Local Pair Research Articles

The subsystem quantum chemistry program Serenity

AbstractSERENITY [J Comput Chem. 2018;39:788–798] is an open‐source quantum chemistry software that provides an extensive development platform focused on quantum‐mechanical multilevel and embedding approaches. In this study, we give an overview over the developments done in Serenity since its original publication in 2018. This includes efficient electronic‐structure methods for ground states such as multilevel domain‐based local pair natural orbital coupled cluster and Møller–Plesset perturbation theory as well as the multistate frozen‐density embedding quasi‐diabatization method. For the description of excited states, SERENITY features various subsystem‐based methods such as embedding variants of coupled time‐dependent density‐functional theory, approximate second‐order coupled cluster theory and the second‐order algebraic diagrammatic construction technique as well as GW/Bethe–Salpeter equation approaches. SERENITY's modular structure allows combining these methods with density‐functional theory (DFT)‐based embedding through various practical realizations and variants of subsystem DFT including frozen‐density embedding, potential‐reconstruction techniques and projection‐based embedding.This article is categorized under: Electronic Structure Theory > Density Functional Theory Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry

Quantum chemical modeling of electron‐deficient hollow TlkPb12–k and TlkBi20–k shells and related endohedral complexes (k = 1; 2)

AbstractThe equilibrium structural parameters, symmetry groups, and dipole moments of the free hollow electron‐deficient TlBi19, Tl2Bi18, p‐, m‐, o‐Tl2Pb10 shells and the endohedral (He, Ne)@Tl2Pb10, (Y, La, Lu, Tl, Bi, Ce)@TlPb11, Tl@(Y, La, Lu) Pb11, Sr@TlBi19, Tl@SrBi19, Yb@TlBi19, Tl@YbBi19, [Y@TlBi19]+, [Lu@TlBi19]+, Sr@Tl2Bi18, and Yb@Tl2Bi18 complexes are predicted by using DFT (U)PBE0 hybrid method. The isomerization of (Sr, Yb)@TlkBi20–k into Tl@(Sr, Yb) Tlk–1Bi20–k is endothermic. The isodesmic substitution of an endo‐atom in the Tl@TlPb11 cluster for a rare‐earth atom is exothermic. The hollow TlkBi20–k (Sr, Yb) complexes with Tl in the shell and with Sr or Yb exo‐atom are impossible. The endo‐atoms plunge in hollow TlPb11 and hollow TlBi19 shells without delay on its surface. The (C5v)‐TlPb11 and (C3v)‐TlBi19 shells are stabilized by an endo‐atom X with oxidation number ΞX = +3 and +2, respectively. No one cerium IV oxidation state has been predicted. The integer number ΞX is presented as a function of the populations of one‐electron states in the shell surrounding the endo‐atom X. Each Pb or Bi atom in the electron‐deficient clusters retains an entirely localized lone electron pair. The change in the IR spectrum when a metal atom is embedded into its cavity indicates a strong interaction between the components of the endohedral complex. Structural aspects of the β‐decay of a radioactive endo‐atom in the cavity of a metal cluster are discussed.

Temperature and pressure dependent rate constants of the reactions of OH• with cyclopentene from variational TST and SS-QRRK methods.

In this work, the pressure- and temperature-dependent reaction rate constants for the hydrogen abstraction and addition of hydroxyl radicals to the unsaturated cyclopentene were studied. Geometries and vibrational frequencies of reactants, products, and transition states were calculated using density functional theory, with single-point energy corrections determined at the domain-based local pair natural orbital-coupled-cluster single double triple/cc-pVTZ-F12 level. The high-pressure limit rate constants were calculated using the canonical variational transition state theory with the small-curvature tunneling approximation. The vibrational partition functions were corrected by the effects of torsional and ring-puckering anharmonicities of the transition states and cyclopentene, respectively. Variational effects are shown to be relevant for all the hydrogen abstraction reactions. The increasing of the rate constants by tunneling is significant at temperatures below 500K. The pressure dependence on the rate constants of the addition of OH• to cyclopentene was calculated using the system-specific quantum Rice-Ramsperger-Kassel model. The high-pressure limit rate constants decrease with increasing temperature in the range 250-1000K. The falloff behavior was studied at several temperatures with pressures varying between 10-3 and 103 bar. At temperatures below 500K, the effect of the pressure on the addition rate constant is very modest. However, at temperatures around and above 1000K, taking pressure into account is mandatory for an accurate rate constant calculation. Branching ratio analyses reveal that the addition reaction dominates at temperatures below 500K, decreasing rapidly at higher temperatures. Arrhenius parameters are provided for all reactions and pressure dependent Arrhenius parameters are given for the addition of OH• to cyclopentene.

