Interlayer Pairing Research Articles

Strong Pairing Originated from an Emergent Z_{2} Berry Phase in La_{3}Ni_{2}O_{7}.

The recent discovery of high-temperature superconductivity in La_{3}Ni_{2}O_{7} offers a fresh platform for exploring unconventional pairing mechanisms. Starting with the basic argument that the electrons in d_{z^{2}} orbitals nearly form local moments, we examine the effect of the Hubbard interaction U on the binding strength of Cooper pairs based on a single-orbital bilayer model with intralayer hopping t_{∥} and interlayer superexchange J_{⊥}. By extensive density matrix renormalization group calculations, we observe a remarkable enhancement in binding energy as much as 10-20 times larger with U/t_{∥} increasing from 0 to 12 at J_{⊥}/t_{∥}∼1. We demonstrate that such a substantial enhancement stems from a kinetic-energy-driven mechanism. Specifically, a Z_{2} Berry phase will emerge at large U due to the Hilbert space restriction (Mottness), which strongly suppresses the mobility of single particle propagation as compared to U=0. However, the kinetic energy of the electrons (holes) can be greatly restored by forming an interlayer spin-singlet pairing, which naturally results in a superconducting state even for relatively small J_{⊥}. An effective hard-core bosonic model is further proposed to estimate the superconducting transition temperature at the mean-field level.

Phase diagram of strongly-coupled Rashba systems

Abstract Motivated by the recent discovery of a possible field-mediated parity switch within the superconducting state of CeRh2As2 [Khim et al., Science 373, 1012 (2021)], we thoroughly investigate the dependence of the superconducting state of a strongly-coupled Rashba mono- and bilayer on internal parameters and an applied magnetic field. The role of interlayer pairing, spin orbit coupling, doping rate and applied magnetic field and their interplay was examined numerically at low temperature within a t-J-like model, uncovering complex phase diagrams and transitions between superconducting states with different symmetry.

Gauge field dynamics in multilayer Kitaev spin liquids

The Kitaev spin liquid realizes an emergent static Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb{Z}}}_{2}$$\\end{document} gauge field with vison excitations coupled to Majorana fermions. We consider Kitaev models stacked on top of each other, weakly coupled by Heisenberg interaction ∝ J⊥. This inter-layer coupling breaks the integrability of the model and makes the gauge fields dynamic. Conservation laws and topology keep single visons immobile. However, an inter-layer vison pairs can hop with a hopping amplitude linear in J⊥ confined to the layer, but their motion is strongly influenced by the type of stacking. For AA stacking, an interlayer pair has a two-dimensional motion but for AB or ABC stacking, sheet conservation laws restrict its motion to a one-dimensional channel within the plane. For all stacking types, an intra-layer vison-pair is constrained to move out-of-plane only. Depending on the anisotropy of the Kitaev couplings Kx, Ky, Kz, the intra-layer vison pairs can display either coherent tunnelling or purely incoherent hopping. When a magnetic field opens a gap for Majorana fermions, there exist two types of intra-layer vison pairs - a bosonic and a fermionic one. Only the bosonic pair obtains a hopping rate linear in J⊥. We use our results to identify the leading instabilities of the spin liquid phase induced by the inter-layer coupling.

Effect of Rare-Earth Element Substitution in Superconducting R3Ni2O7 under Pressure

Abstract Recently, high temperature (T c ≈ 80 K) superconductivity (SC) has been discovered in La3Ni2O7 (LNO) under pressure. This raises the question of whether the superconducting transition temperature T c could be further enhanced under suitable conditions. One possible route for achieving higher T c is element substitution. Similar SC could appear in the Fmmm phase of rare-earth (RE) R3Ni2O7 (RNO, R = RE element) material series under suitable pressure. The electronic properties in the RNO materials are dominated by the Ni 3d orbitals in the bilayer NiO2 plane. In the strong coupling limit, the SC could be fully characterized by a bilayer single 3d x 2–y 2 -orbital t–J ∥–J ⊥ model. With RE element substitution from La to other RE element, the lattice constant of the Fmmm RNO material decreases, and the resultant electronic hopping integral increases, leading to stronger superexchanges between the 3d x 2–y 2 orbitals. Based on the slave-boson mean-field theory, we explore the pairing nature and the evolution of T c in RNO materials under pressure. Consequently, it is found that the element substitution does not alter the pairing nature, i.e., the inter-layer s-wave pairing is always favored in the superconducting RNO under pressure. However, the T c increases from La to Sm, and a nearly doubled T c could be realized in SmNO under pressure. This work provides evidence for possible higher T c R3Ni2O7 materials, which may be realized in further experiments.

