Superconducting Instability Research Articles

Ising superconductors: Interplay of magnetic field, triplet channels, and disorder

We study the superconducting instability in disordered non-centrosymmetric monolayers with intrinsic Ising spin-orbit coupling (SOC) subjected to an in-plane Zeeman magnetic field. The pairing interaction contains the channels allowed by crystal symmetry, such that in general, the pairing state is a mixture of singlet and triplet Cooper pairs. The joint action of SOC and Zeeman field selects a specific in-plane $\mathbf{d}$-vector triplet component to couple with the singlets, which gains robustness against disorder through the coupling. The out-of-plane $\mathbf{d}$-vector component, that in the clean case is immune to both the Zeeman field and SOC is obliterated by a very small impurity scattering rate. We formulate the quasi-classical theory of Ising superconductors and solve the linearized Eilenberger equations to obtain the pair-breaking equations that determine the Zeeman field -- temperature dependence of the continuous superconducting transition. Our discussion emphasizes how the Zeeman field, SOC and disorder affect the different superconducting order parameters, and we show how the spin-fields inevitably induce odd-frequency pairing correlations.

Instability caused by the fermion–fermion interactions combined with rotational and particle-hole asymmetries in three-dimensional materials with quadratic band touching

We investigate the role of four-fermion interactions, rotational and particle-hole asymmetries, and their interplay in three-dimensional systems with a quadratic band touching point by virtue of the renormalization group approach, which allows to treat all these facets unbiasedly. The coupled flow evolutions of interaction parameters are derived by taking into account one-loop corrections in order to explore the behaviors of low-energy states. We find four-fermion interaction can drive Gaussian fixed points to be unstable in the low-energy regime. In addition, the rotational and particle-hole asymmetries, together with the fermion–fermion interactions conspire to split the trajectories of distinct types of fermionic couplings and induce superconductivity instability with appropriate starting conditions. Furthermore, we present the schematic phase diagrams in the parameter space, showing the overall behaviors of states in the low-energy regime caused by both fermionic interactions and asymmetries.

Superconductivity and structural instability in layered BiS2-based LaO1−xBiS2

A new BiS2-based superconductor was synthesized and its crystal structure was investigated.

Kohn-Luttinger superconductivity on two orbital honeycomb lattice

Motivated by experiments on twisted bilayer graphene, we study the emergence of superconductivity from $\textit{weak}$ repulsive interactions in the Hubbard model on a honeycomb lattice, with both spin and orbital degeneracies, and with the filling treated as a tunable control parameter. The attraction is generated through the Kohn-Luttinger mechanism. We find, similar to old studies of single layer graphene, that the leading superconducting instability is in a $d$-wave pairing channel close to Van Hove filling, and is in an $f$-wave pairing channel away from Van Hove filling. The $d$-wave pairing instability further has a twelve-fold degeneracy while the $f$-wave pairing instability has a ten-fold degeneracy. We analyze the symmetry breaking perturbations to this model. Combining this with a Ginzburg-Landau analysis, we conclude that close to Van Hove filling, a spin singlet $d+id$ pairing state should form (consistent with several other investigations of twisted bilayer graphene), whereas away from Van Hove filling we propose an unusual spin and orbital singlet $f$-wave pairing state.

Correlations and electronic order in a two-orbital honeycomb lattice model for twisted bilayer graphene

The recent observation of superconductivity in proximity to an insulating phase in twisted bilayer graphene (TBG) at small `magic' twist angles has been linked to the existence of nearly-flat bands, which make TBG a fresh playground to investigate the interplay between correlations and superconductivity. The low-energy narrow bands were shown to be well-described by an effective tight-binding model on the honeycomb lattice (the dual of the triangular Moir\'e superlattice) with a local orbital degree of freedom. In this paper, we perform a strong-coupling analysis of the proposed $\left(p_{x},\,p_{y}\right)$ two-orbital extended Hubbard model on the honeycomb lattice. By decomposing the interacting terms in the particle-particle and particle-hole channels, we classify the different possible superconducting, magnetic, and charge instabilities of the system. In the pairing case, we pay particular attention to the two-component ($d$-wave) pairing channels, which admit vestigial phases with nematic or chiral orders, and study their phenomenology. Furthermore, we explore the strong-regime by obtaining a simplified spin-orbital exchange model which may describe a putative Mott-like insulating state at quarter-filling. Our mean-field solution reveals a rich intertwinement between ferro- and antiferro-magnetic orders with different types of nematic and magnetic orbital orders. Overall, our work provides a solid framework for further investigations of the phase diagram of the two-orbital extended Hubbard model in both strong- and weak-coupling regimes.

