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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Tractable model of a pair density wave

Here, this Letter describes a simple mechanism for superconducting pairing with finite wave vector (pair density wave) based on weak coupling. The mechanism is illustrated with a quasi-one-dimensional model relevant to certain a class of quasi-one-dimensional materials. Within this model, pair and charge density wave order parameters are intertwined emerging as components of the same matrix field and are related by particle-hole symmetry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Pair density wave and s ± id superconductivity in a strongly coupled lightly doped Kondo insulator

Here, we investigate the large Kondo coupling limit of the Kondo-Heisenberg model on one- and two-dimensional lattices. Focusing on the possible superconducting states when slightly doping the Kondo insulator state, we identify different pairing modes to be most stable in different parameter regimes. Possibilities include uniform s-wave, pair-density-wave with momentum π (in both one and two dimensions) and uniform s ± id x 2 -y 2 wave (in two dimensions). We attribute these exotic pairing states to the presence of various pair-hopping terms with a "wrong'' sign in the effective model, a mechanism that is likely universal for inducing pairing states with spatially modulated pair wavefunctions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Mechanism for fluctuating pair density wave

Abstract In weakly coupled BCS superconductors, only electrons within a tiny energy window around the Fermi energy, E F , form Cooper pairs. This may not be the case in strong coupling superconductors such as cuprates, FeSe, SrTiO 3 or cold atom condensates where the pairing scale, E B , becomes comparable or even larger than E F . In cuprates, for example, a plausible candidate for the pseudogap state at low doping is a fluctuating pair density wave, but no microscopic model has yet been found which supports such a state. In this work, we write an analytically solvable model to examine pairing phases in the strongly coupled regime and in the presence of anisotropic interactions. Already for moderate coupling we find an unusual finite temperature phase, below an instability temperature T i , where local pair correlations have non-zero center-of-mass momentum but lack long-range order. At low temperature, this fluctuating pair density wave can condense either to a uniform d -wave superconductor or the widely postulated pair-density wave phase depending on the interaction strength. Our minimal model offers a unified framework to understand the emergence of both fluctuating and long range pair density waves in realistic systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Smectic pair-density-wave order in EuRbFe 4 As 4

The pair density wave (PDW) is a superconducting state in which Cooper pairs carry centre-of-mass momentum in equilibrium, leading to the breaking of translational symmetry. Experimental evidence for such a state exists in high magnetic field and in some materials that feature density-wave orders that explicitly break translational symmetry. However, evidence for a zero-field PDW state that exists independent of other spatially ordered states has so far been elusive. Here we show that such a state exists in the iron pnictide superconductor EuRbFe 4 As 4 , a material that features co-existing superconductivity (superconducting transition temperature ( T c ) ≈ 37 kelvin) and magnetism (magnetic transition temperature ( T m ) ≈ 15 kelvin). Using spectroscopic imaging scanning tunnelling microscopy (SI-STM) measurements, we show that the superconducting gap at low temperature has long-range, unidirectional spatial modulations with an incommensurate period of about eight unit cells. Upon increasing the temperature above Tm, the modulated superconductor disappears, but a uniform superconducting gap survives to T c . When an external magnetic field is applied, gap modulations disappear inside the vortex halo. The SI-STM and bulk measurements show the absence of other density-wave orders, indicating that the PDW state is a primary, zero-field superconducting state in this compound. FInally, both four-fold rotational symmetry and translation symmetry are recovered above T m , indicating that the PDW is a smectic order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Triplet pair density wave superconductivity on the π -flux square lattice

Pair-density waves (PDWs) are superconducting states that spontaneously break translation symmetry in systems with time-reversal symmetry (TRS). Evidence for PDWs has been seen in several recent experiments, as well as in the pseudogap regime in cuprates. Theoretical understanding of PDWs has been largely restricted to phenomenological and numerical studies, while microscopic theories typically require strong coupling or fine tuning. In this work, we provide a symmetry-based mechanism under which PDWs emerge as a weak-coupling instability of a two-dimensional TRS metal. Combining mean-field and renormalization-group analyses, we identify a weak-coupling instability towards a triplet PDW realized in the π-flux square lattice model with on-site repulsion and moderate nearest-neighbor attraction when the Fermi level crosses Van Hove singularities at 1/4 and 3/4 fillings. Further, this PDW is protected by the magnetic translation symmetries characteristic of Hofstadter systems, of which the π-flux lattice is a special time-reversal-symmetric case.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Microscopic Theory of Pair Density Waves in Spin-Orbit Coupled Kondo Lattice