Interlayer Biatomic Pair Bridging the van der Waals Gap for 100% Activation of 2D Layered Material.

2D layered materials are regarded as prospective catalyst candidates due to their advantageous atomic exposure ratio. Nevertheless, the predominant population of atoms residing on the basal plane with saturated coordination, exhibit inert behavior, while a mere fraction of atoms located at the periphery display reactivity. Here, a novel approach is reported to attain complete atom activation in 2D layered materials through the construction of an interlayer biatomic pair bridge. The atoms in question have been strategically optimized to achieve a highly favorable state for the adsorption of intermediates. This optimization results from the introduction of new gap states around the Fermi level. Moreover, the presence of the interlayer bridge facilitates the electron transfer across the van der Waals gap, thereby enhancing the reaction kinetics. The hydrogen evolution reaction exhibits an impressive ultrahigh current density of 2000mA cm-2 at 397mV, surpassing the pristine MoS2 by approximately two orders of magnitude (26mA cm-2 at 397mV). This study provides new insights for enhancing the efficacy of 2D layered catalysts.

Frustrated superconductivity and intrinsic reduction of <i>T</i><sub><i>c</i></sub> in trilayer nickelate

<p>Identifying the key factors controlling the magnitude of <i>T</i><sub><i>c</i></sub> is of critical importance in the pursuit of high-temperature superconductivity. In cuprates, <i>T</i><sub><i>c</i></sub> reaches its maximal value in trilayer structure, leading to the belief that interlayer coupling may help promote the pairing. In contrast, for the recently discovered nickelate superconductors under high pressure, the maximum <i>T</i><sub><i>c</i></sub> is reduced from about 80 K in the bilayer La<sub>3</sub>Ni<sub>2</sub>O<sub>7</sub> to 30 K in the trilayer La<sub>4</sub>Ni<sub>3</sub>O<sub>10</sub>. Motivated by this opposite trend, we propose an interlayer pairing scenario for the superconductivity of La<sub>4</sub>Ni<sub>3</sub>O<sub>10</sub>. Our theory reveals intrinsic frustration in the spin-singlet pairing that the inner layer tends to form with both of the two outer layers respectively, leading to strong superconducting fluctuations between layers. This explains the reduction of its maximum <i>T</i><sub><i>c</i></sub> compared to that of the bilayer La<sub>3</sub>Ni<sub>2</sub>O<sub>7</sub>. Our findings support a fundamental distinction between multilayer nickelate and cuprate superconductors, and ascribe it to their different (interlayer versus intralayer) pairing mechanisms. Furthermore, our theory predicts extended <i>s</i><sup><i>±</i></sup>-wave gap structures in La<sub>4</sub>Ni<sub>3</sub>O<sub>10</sub>, with varying signs and possible nodes on different Fermi pockets. We also find an intrinsic Josephson coupling with potentially interesting consequences that may be examined in future experiments. Our work reveals the possibility of rich novel physics in multilayer superconductors with interlayer pairing.</p>

Interlayer coupling in the superconducting state of iron-based superconductors

High-temperature superconducting paring is generally believed to be mediated by the magnetic fluctuations that mostly occur within the two-dimensional conducting layers (Cu-O, Fe-As, or Fe-Se) in copper oxides, iron pnictides, iron chalcogenides, etc. Here, on the basis of inelastic neutron scattering measurements on a superconducting iron pnictide ${\mathrm{Ca}}_{0.33}{\mathrm{Na}}_{0.67}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$, we have discovered a highly three-dimensional spin resonance mode with upward V-shape dispersions both in the $ab$ plane and along the $c$ axis. The superconducting gaps exhibit strong ${k}_{z}$ modulations involved with significant changes on the size of one hole pocket and the density state of the ${d}_{{z}^{2}}$ orbital of Fe. The resonance dispersions don't always seem confined by the total gaps summed on those imperfectly nesting Fermi sheets. It is demonstrated that the $c$-axis dependence of both the resonance energy and its intensity in iron pnictides can be universally scaled with the distance between two adjacent Fe-As layers ($d$), and the ${k}_{z}$ modulation of the gap is also anticorrelated with $d$. These results highlight the role of interlayer coupling in iron-based superconductivity, suggesting that the interlayer pairing may also be driven by magnetic fluctuations under certain spin-orbit couplings.