Dynamic generation of nonequilibrium superconducting states in a Kitaev chain

Non-equilibrium state can exhibit the same macroscopic properties, such as conductivity or superconductivity, as a static state when they share the identical average of an observable over a period of time. We investigate the quench dynamics of a Kitaev chain by introducing two kinds of order parameters which relate to two channels of pairing, local pair in real space and BCS-like pair in momentum space. Based on exact solutions, we find that two order parameters are identical for the ground state, indicating the balance between two kinds of pairing channels, and can identify the quantum phase diagram. However, for a non-equilibrium state obtained by the time evolution from initially prepared vacuum state, the two are different but both can still clearly identify the phase diagram. In the topologically non-trivial region, the non-equilibrium states prefer the BCS-like pairing state. Our finding provides an alternative way to dynamically generate a superconducting state from a trivial empty state and sheds light on the mechanism of pairing.

Cysteine-Dependent Conformational Heterogeneity of Shigella flexneri Autotransporter IcsA and Implications of Its Function.

Shigella IcsA is a versatile surface virulence factor required for early and late pathogenesis stages extracellularly and intracellularly. Despite IcsA serving as a model Type V secretion system (T5SS) autotransporter to study host-pathogen interactions, its detailed molecular architecture is poorly understood. Recently, IcsA was found to switch to a different conformation for its adhesin activity upon sensing the host stimuli by Shigella Type III secretion system (T3SS). Here, we reported that the single cysteine residue (C130) near the N terminus of the IcsA passenger had a role in IcsA adhesin activity. We also showed that the IcsA passenger (IcsAp) existed in multiple conformations, and the conformation populations were influenced by a central pair of cysteine residues (C375 and C379), which was not previously reported for any Type V autotransporter passengers. Disruption of either or both central cysteine residues altered the exposure of IcsA epitopes to polyclonal anti-IcsA antibodies previously shown to block Shigella adherence, yet without loss of IcsA intracellular functions in actin-based motility (ABM). Anti-IcsA antibody reactivity was restored when the IcsA-paired cysteine substitution mutants were expressed in an ΔipaD background with a constitutively active T3SS, highlighting an interplay between T3SS and T5SS. The work here uncovered a novel molecular switch empowered by a centrally localized, short-spaced cysteine pair in the Type V autotransporter IcsA that ensured conformational heterogeneity to aid IcsA evasion of host immunity. IMPORTANCE Shigella species are the leading cause of diarrheal-related death globally by causing bacillary dysentery. The surface virulence factor IcsA, which is essential for Shigella pathogenesis, is a unique multifunctional autotransporter that is responsible for cell adhesion, and actin-based motility, yet detailed mechanistic understanding is lacking. Here, we showed that the three cysteine residues in IcsA contributed to the protein's distinct functions. The N-terminal cysteine residue within the IcsA passenger domain played a role in adhesin function, while a centrally localized cysteine pair provided conformational heterogeneity that resulted in IcsA molecules with different reactivity to adhesion-blocking anti-IcsA antibodies. In synergy with the Type III secretion system, this molecular switch preserved biological function in distinct IcsA conformations for cell adhesion, actin-based motility, and autophagy escape, providing a potential strategy by which Shigella evades host immunity and targets this essential virulence factor.

Nematic superconductivity in a one-dimensional system of massless fermions

The superconducting properties of the one-dimensional model of “relativistic” fermions with attraction generated by antiferromagnetic (Heisenberg) pair superexchange spin interaction are studied. Namely, we demonstrate that such a pairing in this system takes place in the nematic channel, with extended s-wave symmetry, where the attraction between fermions mostly takes place when the fermions occupy the nearest sites. It is demonstrated, that the zero-temperature properties of such a system are rather different from the “standard” case of superconductivity with local attraction. For instance, the order parameter has an unusual helical momentum dependence, ∼e−ika, where a is the lattice parameter and the dependence of the gap on doping has a bell shape, qualitatively similar to cuprate high-Tc superconductors. Finally, the smooth transition from the overlapping pair to the local pair regime (or BCS–BEC crossover) in the nematic phase takes place at much lower values of doping as compared to the local pairing case, i.e., the “relativistic 1D” nematic superconductor is much less “friendly” to the local pairs. We also discuss the possible relation of the properties of this model to the superconducting properties of twisted graphene.

