of on-site interaction U=0 in the thermodynamic limit [2]. In this study, we systematically investigate this mechanism in the fermionic Hubbard model on a square lattice with finite on-site interactions. We thoroughly explore the behaviors of various pairing channels by suppressing different orders beyond the s-wave channel, utilizing density matrix renormalization groups (DMRG) and exact diagonalization (ED) techniques. Our findings provide numerical evidence supporting the existence of 'Order by Projection' in this system. Additionally, we observe that when one of pairing channels is suppressed, the introduction of the next-nearest neighbor hopping term could result in markedly different performances in other channels, representing a supplementary extension of this mechanism.

[1] Shastry, B.S., 1997. Uncertainty principle enhanced pairing correlations in projected Fermi systems near half filling. Journal of Physics A: Mathematical and General, 30(18), p.L635.

[2] Krishnamurthy, H.R. and Shastry, B.S., 2000. Exact solution of a repulsive Fermi model with enhanced superconducting correlations. Physical Review Letters, 84(21), p.4918.   

Microscopic Theory of the Tolmachev-Morel-Anderson Pseudopotential

The Tolmachev-Morel-Anderson pseudopotential is a widely used element in the conventional superconductivity theory, but a controllable first principle approach to this quantity remains absent. We re-examined the interplay between the electron-phonon and Coulomb interactions in the superconductivity problem by leveraging modern quantum field theoretical frameworks, and established a microscopic theory for the pseudopotential. Based on the theory we developed a controllable first principle diagrammatic Monte Carlo technique to compute this quantity for small to moderate values of r_s in a uniform electron gas with weak phonon coupling. The results showed the applicability of our approach from conventional cases to the realm of ultralow-temperature superconductors.   

Z2 Spin liquid mediated odd frequency triplet superconductivity

We present an exactly solvable Kondo Lattice model i.e., CPT Model, where the Kondo coupling between Yao-Lee spin liquid and conduction electron results in odd frequency triplet superconductivity. Novel nature of the system stems from order-fractionalization, where fractionalized Majorana excitations and conduction electrons condense together to form a S=1/2 spinor ordered states. The consequence of spinor ordering is an odd-frequency superconductor exhibiting pair-density wave state. The breakdown of the spinor ordering due to thermal Z₂ gauge fluctuations is examined analytically by computing vison gap energy in the ordered state. Another cause of breakdown of the spinor ordering in Large Kondo coupling limit is demonstrated using perturbation theory. Following the description of various phases of CPT Model, we propose candidate materials such as UTe₂, 4Hb-TaS₂ , SmB₆ etc, where CPT model can be experimentally realized.    

Feshbach hypothesis of high-Tc superconductivity in cuprates

Resonant interactions associated with the emergence of a bound state constitute one of the cornerstones of modern many-body physics. Here, we perform theoretical analysis of interactions between charge carriers in doped Mott insulators and we find strong evidence of Feshbach resonance type interactions in the d_{x^2-y^2} channel that can support strong pairing. Here we argue that this paradigm possibly extends to Feshbach resonances between the low-energy emergent constituents in a class of strongly correlated high-temperature superconductors. We perform theoretical analysis of interactions between charge carriers in doped Mott insulators, modelled by a near-resonant two-channel scattering problem, and find strong theoretical evidence for Feshbach-type interactions in the $d_{x^2-y^2}$ channel that can support strong pairing, consistent with the established phenomenology of cuprates. Existing experimental and numerical results on hole-doped cuprates lead us to conjecture the existence of a long-lived, low-energy excited state of two holes with bipolaron character in these systems, which enables near-resonant interactions and can thus provide a microscopic foundation for theories of high-temperature superconductivity involving strong attraction, as assumed e.g. in BEC-BCS crossover scenarios. The emergent Feshbach resonance we propose could also underlie superconductivity in other doped antiferromagnets, as recently proposed for bilayer nickelates, highlighting its potential as a unifying strong-coupling pairing mechanism rooted in quantum magnetism.   

Mechanism of d-wave charge-4e superconductivity from fluctuating pair density waves

We present a theory for charge-4e superconductivity as a leading low-temperature instability with a nontrivial d-wave symmetry. We show that in several microscopic models for the pair-density-wave (PDW) state, when the PDW wave vectors connect special parts of the Fermi surface, the predomi- nant interaction is in the bosonic pairing channel mediated by exchanging low-energy fermions. This bosonic pairing interaction is repulsive in the s-wave channel but attractive in the d-wave one, lead- ing to a d-wave charge-4e superconductor. By analyzing the Ginzburg-Landau free energy including higher-order fluctuation effects of PDW, we find that the charge-4e superconductivity emerges as a vestigial order of PDW, and sets in via a first-order transition. Both the gap amplitude and the tran- sition temperature decay monotonically with increasing superfluid stiffness of the PDW order. Our work provides a microscopic mechanism of higher-charge condensates with unconventional ordering symmetry in strongly-correlated materials.   

Pair density wave characterized by a hidden string order parameter

A composite pairing structure of the superconducting state is revealed by a density matrix renormalization group study in a two-leg t−J model. The pairing order parameter is composed of a pairing amplitude and a phase factor, in which the latter explicitly depends on the spin background with an analytic form. Such a stringlike phase factor is responsible for a pair density wave (PDW) induced by spin polarization m with a wave vector Q_PDW=2πm. By contrast, the pairing amplitude remains smooth, unchanged by the PDW. Moreover, local spin polarization can give rise to a sign change of the order parameter across the local defect. Unlike in a Fulde-Ferrell-Larkin-Ovchinnikov state, the nonlocal phase factor here plays the role of the new order parameter characterizing the PDW, whose origin can be traced back to the essential sign structure of the doped Mott insulator.