Collective interlayer pairing and pair superfluidity in vertically stacked layers of dipolar excitons

Layered bosonic dipolar fluids have been suggested to host a condensate of interlayer molecular bound states. However, experimental observation has remained elusive. Motivated by two recent experimental works [C. Hubert et al., Phys. Rev. X9, 021026 (2019) and D. J. Choksy et al., Phys. Rev. B 103, 045126 (2021)], we theoretically study, using numerically exact quantum Monte Carlo calculations, the experimental signatures of collective interlayer pairing in vertically stacked indirect exciton (IX) layers. We find that IX energy shifts associated with each layer evolve nontrivially as a function of density imbalance following a nonmonotonic trend with a jump discontinuity at density balance, identified with the interlayer IX molecule gap. This behavior discriminates between the superfluidity of interlayer bound pairs and independent dipole condensation in distinct layers. Considering finite temperature and finite density imbalance conditions, we find a cascade of Berezinskii-Kosterlitz-Thouless (BKT) transitions, initially into a pair superfluid and only then, at lower temperatures, into complete superfluidity of both layers. Our results may provide a theoretical interpretation of existing experimental observations in GaAs double quantum well (DQW) bilayer structures. Furthermore, to optimize the visibility of pairing dynamics in future studies, we present an analysis suggesting realistic experimental settings in GaAs and transition metal dichalcogenide (TMD) bilayer DQW heterostructures where collective interlayer pairing and pair superfluidity can be clearly observed.

Light-matter interactions in van der Waals photodiodes from first principles

Strong light-matter interactions in van der Waals heterostructures (vdWHs) made of two-dimensional (2D) transition metal dichalcogenides (TMDs) provide a fertile ground for optoelectronic applications. Of particular interest are photoexcited interlayer electron-hole pairs, where electrons and holes are localized in different monolayers. Here, we present an ab initio quantum transport framework relying on maximally localized Wannier functions and the nonequilibrium Green's functions to explore light-matter interactions and charge transport in 2D vdWHs from first principles. Electron-photon scattering is accurately taken into account through dedicated self-energies. As testbed, the behavior of a ${\mathrm{MoSe}}_{2}\text{\ensuremath{-}}{\mathrm{WSe}}_{2}$ PIN photodiode is investigated under the influence of a monochromatic electromagnetic signal. Interlayer electron-hole pair generations are observed even in the absence of phonon-assisted processes. The origin of this phenomenon is identified as the delocalization of one valence band state over both monolayers composing the vdWH.

Two-dimensional paired topological superfluids of Rydberg Fermi gases

We systematically investigate the topological properties of spin polarized Rydberg-dressed fermionic atoms loaded in a bilayer optical lattice. Through tuning the Rydberg coupling strength and the interlayer tunneling amplitude, we identify different types of topological superfluid states generated from the interlayer pairing and relative pairing phase modulation of the coupled two-dimensional $p$-wave superfluids. These phases include gapped/gapless with/without time-reversal symmetry. One of the most interesting states is a gapless paired topological superfluid with both the time-reversal symmetry and particle-hole symmetry, which is a realization of a DIII gapless topological superconductor. The flexibility of experimental manipulation in such Rydberg-dressed fermionic systems therefore becomes a promising system for realizing interesting topological superfluids.

Emergent force and work fluctuations in a bilayer superfluid Bose–Fermi mixture in mixed dimensions

We investigate a system of two-atomic species in mixed dimensions, in which one species is spread in a three-dimensional space and the other species is confined in two parallel layers. The presence of atoms in three-dimensions creates an induced potential for the ones confined in layers. Depending on the scattering (coherence) length and the layer separation, the formation of p-wave pairing within the same layer or s-wave pairing between different layers has been suggested. It was shown that these pairs cannot coexist when time-reversal symmetry is on, and there appears a transition from p-wave to s-wave as the ratio of the layer separation and the effective scattering length decreases. Here, we study the thermodynamical signatures of such transition and find that with the formation of the inter-layer pairing, an emergent force to be present at the critical point and show that it can be derived from the ground state energy. This result offers a tool for experimentally realizing such transitions, and can find notable potential in the field of quantum-thermodynamics.

Electron pairing with gapless excitations in mixed double layers

We study the interlayer pairing states in layered systems of two different 2d electronic subsystems, one with relativistic linear and the other with non-relativistic parabolic spectrum. The complex order parameter of the paired state has a two component structure. We investigate the pairing state formation on the mean-field level, determine the critical interaction strength and evaluate the effective potential. The anisotropic three-band spectrum of quasiparticles depends explicitly on the phase difference of the order parameter components, rotates in momentum space as it changes. It is subject to the strong band deformation due to the pairing. It leads to the fusion and hybridization of initially decoupled bands. The quasiparticle spectrum has the shape of deformed Dirac cones in the vicinity of the two touching points between neighboring bands. The density of states exhibits a number of specific features due to band deformation, such as a van Hove singularity.