We demonstrate that the discommensuration between the Fermi surfaces of a conduction sea and an underlying spin liquid provides a natural mechanism for the spontaneous formation of pair density waves. Using a recent formulation of the Kondo lattice model that incorporates a Yao Lee spin liquid proposed by the authors, we demonstrate that doping away from half filling induces finite-momentum electron-Majorana pair condensation, resulting in amplitude-modulated pair density waves (PDWs). Our approach provides a precise, analytically tractable pathway for understanding the spontaneous formation of PDWs in higher dimensions and offers a natural mechanism for PDW formation in the absence of Zeeman splitting.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Nondegenerate surface pair density wave in the kagome superconductor CsV 3 Sb 5 : Application to vestigial orders

On the Sb layer of the kagome superconductor CsV 3 ⁢Sb 5 , pair density wave states have been observed. When the high-temperature charge orderings are treated as static backgrounds, these pair density wave (PDW) states exhibit the same wave vector in the effective two-dimensional Brillouin zone. Interestingly, these PDW states break the same symmetry on the surface. Considering the presence of this nondegenerate PDW, we investigate the implications for the possible existence of a vestigial charge-4⁢ e phase with a nonzero center-of-mass momentum. To distinguish between different vestigial phases, we propose scanning tunneling microscopy experiments. Here we aim to provide insights into the nature of the vestigial phases and their distinct characteristics in CsV 3 ⁢Sb 5 . This research sheds light on the interplay between PDW states, charge orderings, and superconductivity of the kagome superconductor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Pair density wave in the doped three-band Hubbard model on two-leg square cylinders

A pair density wave (PDW) is a superconducting (SC) state with a spatially modulated order parameter. Although much is known about the properties of the PDW state, its realization in microscopic models with divergent susceptibility has been challenging. Here, in this work, we report a density-matrix renormalization group study of a three-band Hubbard model (also known as the Emery model) for cuprates on long two-leg square cylinders. Upon light doping, we find that the ground state of the system is consistent with that of a PDW state with mutually commensurate and power-law SC, charge (CDW), and spin (SDW) density wave correlations. The SC correlations are dominant between neighboring Cu sites with d-wave pairing symmetry. Interestingly, we find that the near-neighbor interactions, especially the near-neighbor attractive V pd interaction between neighboring Cu and oxygen sites, can notably enhance the SC correlations while simultaneously suppressing the CDW correlations. For a modestly strong attractive V pd , the SC correlations become quasi-long-ranged with a divergent PDW susceptibility.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Emergent pair density wave order across a Lifshitz transition

We numerically investigate the telltale signs of pair-density-wave order (PDW) in the Kondo-Heisenberg chain by focusing on the momentum resolved spectrum in different parameter regimes. Density matrix renormalization group calculations reveal that this phase is characterized by a dispersion with two minima and four Fermi points, indicating the emergence of an effective next-nearest-neighbor hopping that arises as a second-order effect to avoid magnetic frustration. The pairs appear in the spectrum as in-gap bound states with weight concentrated in the hole pockets. The low-energy physics can be understood by means of a generalized t−J model with next-nearest-neighbor hopping. Our results offer a guide for searching for experimental signatures, and for other models that can realize PDW physics.

Yang, Luhang [University of Tennessee Knoxville]↗
DOE OSTI2024

Enhanced Pair-Density-Wave Vertices in a Bilayer Hubbard Model at Half Filling

Motivated by the pair-density-wave (PDW) state found in the one-dimensional Kondo-Heisenberg chain, we report on a determinant quantum Monte Carlo study of pair fields for a two-dimensional half-filled Hubbard layer coupled to an itinerant, noninteracting layer with one electron per site. In a specific range of interlayer hopping, the pairing vertex associated with PDW order becomes more attractive than that for uniform d-wave pairing, although both remain subdominant to the leading antiferromagnetic correlations at half filling. In conclusion, our result sheds light on where one potentially may find a PDW state in such a model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Singlet, triplet, and pair density wave superconductivity in the doped triangular-lattice moiré system

Recent experimental progress has established the twisted bilayer transition metal dichalcogenide (TMD) as a highly tunable platform for studying many-body physics. Particularly, the homobilayer TMDs under displacement field are believed to be described by a generalized triangular-lattice Hubbard model with a spin-dependent hopping phase θ. To explore the effects of θ on the system, we perform density matrix renormalization group calculations for the relevant triangular lattice t-J model. By changing θ at small hole doping, we obtain a region of quasi-long-range superconducting order coexisting with charge and spin density wave within 0 < θ < π/3. The superconductivity is composed of a dominant spin singlet d-wave and a subdominant triplet p-wave pairing. Intriguingly, the S z = ±1 triplet pairing components feature pair-density waves. In addition, we find a region of triplet superconductivity coexisting with charge-density wave and ferromagnetism within π/3 < θ < 2π/3, which is related to the former phase at smaller θ by a combined operation of spin-flip and gauge transformation. Furthermore, our findings provide insights and directions for experimental search for exotic superconductivity in twisted TMD systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Emergence of the Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model