Band-Renormalization Effect on Superconductivity and Antiferromagnetism in Two-Dimensional t–J Model

The coexistence or exclusivity of \(d_{x^{2} - y^{2}}\)-wave superconducting (d-SC) and antiferromagnetic (AF) orders and instability toward phase separation (PS) are reconsidered for the square-la...

Effect of Background Magnetic Field on Type-II Superconductor under Oscillating Magnetic Field Simulated Using Ginzburg-Landau Model

Cubic superconducting sample was simulated using time-dependent Ginzburg-Landau model under oscillating magnetic field with and without additional background static magnetic field. Vortex dynamics including entrance and exit from the sample was simulated. Magnetization and carrier concentration densities of the sample were studied as a function of external magnetic field variations. Anomalies in carrier concentration density were observed at certain values of the magnetic field which were correlated with the entrance and exit processes of vortices. Area swept by superconductor magnetization with magnetic field was observed to have a hysteresis-like behavior where area representing energy dissipated per cycle. This energy accumulation was suggested to cause instability in superconductor over the number of cycles and may result in thermal quenching. Temporal distribution of energy components showed consistency with the pattern observed for carrier concentration and magnetization under oscillating magnetic field. Rapid phase changes with magnetic oscillations resulted in oscillations in energy components, and irregular peaks and ripples in superconducting energy represent the situation of exit and entry of vortices. While the rise in interaction energy with cycles is referred to vortex relaxation time in a cycle, this energy is expected to accumulate and take other forms (e.g., heat) and is predicted to cause thermal quenching. In the presence of background static magnetic field, this energy dissipation was calculated to increase significantly while superconductor is subjected to oscillating magnetic field.

Bond-ordered states and f -wave pairing of spinless fermions on the honeycomb lattice

Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behaviour in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the van-Hove filling, the free Fermi surface is hole-like and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the van-Hove filling the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling the free Fermi surface becomes electron-like and a superconducting instability with $f$-wave symmetry is found to emerge from the interplay of intra-unitcell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.

Fate of superconductivity in three-dimensional disordered Luttinger semimetals

Superconducting instability can occur in three-dimensional quadratic band crossing semimetals only at a finite coupling strength due to the vanishing of density of states at the quadratic band touching point. Since realistic materials are always disordered to some extent, we study the effect of short-ranged-correlated disorder on this superconducting quantum critical point using a controlled loop-expansion applying dimensional regularization. The renormalization group (RG) scheme allows us to determine the RG flows of the various interaction strengths and shows that disorder destroys the superconducting quantum critical point. In fact, the system exhibits a runaway flow to strong disorder.

Superconductivity in a two-dimensional repulsive Rashba gas at low electron density

We study the superconducting instability and the resulting superconducting states in a two-dimensional repulsive Fermi gas with Rashba spin–orbit coupling at low electron density (namely the Fermi energy EF is lower than the energy ER of the Dirac point induced by Rashba coupling). We find that superconductivity is enhanced as the dimensionless Fermi energy () decreases, due to two reasons. First, the density of states at increases as . Second, the particle–hole bubble becomes more anisotropic, resulting in an increasing effective attraction. The superconducting state is always in the total angular momentum (or ) channel with Chern number C = 4 (or ), breaking time reversal symmetry spontaneously. Although a putative Leggett mode is expected due to the two-gap nature of the superconductivity, we find that it is always damped. More importantly, once a sufficiently large Zeeman coupling is applied to the superconducting state, the Chern number can be tuned to be ±1 and Majorana zero modes exist in the vortex cores.

Strong correlations and the search for high- Tc superconductivity in chromium pnictides and chalcogenides

Undoped iron superconductors accommodate $n=6$ electrons in five d-orbitals. Experimental and theoretical evidence shows that the strength of correlations increases with hole-doping, as the electronic filling approaches half-filling with $n=5$ electrons. This evidence delineates a scenario in which the parent compound of iron superconductors is the half-filled system, in analogy to cuprate superconductors. In cuprates the superconductivity can be induced upon electron or hole doping. In this work we propose to search for high-Tc superconductivity and strong correlations in chromium pnictides and chalcogenides with $n<5$ electrons. By means of ab-initio, slave spin and multi-orbital RPA calculations we analyse the strength of the correlations and the superconducting and magnetic instabilities in these systems with main focus on LaCrAsO. We find that electron-doped LaCrAsO is a strongly correlated system with competing magnetic interactions, being $(\pi,\pi)$ antiferromagnetism and nodal d-wave pairing the most plausible magnetic and superconducting instabilities, respectively.