Reliable Isotropic Electron-Paramagnetic-Resonance Hyperfine Coupling Constants from the Frozen-Density Embedding Quasi-Diabatization Approach.

We present a systematic benchmark of isotropic electron-paramagnetic-resonance hyperfine coupling constants calculated for radical cation and anion complexes of molecules contained in the S22 test set using the frozen-density embedding quasi-diabatization (FDE-diab) approach. The results are compared to those from Kohn-Sham density-functional theory and frozen-density embedding, employing the domain-based local pair natural orbital coupled cluster singles and doubles method as a reference. We demonstrate that our new approach outperforms frozen-density embedding in all cases and provides reliable hyperfine couplings for radical cations using rather simple generalized-gradient approximation-type functionals. By contrast, more sophisticated and computationally less efficient exchange-correlation approximations are required for Kohn-Sham density-functional theory. For the radical anions, FDE-diab can at least provide an accuracy similar to that of Kohn-Sham density-functional theory. Finally, we demonstrate the computational advantages of FDE-diab for a π-stacked benzene octamer radical cation.

Cluster-in-Molecule Method Combined with the Domain-Based Local Pair Natural Orbital Approach for Electron Correlation Calculations of Periodic Systems.

The cluster-in-molecule (CIM) method was extended to systems with periodic boundary conditions (PBCs) in a previous work (PBC-CIM) [J. Chem. Theory Comput.2019, 15, 2933], which is able to compute the electronic structures of periodic systems at second-order Møller-Plesset perturbation theory (MP2) and coupled cluster singles and doubles (CCSD) levels. However, the high computational costs of CCSD with respect to the size of clusters limit the usage of PBC-CIM to crystals with small or medium unit cells. In this work, we further develop the PBC-CIM method by employing the domain-based local pair natural orbital (DLPNO) methods for the electron correlation calculations of clusters to reduce the computational costs. The combined approach allows CCSD with perturbative triples, denoted as CCSD(T), to be computationally available for accurate descriptions of periodic systems. The distant-pair correction is also implemented to improve the accuracy of PBC-CIM. As in the molecular cases, the distant pair correction significantly improves the accuracy of various PBC-CIM methods with few additional costs. The PBC-CIM-DLPNO-CCSD(T) approach has been applied to investigate the optimized lattice parameter of the cubic LiCl crystal and two adsorption problems (CO on the NaCl(100) surface and H2O on the h-BN surface). The results show that the CIM-DLPNO-CCSD(T) method offers accurate and efficient descriptions for the studied systems. Another application to the cohesive energy of the acetic acid crystal reveals that large basis sets are necessary for reliable calculations on the cohesive energies of molecular crystals.

Numerical investigation of a propeller operating under different inflow conditions

This work investigates the flow physics in propeller wakes to better understand how propeller wakes evolve under different inflow conditions from near field to far field. A rotating propeller is numerically modeled by using a dynamic overset technique that involves the improved delayed detached-eddy simulation method. To validate the numerical approach, its results are compared against experimentally determined thrust and torque coefficients and flow fields. The results show that, compared with uniform inflow, turbulent inflow significantly modifies the morphology of the vortex system behind the propeller. Under turbulent-inflow conditions, turbulent structures appear around the boundary layer of the propeller blades and interact with the boundary layer flow of the propeller blades, leading to instability and diffusion of primary tip vortices shed by the blade tips. Multiple local pairing in the circumferential direction leads to the rapid breakdown of the tip vortex system, accompanied by the generation of numerous secondary vortex structures. Tip vortices quickly lose coherence in the middle field and far field and tend to be homogeneously distributed when there is inflow turbulence. The present study gives a deeper insight into the flow physics driving the tip vortex pairing process for a propeller operating under uniform- and turbulent-inflow conditions.

Reduced-Scaling Double Hybrid Density Functional Theory with Rapid Basis Set Convergence through Localized Pair Natural Orbital F12.

Following earlier work [Mehta, N.; Martin, J. M. L. J. Chem. Theory Comput.2022, 10.1021/acs.jctc.2c00426] that showed how the slow basis set convergence of the double hybrid density functional theory can be obviated by the use of F12 explicit correlation in the GLPT2 step (second order Görling-Levy perturbation theory), we demonstrate here for the very large and chemically diverse GMTKN55 benchmark suite that the CPU time scaling of this step can be reduced (asymptotically linearized) using the localized pair natural orbital (PNO-L) approximation at negligible cost in accuracy.