Collective excitations and quantum incompressibility in electron-hole bilayers

We apply quantum continuum mechanics to the calculation of the excitation spectrum of a coupled electron-hole bilayer. The theory expresses excitation energies in terms of ground-state intra- and inter-layer pair correlation functions, which are available from Quantum Monte Carlo calculations. The final formulas for the collective modes deduced from this approach coincide with the formulas obtained in the "quasi-localized particle approximation" by Kalman et al., and likewise, the theory predicts the existence of gapped excitations in the charged channels, with the gap arising from electron-hole correlation. An immediate consequence of the gap is that the static density-density response function of the charged channel vanishes as $q^2$ for wave vector $q \to 0$, rather than linearly in $q$, as commonly expected. In this sense, the system is {\it incompressible}. This feature, which has no analogue in the classical electron-hole plasma, is consistent with the existence of an excitonic ground state and implies the existence of a discontinuity in the chemical potential of electrons and holes when the numbers of electrons and holes are equal. It should be experimentally observable by monitoring the densities of electrons and holes in response to potentials that attempt to change these densities in opposite directions.

Fulde–Ferrell–Larkin–Ovchinnikov State in Perpendicular Magnetic Fields in Strongly Pauli-Limited Quasi-Two-Dimensional Superconductors

We examine the Fermi-surface effect called the nesting effect for the FFLO state in strongly Pauli-limited Q2D superconductors, focusing on the effect of 3D factors, such as interlayer electron transfer, interlayer pairing, and off-plane magnetic fields including those perpendicular to the most conductive layers. We examine the systems with a large Maki parameter so that the orbital pair-breaking effect is negligible, except for the locking of the direction of the FFLO vector q in the field direction.It is known that the nesting effect for the FFLO state can be strong in QLD systems in which the orbital pair-breaking effect is suppressed by applying the mag. field parallel to the layers. Hence, it has sometimes been suggested that the nesting effect may hardly enhance the stability of the FFLO state for perpendicular fields. We illustrate that, contrary to this view, the nesting effect can strongly stabilize the FFLO state for perpendicular fields as well as for parallel fields when tz is small so that the Fermi surfaces are open in the kz-direction, where tz denotes the interlayer transfer energy. In particular, the nesting effect in perpendicular fields can be strong in interlayer states. For example, in systems with cylindrical Fermi surfaces warped by tz /= 0, interlayer states with Dlt_k prop sin k_z exhibit mu_e Hc=1.65 Dlt_a0 for perpendicular fields, which is much larger than typical values for parallel fields, such as mu_e Hc=Dlt_s0 of the s-wave state and mu_e Hc = 1.28 Delta_d0 of the d-wave state in cylindrical systems with tz=0. The present result could potentially provide a physical reason why the areas in the phase diagrams occupied by the high-field phases for the perpendicular and parallel fields are of the same order in CeCoIn5 and FeSe.

Dipolar evaporation of reactive molecules to below the Fermi temperature.

SummaryMolecules are the building blocks of matter and their control is key to the investigation of new quantum phases, where rich degrees of freedom can be used to encode information and strong interactions can be precisely tuned1. Inelastic losses in molecular collisions2–5, however, have greatly hampered the engineering of low-entropy molecular systems6. So far, the only quantum degenerate gas of molecules has been created via association of two highly degenerate atomic gases7,8. Here, we use an external electric field along with optical lattice confinement to create a two-dimensional (2D) Fermi gas of spin-polarized potassium-rubidium (KRb) polar molecules, where elastic, tunable dipolar interactions dominate over all inelastic processes. Direct thermalization among the molecules in the trap leads to efficient dipolar evaporative cooling, yielding a rapid increase in phase-space density. At the onset of quantum degeneracy, we observe the effects of Fermi statistics on the thermodynamics of the molecular gas. These results demonstrate a general strategy for achieving quantum degeneracy in dipolar molecular gases where strong, long-range, and anisotropic dipolar interactions can drive the emergence of exotic many-body phases, such as interlayer pairing and p-wave superfluidity.

Josephson effect in graphene bilayers with adjustable relative displacement

The Josephson current is investigated in a superconducting graphene bilayer where pristine graphene sheets can make in-plane or out-of-plane displacements with respect to each other. The superconductivity can be of an intrinsic nature, or due to a proximity effect. The results demonstrate that the supercurrent responds qualitatively differently to relative displacement if the superconductivity is due to either intralayer or interlayer spin-singlet electron-electron pairing, thus providing a tool to distinguish between the two mechanisms. Specifically, both the AA and AB stacking orders are studied with antiferromagnetic spin alignment. For the AA stacking order with intralayer and on-site pairing no current reversal is found. In contrast, the supercurrent may switch its direction as a function of the in-plane displacement and out-of-plane interlayer coupling for the cases of AA ordering with interlayer pairing and AB ordering with either intralayer or interlayer pairing. In addition to sign reversal, the Josephson signal displays many characteristic fingerprints which derive directly from the pairing mechanism. Thus, measurements of the Josephson current as a function of the graphene bilayer displacement open up the means achieve deeper insights into the superconducting pairing mechanism.