While advances in electronic band theory have brought to light new topological systems, understanding the interplay of band topology and electronic interactions remains a frontier question. In this work, we predict new interacting electronic orders emerging near higher-order Van Hove singularities present in the Chern bands of the Haldane model. We classify the nature of such singularities and employ unbiased renormalization group methods that unveil a complex landscape of electronic orders, which include ferromagnetism, density waves, and superconductivity. Importantly, we show that repulsive interactions can stabilize the long-sought pair-density-wave state and an exotic Chern supermetal, which is a new class of non-Fermi liquid with anomalous quantum Hall response. Further, this framework opens a new path to explore unconventional electronic phases in two-dimensional chiral bands through the interplay of band topology and higher-order Van Hove singularities.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Competing pair density wave and uniform 𝑑-wave superconductivity in phase-separated 214 cuprates at the 1/8 anomaly

Compelling evidence exists for electronic phase separation in cuprate high-𝑇𝑐 superconductors, emerging near 1/8 hole doping. At these dopings and low temperatures, intertwined charge and spin stripes coexist with more uniformly doped regions in the two-dimensional (2D) copper-oxide planes. Each region is capable of developing superconducting pairing, either as a pair density wave (PDW) within the stripes or as a uniform 𝑑-wave condensate (𝑑-SC) in the more homogeneous regions. Using neutron scattering on single crystals of La1.875−𝑦⁢Nd𝑦⁢Sr0.125⁢CuO4, we demonstrate that the onset temperatures for spin stripe order (𝑇𝑁) and superconductivity (𝑇𝑐) merge as the average ordered moment vanishes in LSCO (𝑦=0), whereas Nd doping stabilizes static stripe order and suppresses 𝑇𝑐. Because the spin stripes possess the same in-plane periodicity (8⁢𝑎) as the PDW and establish the framework within which the PDW resides, the stabilization of spin stripe order enhances PDW correlations. Thus, the competition between 𝑑-wave pairing in the uniform regions and PDW pairing in the stripe-ordered regions can be controlled by the Nd concentration in La1.875−𝑦⁢Nd𝑦⁢Sr0.125⁢CuO4, allowing the superconducting 𝑇𝑐 to vary by nearly an order of magnitude at a fixed 1/8-hole doping.

Aczel, Adam [ORNL] (ORCID:0000000319641943)↗
DOE OSTI2024

Phase diagram of the one-dimensional t 1 - t 2 - J model: Ferromagnetism, triplet pairing, and charge and pair density waves

Here, we present a density matrix renormalization group (DMRG) study of an extended t-J model with hopping to the first and second neighbors -- the one dimensional t 1 -t 2 -J model. The full phase diagram as a function of the density n and exchange strength J, for both positive and negative values of t 2 , is obtained. For t 2 = -0.5 we observe that, in the strongly interacting region, Nagaoka Ferromagnetism (FM) is accompanied by a triplet pair density wave (PDW) upon doping. As the spin exchange J increases, a charge density wave (CDW) phase emerges and then gives way to singlet superconductivity (SC). This phase behaves as a singlet PDW with vanishing spacial average of the order parameter and a spin gap. When t 2 = 0.5, the physics is basically reminiscent of the conventional t-J model, undergoing a transition from a metallic to a SC phase as a function of J.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Detection of a pair density wave state in UTe2

Abstract Spin-triplet topological superconductors should exhibit many unprecedented electronic properties, including fractionalized electronic states relevant to quantum information processing. Although UTe 2 may embody such bulk topological superconductivity 1–11 , its superconductive order parameter Δ( k ) remains unknown 12 . Many diverse forms for Δ( k ) are physically possible 12 in such heavy fermion materials 13 . Moreover, intertwined 14,15 density waves of spin (SDW), charge (CDW) and pair (PDW) may interpose, with the latter exhibiting spatially modulating 14,15 superconductive order parameter Δ( r ), electron-pair density 16–19 and pairing energy gap 17,20–23 . Hence, the newly discovered CDW state 24 in UTe 2 motivates the prospect that a PDW state may exist in this material 24,25 . To search for it, we visualize the pairing energy gap with μeV-scale energy resolution using superconductive scanning tunnelling microscopy (STM) tips 26–31 . We detect three PDWs, each with peak-to-peak gap modulations of around 10 μeV and at incommensurate wavevectors P i =1,2,3 that are indistinguishable from the wavevectors Q i =1,2,3 of the prevenient 24 CDW. Concurrent visualization of the UTe 2 superconductive PDWs and the non-superconductive CDWs shows that every P i : Q i pair exhibits a relative spatial phase δϕ ≈ π. From these observations, and given UTe 2 as a spin-triplet superconductor 12 , this PDW state should be a spin-triplet PDW 24,25 . Although such states do exist 32 in superfluid 3 He, for superconductors, they are unprecedented.

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