Improved Estimates of Host-Guest Interaction Energies for Endohedral Fullerenes Containing Rare Gas Atoms, Small Molecules, and Cations.

Endohedral fullerenes have evinced much interest from the fundamental and applications points of view. However, given the nature of the weak interaction between the guest species and the host cage in these confined systems, the interaction energy values obtained using various theoretical methods, and different basis sets vary over a wide range. For example, the reported interaction energy for the HF@C60 system ranges from -2.5 kcal/mol to -14.9 kcal/mol. In the present manuscript, we report reliable interaction energy values for different endohedral fullerenes (He@C60 , Ne@C60 , Ar@C60 , Kr@C60 , H2 @C60 , HF@C60 , H2 O@C60 , NH3 @C60 , CH4 @C60 , Li+ @C60 , Na+ @C60 , and K+ @C60 ) obtained using the domain-based local pair natural orbital coupled-cluster singles, doubles, and perturbative triples (DLPNO-CCSD(T)) method and the def2-TZVP basis set. We believe that these energy values could be considered as benchmark values, and the performance of other quantum chemical methods could be assessed accordingly. Local energy decomposition analysis within the DLPNO-CCSD(T) framework is used to estimate the electrostatic, exchange, and dispersion components of the interaction energy for some of the endohedral fullerenes.

Effective magnetic monopole mechanism for localized electron pairing in HTS

The mechanism responsible for spatially localized strong coupling electron pairing characteristic of high-temperature superconductors (HTS) remains elusive and is a subject of hot debate. Here we propose a new HTS pairing mechanism which is the binding of two electrons residing in adjacent conducting planes of layered HTS materials by effective magnetic monopoles forming between these planes. The pairs localized near the monopoles form real-space seeds for superconducting droplets and strong coupling is due to the topological Dirac quantization condition. The pairing occurs well above the superconducting transition temperature Tc. Localized electron pairing around effective monopoles promotes, upon cooling, the formation of superconducting droplets connected by Josephson links. Global superconductivity arises when strongly coupled granules form an infinite cluster, and global superconducting phase coherence sets in. The resulting Tc is estimated to fall in the range from hundred to thousand Kelvins. Our findings pave the way for tailoring materials with elevated superconducting transition temperatures.

Explicitly Correlated Double-Hybrid DFT: A Comprehensive Analysis of the Basis Set Convergence on the GMTKN55 Database.

Double-hybrid density functional theory (DHDFT) offers a pathway to accuracy approaching composite wavefunction approaches such as G4 theory. However, the Görling–Levy second-order perturbation theory (GLPT2) term causes them to partially inherit the slow ∝L–3 (with L the maximum angular momentum) basis set convergence of correlated wavefunction methods. This could potentially be remedied by introducing F12 explicit correlation: we investigate the basis set convergence of both DHDFT and DHDFT-F12 (where GLPT2 is replaced by GLPT2-F12) for the large and chemically diverse general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) benchmark suite. The B2GP-PLYP-D3(BJ) and revDSD-PBEP86-D4 DHDFs are investigated as test cases, together with orbital basis sets as large as aug-cc-pV5Z and F12 basis sets as large as cc-pVQZ-F12. We show that F12 greatly accelerates basis set convergence of DHDFs, to the point that even the modest cc-pVDZ-F12 basis set is closer to the basis set limit than cc-pV(Q+d)Z or def2-QZVPPD in orbital-based approaches, and in fact comparable in quality to cc-pV(5+d)Z. Somewhat surprisingly, aug-cc-pVDZ-F12 is not required even for the anionic subsets. In conclusion, DHDF-F12/VDZ-F12 eliminates concerns about basis set convergence in both the development and applications of double-hybrid functionals. Mass storage and I/O bottlenecks for larger systems can be circumvented by localized pair natural orbital approximations, which also exhibit much gentler system size scaling.

Thermal stability of energetic 6,8-dinitrotriazolo[1,5-a]pyridines: Interplay of thermal analysis and quantitative quantum chemical calculations