Pairing transition in a double layer with interlayer Coulomb repulsion

We study the effect of interlayer Coulomb interaction in an electronic double layer. Assuming that each of the layers consists of a bipartite lattice, a sufficiently strong interlayer interaction leads to an interlayer pairing of electrons with a staggered order parameter. We show that the correlated pairing state is dual to the excitonic pairing state with uniform order parameter in an electron-hole double layer. The interlayer pairing of electrons leads to strong current-current correlations between the layers. We also analyze the interlayer conductivity and the fluctuations of the order parameter, which consists of a gapped and a gapless mode.

Spectroscopic evidence of bilayer splitting and strong interlayer pairing in the superconductor KCa2Fe4As4F2

In high temperature cuprate superconductors, the interlayer coupling between the CuO$_2$ planes plays an important role in dictating superconductivity, as indicated by the sensitive dependence of the critical temperature (T$_C$) on the number of CuO$_2$ planes in one structural unit. In Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ superconductor with two CuO$_2$ planes in one structural unit, the interaction between the two CuO$_2$ planes gives rise to band splitting into two Fermi surface sheets (bilayer splitting) that have distinct superconducting gap. The iron based superconductors are composed of stacking of the FeAs/FeSe layers; whether the interlayer coupling can cause similar band splitting and its effect on superconductivity remain unclear. Here we report high resolution laser-based angle-resolved photoemission spectroscopy (ARPES) measurements on a newly discovered iron based superconductor, KCa$_2$Fe$_4$As$_4$F$_2$ (T$_C$=33.5\,K) which consists of stacking FeAs blocks with two FeAs layers separated by insulating Ca$_2$F$_2$ blocks. Bilayer splitting effect is observed for the first time that gives rise to totally five hole-like Fermi surface sheets around the Brilliouin zone center. Band structure calculations reproduce the observed bilayer splitting by identifying interlayer interorbital interaction between the two FeAs layers within one FeAs block. All the hole-like pockets around the zone center exhibit Fermi surface-dependent and nodeless superconducting gap. The gap functions with short-range antiferromagetic fluctuations are proposed and the gap symmetry can be well understood when the interlayer pairing is considered. The particularly strong interlayer pairing is observed for one of the bands. Our observations provide key information on the interlayer coupling and interlayer pairing in understanding superconductivity in iron based superconductors.

Voltage-tunable Majorana bound states in time-reversal symmetric bilayer quantum spin Hall hybrid systems

We investigate hybrid structures based on a bilayer quantum spin Hall system in proximity to an s-wave superconductor as a platform to mimic time-reversal symmetric topological superconductors. In this bilayer setup, the induced pairing can be of intra- or inter-layer type, and domain walls of those different types of pairing potentials host Kramers partners (time-reversal conjugate pairs) of Majorana bound states. Interestingly, we discover that such topological interfaces providing Majorana bound states can also be achieved in an otherwise homogeneous system by a spatially dependent inter-layer gate voltage. This gate voltage causes the relative electron densities of the two layers to vary accordingly which suppresses the inter-layer pairing in regions with strong gate voltage. We identify particular transport signatures (zero-bias anomalies) in a five-terminal setup that are uniquely related to the presence of Kramers pairs of Majorana bound states.

Higher-order topological superconductivity: Possible realization in Fermi gases and Sr2RuO4

We propose to realize second-order topological superconductivity in bilayer spin-polarized Fermi gas superfluids. We focus on systems with intralayer chiral $p$-wave pairing and with tunable interlayer hopping and interlayer interactions. Under appropriate circumstances, an interlayer even-parity $s$- or $d$-wave pairing may coexist with the intralayer $p$-wave. Our model supports localized Majorana zero modes not only at the corners of the system geometry, but also at the terminations of certain one-dimensional defects, such as lattice line defects and superfluid domain walls. We show how such topological phases and the Majorana zero modes therein can be manipulated in a multitude of ways by tuning the interlayer pairing and hopping. Generalized to spinful systems, we further propose that the putative $p$-wave superconductor Sr$_{2}$RuO$_{4}$, when subject to uniaxial strains, may also realize the desired topological phase.