Electrons at the monkey saddle: A multicritical Lifshitz point

We consider 2D interacting electrons at a monkey saddle with dispersion $\propto p_x^3-3p_xp_y^2$. Such a dispersion naturally arises at the multicritical Lifshitz point when three van Hove saddles merge in an elliptical umbilic elementary catastrophe, which we show can be realized in biased bilayer graphene. A multicritical Lifshitz point of this kind can be identified by its signature Landau level behavior $E_m\propto (Bm)^{3/2}$ and related oscillations in thermodynamic and transport properties, such as de Haas-van Alphen and Shubnikov-de Haas oscillations, whose period triples as the system crosses the singularity. We show, in the case of a single monkey saddle, that the non-interacting electron fixed point is unstable to interactions under the renormalization group flow, developing either a superconducting instability or non-Fermi liquid features. Biased bilayer graphene, where there are two non-nested monkey saddles at the $K$ and $K^\prime$ points, exhibits an interplay of competing many-body instabilities, namely s-wave superconductivity, ferromagnetism, and spin- and charge-density wave.

Instability of three-band Tomonaga-Luttinger liquid: Renormalization group analysis and possible application toK2Cr3As3

Motivated by recently discovered quasi-one-dimensional superconductor K$_{2}$Cr$_{3}$As$_{3}$ with $D_{3h}$ lattice symmetry, we study one-dimensional three-orbital Hubbard model with generic electron repulsive interaction described by intra-orbital repulsion $U$, inter-orbital repulsion, and Hund's coupling $J$. As extracted from density functional theory calculation, two of the three atomic orbitals are degenerate ($E^{\prime}$ states) and the third one is non-degenerate ($A^{\prime}_1$), and the system is presumed to be at an incommensurate filling. With the help of bosonization, we have usual three-band Tomonaga-Luttinger liquid for the normal state. Possible charge density wave (CDW), spin density wave (SDW) and superconducting (SC) instabilities are analyzed by renormalization group. The ground state depends on the ratio $J/U$ and is sensitive to the degeneracy of $E^{\prime}$ bands. At $0<J<U/3$, spin-singlet SC state is favored, while spin-triplet superconductivity will be favored in the region $U/3<J<U/2$. The SDW state has the lowest energy only in the unphysical parameter region $J>U/2$. When the two-fold degeneracy of $E^{\prime}$ bands is lifted, SDW instability has the tendency to dominate over the spin-singlet SC state at $0<J<U/3$, while the order parameter of the spin-triplet SC state will be modulated by a phase factor $2\Delta k_F x$ at $U/3<J<U/2$. Possible experimental consequences and applications to K$_{2}$Cr$_{3}$As$_{3}$ are discussed.

Multi-layered Chalcogenides with potential for magnetism and superconductivity

Layered thallium copper chalcogenides can form single, double, or triple layers of Cu–Ch separated by Tl sheets. Here we report on the preparation and properties of Tl-based materials of TlCu2Se2, TlCu4S3, TlCu4Se3 and TlCu6S4. Having no long-range magnetism for these materials is quite surprising considering the possibilities of inter- and intra-layer exchange interactions through Cu 3d, and we measure by magnetic susceptibility and confirm by neutron diffraction. First principles density-functional theory calculations for both the single-layer TlCu2Se2 (isostructural to the ‘122’ iron-based superconductors) and the double-layer TlCu4Se3 suggest a lack of Fermi-level spectral weight that is needed to drive a magnetic or superconducting instability. However, for multiple structural layers with Fe, there is much greater likelihood for magnetism and superconductivity.

Evolution of superconducting gap anisotropy in hole‐doped 122 iron pnictides

AbstractMotivated by recent experimental findings, we investigate the evolution of the superconducting gap anisotropy in 122 iron pnictides as a function of hole doping. Employing both a functional and a weak coupling renormalization group approach (FRG and WRG), we analyze the Fermi surface instabilities of an effective 122 model band structure at different hole dopings x, and derive the gap anisotropy from the leading superconducting instability. In the transition regime from collinear magnetism to ‐wave, where strong correlations are present, we employ FRG to identify a non‐monotonous change of the gap anisotropy in qualitative agreement with new experimental findings. From the WRG, which is asymptotically exact in the weak coupling limit, we find an ‐wave to d‐wave transition as a function of hole doping, complementing previous findings from FRG [Thomale et al., Phys. Rev. Lett. 107, 117001 (2011)]. The gap anisotropy of the ‐wave monotonously increases towards the transition to d‐wave as a function of x.