Understanding the thermal stability of energetic materials is of great importance for storage and safety issues. In the present work, we report on the thermolysis kinetics and mechanism of the two fused energetic heterocycles, viz., 6,8-dinitrotriazolo[1,5-a]pyridine (1) and 2-amino-6,8-dinitro[1,2,4]triazolo[1,5-a]pyridine (2). The experimental kinetics obtained with the aid of advanced thermal analysis techniques was complemented by mechanistic insights from high-level quantum chemical calculations. More specifically, the simultaneous thermal analysis (STA) revealed that both compounds evaporate under atmospheric pressure. To shift the evaporation to higher temperatures and to study the sole decomposition kinetics, we employed the differential scanning calorimetry (DSC) under elevated external pressure (2.0 MPa). The analysis of DSC data was performed using the Kissinger, isoconversional, and model-fitting approaches. The thermolysis of 1 occurs in the melt and is described by the kinetic scheme comprised of two independent non-integer order autocatalytic reactions with the kinetic parameters Ea1=124.2±0.5 kJ mol−1, log(A1/s−1)=9.34±0.04 and Ea2=80.8±0.7 kJ mol−1, log(A1/s−1)= 4.86±0.07. At the same time, the obtained kinetic parameters for 2 are too large to be realistic, which is a consequence of the overlap of melting and decomposition processes near the melting point. To get a deeper insight into the decomposition mechanism, the experimental data were complemented by theoretical thermolysis pathways with the activation barriers calculated using the domain-based local pair natural orbital (DLPNO) modifications of coupled cluster techniques. The same primary decomposition channels, viz., the nitro-nitrite isomerization and CNO2 bond cleavage turned out to compete in the thermolysis of 1 and 2. Due to a lower activation barrier (∼240 kJ mol−1), the former reaction path dominates at lower temperatures, whereas in the experimental temperature ranges (>500 K) the CNO2 bond cleavage with a higher preexponential factor is the fastest elementary reaction (the activation barrier ∼280 kJ mol−1). The obtained experimental and theoretical Arrhenius parameters exhibit a kinetic compensation effect, that is, the rate constant values in solid, melt, and gas phases are close to each other.

Double nested Hilbert schemes and the local stable pairs theory of curves

We propose a variation of the classical Hilbert scheme of points, thedouble nested Hilbert scheme of points, which parametrizes flags of zero-dimensional subschemes whose nesting is dictated by a Young diagram. Over a smooth quasi-projective curve, we compute the generating series of topological Euler characteristic of these spaces, by exploiting the combinatorics of reversed plane partitions. Moreover, we realize this moduli space as the zero locus of a section of a vector bundle over a smooth ambient space, which therefore admits a virtual fundamental class. We apply this construction to the stable pair theory of a local curve, that is the total space of the direct sum of two line bundles over a curve. We show that the invariants localize to virtual intersection numbers on double nested Hilbert scheme of points on the curve, and that the localized contributions to the invariants are controlled by three universal series for every Young diagram, which can be explicitly determined after the anti-diagonal restriction of the equivariant parameters. Under the anti-diagonal restriction, the invariants are matched with the Gromov–Witten invariants of local curves of Bryan–Pandharipande, as predicted by the Maulik–Nekrasov–Okounkov–Pandharipande (MNOP) correspondence. Finally, we discuss$K$-theoretic refinements à la Nekrasov–Okounkov.

Influence of electron irradiation on fluctuation conductivity and pseudogap in YBa2Cu3O7−δ single crystals

The effect of electron irradiation with the energy of 2.5 MeV on the temperature dependences of the resistivity ρ(T) of an optimally doped YBa2Cu3O7−δ single crystal has been studied. The temperature dependences of both fluctuation conductivity σ′ (T) and the pseudogap Δ*(T) on irradiation dose φ have been calculated within the local pair model. Here we show that with an increase in φ, the value of ρ(300 K) increases linearly, while Tc decreases linearly. Concurrently, the value of ρ(100 K) increases nonlinearly, demonstrating a feature for φ3 = 4.3⋅1018 e/cm2, which is also observed in the number of other dose-dependent parameters. Regardless of the irradiation dose, in the temperature range from Tc up to T01, σ′(T) obeys the classical fluctuation theories of Aslamazov-Larkin (3D-AL) and Maki-Thompson (2D-MT), demonstrating 3D-2D crossover with increasing temperature. The crossover temperature T0 makes it possible to determine the coherence length along the c axis, ξc(0), which increases by ∼3 times under irradiation. Furthermore, the range of superconducting fluctuations above Tc also noticeably increases. At φ1 = 0, the dependence Δ*(T) typical for single crystals containing pronounced twin boundaries is observed with a maximum at Tpair ∼120 K and a distinct minimum at T = T01. It was determined for the first time that at φ3 = 4.3⋅1018 e/cm2 the shape of Δ*(T) changes strongly and becomes the same as in optimally doped YBa2Cu3O7−δ single crystals with a very low pseudogap opening temperature T* and noticeably reduced Tpair, while at Tc(φ) there are no singularities. With an increase in the irradiation dose up to φ4 = 8.81018 e/cm2, the shape of Δ*(T) is restored and becomes the same as in well-structured YBa2Cu3O7−δ films and untwined single crystals. Moreover, in this case, Tpair and T* increase noticeably.

Information scrambling and redistribution of quantum correlations through dynamical evolution in spin chains

We investigate the propagation of local bipartite quantum correlations, along with the tripartite mutual information to characterize the information scrambling through dynamical evolution of spin chains. Starting from an initial state with the first pair of spins in a Bell state, we study how quantum correlations spread to other parts of the system, using different representative spin Hamiltonians, viz. the Heisenberg Model, a spin-conserving model, the transverse-field XY model, a non-conserving but integrable model, and the kicked Harper model, a spin conserving but nonintegrable model. We show that the local correlations spread consistently in the case of spin-conserving dynamics in both integrable and nonintegrable cases, with a strictly nonnegative tripartite mutual information. In contrast, in the case of non-conserving dynamics, tripartite mutual information is negative and local pair correlations do not propagate.

Orbital pair selection for relative energies in the domain-based local pair natural orbital coupled-cluster method

For the accurate computation of relative energies, domain-based local pair natural orbital coupled-cluster [DLPNO-CCSD(T0)] has become increasingly popular. Even though DLPNO-CCSD(T0) shows a formally linear scaling of the computational effort with the system size, accurate predictions of relative energies remain costly. Therefore, multi-level approaches are attractive that focus the available computational resources on a minor part of the molecular system, e.g., a reaction center, where changes in the correlation energy are expected to be the largest. We present a pair-selected multi-level DLPNO-CCSD(T0) ansatz that automatically partitions the orbital pairs according to their contribution to the overall correlation energy change in a chemical reaction. To this end, the localized orbitals are mapped between structures in the reaction; all pair energies are approximated through computationally efficient semi-canonical second-order Møller-Plesser perturbation theory, and the orbital pairs for which the pair energies change significantly are identified. This multi-level approach is significantly more robust than our previously suggested, orbital selection-based multi-level DLPNO-CCSD(T0) ansatz [M. Bensberg and J. Neugebauer, J. Chem. Phys. 155, 224102 (2021)] for reactions showing only small changes in the occupied orbitals. At the same time, it is even more efficient without added input complexity or accuracy loss compared to the full DLPNO-CCSD(T0) calculation. We demonstrate the accuracy of the multi-level approach for a total of 128 chemical reactions and potential energy curves of weakly interacting complexes from the S66x8 benchmark set.

Closely spaced co-rotating helical vortices: long-wave instability

We consider as base flow the stationary vortex filament solution obtained by Castillo-Castellanos et al. (Phys. Rev. Fluids, vol. 6, 2021, 114701) in the far wake of a rotor with tip-splitting blades. The cases of a single blade and of two blades with a hub vortex are studied. In these solutions, each blade generates two closely spaced co-rotating tip vortices that form a braided helical pattern in the far wake. The long-wave stability of these solutions is analysed using the same vortex filament framework. Both the linear spectrum and the linear impulse response are considered. We demonstrate the existence of different types of instability modes. A first type corresponds to the local pairing of consecutive turns of the helical pattern, which is well described by the instability of a uniform helical vortex with a core size given by the mean separation distance of the vortices in the pair. A second type corresponds to the pairing of consecutive turns of the vortex pair and is observed only for densely braided patterns, which is well described by the instability of two interlaced helical vortices by straightening out the baseline helix. A third type of unstable modes modifies the separation distance between the vortices in each pair and amplifies specific (linear) wavelengths. These unstable modes also spread spatially with a weaker rate.

Preformed Cooper pairs in flat-band semimetals

We study conditions for the emergence of the preformed Cooper pairs in materials hosting flat bands. As a particular example, we consider a semimetal, with a pair of three-band crossing points at which a flat band intersects with a Dirac cone, and focus on the s-wave intervalley pairing channel. The nearly dispersionless nature of the flat band at strong attraction between electrons promotes local Cooper pair formation so that the system may be modeled as an array of superconducting grains. Due to dispersive bands, Andreev scattering between the grains gives rise to the global phase-coherent superconductivity at low temperatures. We develop a mean-field theory to calculate transition temperature between the preformed Cooper pair state and the phase-coherent state for different interaction strengths in the Cooper channel. The transition temperature between semimetal and preformed Cooper pair phases is proportional to the interaction constant, the dependence of the transition temperature to the phase-coherent state on the interaction constant is weaker.