Superconductivity in Pd-intercalated charge-density-wave rare earth poly-tellurides RETen

Charge density waves (CDWs) are periodic modulations of the conduction electron density in solids, which are generally considered to remove electrons from the Fermi level, and thus preclude a superconducting state. However, in a variety of CDW materials, such as the prototypical transition metal chalcogenides, superconductivity has also been observed at very low temperature (Yokoya et al 2001 Science 294 2518; Morosan et al 2006 Nat. Phys. 2 544; Kiss et al 2007 Nat. Phys. 3 720), in which, although the two electronic correlated states are believed to occur in different parts of Fermi surface sheets derived mainly from chalcogen p-states and transition metal d-states, the nature of the relationship between them has not yet been unambiguously determined. Here we report the discovery of superconductivity in Pd-intercalated RETen (RE = rare earth; n = 2.5, 3) CDW systems, in which the chalcogen layers alone are responsible for both superconductivity and CDW instability. Our finding could provide an ideal model system for comprehensive study of the interplay between CDW and superconductivity due to the remarkable simplicity of the electronic structure of Te planes.

Normal state incoherent pseudogap in FeSe superconductor

The normal state of Iron chalcogenide superconductors show a range of unconventional features. Bad-metallic resistivity and proximity to insulating state manifest themselves in spectral and transport responses. In particular, obervation of low-energy pseudogap feature in the normal state raises the issue of the nature of processes underpinning its emergence as well as its relation to unconventional superconductivity. Here, using the LDA+DMFT method, we show how correlation-induced orbital-selective pseudogap-like physics underpin these incoherent features in stoichimetric and electron-doped FeSe superconductor. We discuss the pseudogap regime microscopically, along with implications for the superconductive instability.

Topological superconducting phases from inversion symmetry breaking order in spin-orbit-coupled systems

We analyze the superconducting instabilities in the vicinity of the quantum-critical point of an inversion symmetry breaking order. We first show that the fluctuations of the inversion symmetry breaking order lead to two degenerate superconducting (SC) instabilities, one in the $s$-wave channel, and the other in a time-reversal invariant odd-parity pairing channel (the simplest case being the same as the of $^3$He-B phase). Remarkably, we find that unlike many well-known examples, the selection of the pairing symmetry of the condensate is independent of the momentum-space structure of the collective mode that mediates the pairing interaction. We found that this degeneracy is a result of the existence of a conserved fermionic helicity, $\chi$, and the two degenerate channels correspond to even and odd combinations of SC order parameters with $\chi=\pm1$. As a result, the system has an enlarged symmetry $U(1)\times U(1)$, with each $U(1)\times U(1)$ corresponding to one value of the helicity $\chi$. Because of the enlarged symmetry, this system admits exotic topological defects such as a fractional quantum vortex, which we show has a Majorana zero mode bound at its core. We discuss how the enlarged symmetry can be lifted by small perturbations, such as the Coulomb interaction or Fermi surface splitting in the presence of broken inversion symmetry, and we show that the resulting superconducting state can be topological or trivial depending on parameters. The $U(1)\times U(1)$ symmetry is restored at the phase boundary between the topological and trivial SC states, and allows for a transition between topologically distinct SC phases without the vanishing of the order parameter. We present a global phase diagram of the superconducting states and discuss possible experimental implications.

Weyl and Dirac loop superconductors

We study three dimensional systems where the parent metallic state contains a loop of Weyl or Dirac points. We introduce the minimal $\vec{k} \cdot \vec{p}$ Hamiltonian , and discuss its symmetries. Guided by this symmetry analysis, we classify the superconducting instabilities that may arise. For a doped Weyl loop material, we argue that - independent of microscopic details - the leading superconducting instability should be to a fully gapped chiral superconductor in three dimensions- an unusual state made possible only by the non-trivial topology of the Fermi surface. This state - which we dub the `meron superconductor' - is neither fully topological nor fully trivial. Meanwhile, at perfect compensation additional states are possible (including some that are fully topological), but the leading instability depends on microscopic details. We discuss the influence of disorder on pairing. In the presence of a spin degeneracy (`Dirac loops') still more complex superconducting states can arise, including a `skyrmion' superconductor with topological properties similar to superfluid He III-B, which additionally breaks lattice rotation symmetry and exhibits nematic order.

Superconductivity in transition metals.

A qualitative account of the occurrence and magnitude of superconductivity in the transition metals is presented, with a primary emphasis on elements of the first row. Correlations of the important parameters of the Bardeen-Cooper-Schrieffer theory of superconductivity are highlighted with respect to the number of d-shell electrons per atom of the transition elements. The relation between the systematics of superconductivity in the transition metals and the periodic table high-lights the importance of short-range or chemical bonding on the remarkable natural phenomenon of superconductivity in the chemical elements. A relationship between superconductivity and lattice instability appears naturally as a balance and competition between localized covalent bonding and so-called broken covalency, which favours d-electron delocalization and superconductivity. In this manner, the systematics of superconductivity and various other physical properties of the transition elements are related and unified.