Two-band Superconductor Research Articles

Thermal Conductivity of the Iron-Based Superconductor FeSe: Nodeless Gap with a Strong Two-Band Character.

The thermal conductivity κ of the iron-based superconductor FeSe was measured at temperatures down to 75mK in magnetic fields up to 17T. In a zero magnetic field, the electronic residual linear term in the T=0 K limit, κ_{0}/T, is vanishingly small. The application of a magnetic field B causes an exponential increase in κ_{0}/T initially. Those two observations show that there are no zero-energy quasiparticles that carry heat and therefore no nodes in the superconducting gap of FeSe. The full field dependence of κ_{0}/T has the classic two-step shape of a two-band superconductor: a first rise at very low field, with a characteristic field B^{⋆}≪B_{c2}, and then a second rise up to the upper critical field B_{c2}. This shows that the superconducting gap is very small (but finite) on one of the pockets in the Fermi surface of FeSe. We estimate that the minimum value of the gap, Δ_{min}, is an order of magnitude smaller than the maximum value, Δ_{max}.

Theoretical study on the two-band degenerate-gaps superconductors: Application to SrPt3P

We study the magnetic properties of two-band degenerate-gaps superconductors with two-band isotropic Ginzburg–Landau theory. The exact solutions of upper critical field and London penetration depth are obtained, and the calculations reproduce the experimental data of the recently observed superconducting crystal SrPt3P in a broad temperature range. It directly underlies that SrPt3P is a multi-band superconductor with equal gaps in two Fermi surface sheets.

Coupling of Higgs and Leggett modes in non-equilibrium superconductors.

In equilibrium systems amplitude and phase collective modes are decoupled, as they are mutually orthogonal excitations. The direct detection of these Higgs and Leggett collective modes by linear-response measurements is not possible, because they do not couple directly to the electromagnetic field. In this work, using numerical exact simulations we show for the case of two-gap superconductors, that optical pump–probe experiments excite both Higgs and Leggett modes out of equilibrium. We find that this non-adiabatic excitation process introduces a strong interaction between the collective modes, which is absent in equilibrium. Moreover, we propose a type of pump–probe experiment, which allows to probe and coherently control the Higgs and Leggett modes, and thus the order parameter directly. These findings go beyond two-band superconductors and apply to general collective modes in quantum materials.

Vortex in holographic two-band superfluid/superconductor

We construct numerically static vortex solutions in a holographic model of two-band superconductor with an interband Josephson coupling in both the superfluid and superconductor regime. We investigate the effects of the interband coupling on the order parameter of each superconducting band in the vortex solution, and we find that it is different for each of the two bands. We compute also the free energy, critical magnetic field, magnetic penetration length and coherence lengths for the two bands, and we study their dependence on the interband coupling and temperature. Interestingly, we find that the coherence lengths of the two bands are close to identical.

Fluctuation diamagnetism in two-band superconductors

Anomalously large fluctuation diamagnetism around the superconducting critical temperature has been recently observed on iron selenide (FeSe) [S. Kasahara et al., unpublished]. This indicates that superconducting fluctuations (SCFs) play a more significant role in FeSe, which supposedly has two-band structure, than in the familiar single-band superconductors. Motivated by the data in FeSe, SCF-induced diamagnetism is examined in a two-band system, on the basis of a phenomenological approach with a Ginzburg-Landau functional. The obtained results indicate that the SCF-induced diamagnetism may be more enhanced than that in a single-band system due to the existence of two distinct fluctuation modes. Such enhancement of diamagnetism unique to a two-band system seems consistent with the large diamagnetism observed on FeSe, though still far from a quantitative agreement.

Granular superconductor in a honeycomb lattice as a realization of bosonic Dirac material

We examine the low energy effective theory of phase oscillations in a two-dimensional granular superconducting sheet where the grains are arranged in honeycomb lattice structure. Using the example of graphene we present the evidence for the engineered Dirac nodes in the bosonic excitations: the spectra of the collective bosonic modes cross at the K and K points in the Brillouin zone and form Dirac nodes. We show how two different types of collective phase oscillations are obtained and that they are analogous to the Leggett and the Bogoliubov-Anderson-Gorkov modes in a two-band superconductor. We show that the Dirac node is preserved in the presence of an inter-grain interaction, despite induced changes of the qualitative features of the two collective modes. Finally, breaking the sublattice symmetry by choosing different on-site potentials for the two sublattices leads to a gap opening near the Dirac node, in analogy with Fermionic Dirac materials. Dirac node dispersion of bosonic excitations is thus expanding the discussion of the conventional Dirac cone excitations to the case of bosons. We call this case as a representative of Bosonic Dirac Materials (BDM), similar to the case of Fermionic Dirac materials extensively discussed in the literature.

Effective Ginzburg–Landau free energy functional for multi-band isotropic superconductors

It has been shown that interband mixing of gradients of two order parameters (drag effect) in an isotropic bulk two-band superconductor plays important role – such a quantity of the intergradients coupling exists that the two-band superconductor is characterized with a single coherence length and a single Ginzburg–Landau (GL) parameter. Other quantities or neglecting of the drag effect lead to existence of two coherence lengths and dynamical instability due to violation of the phase relations between the order parameters. Thus so-called type-1.5 superconductors are impossible. An approximate method for solving of set of GL equations for a multi-band superconductor has been developed: using the result about the drag effect it has been shown that the free-energy functional for a multi-band superconductor can be reduced to the GL functional for an effective single-band superconductor.

Two-Band Calculations on the Superconducting Property of SrPt $$_{2}\mathrm{As}_{2}$$ 2 As 2

Recently, electronic specific heat experiments suggest that SrPt\(_{2}\mathrm{As}_{2}\) has two superconducting energy gaps. We have therefore investigated the temperature and angular dependence of the upper critical field and the critical velocity of Cooper pairs for superconductor SrPt\(_{2}\mathrm{As}_{2}\) based on the two-band Ginzburg–Landau theory. The theoretical result for the temperature dependence of the upper critical field fits the experimental data very well over a broad temperature range. Contrary to the two-band superconductor Lu\(_{2}\mathrm{Fe}_{3}\mathrm{Si}_{5}\), both the upper critical field and the reduced critical velocity of Cooper pairs increase as the angle increases.

Pauli limiting and metastability regions of superconducting graphene and intercalated graphite superconductors

We present a study of metastability regions in the in-plane magnetic field versus temperature phase diagram of graphene and intercalated graphite superconductors. Due to the vanishing density of states, undoped graphene requires a finite BCS interaction ${V}_{c}$ to become superconducting (any finite doping drives this critical value to zero). Above ${V}_{c}$, superconducting graphene under in-plane magnetic field displays the conventional low temperature first-order transition (FOT) to the normal phase, but the width of the associated metastability region (normalized to the zero-temperature critical field) vanishes when doping goes to zero and the interaction approaches ${V}_{c}$. In the case of intercalated graphite superconductors, modeled as two-dimensional two-band superconductors (a graphene-like band and a metallic interlayer band), a critical graphene intraband interaction is required for the appearance of a second metastability region in the superconducting region of the phase diagram. The width of this metastability region also goes to zero as the graphene intraband interaction approaches, from above, its critical value and the metastability region vanishes at the zero-temperature supercooling field associated with the metallic interlayer band. Slightly above this critical value, the low-temperature FOT line bifurcates at an intermediate temperature into a FOT line and a second-order transition line.

Theoretical analysis of the upper critical field of two-band superconductor LaNiC2

LaNiC2 is one of ternary RNiC2 compounds, where R is a rare earth or Y. Its space group is Amm2. the symmetry along the c-axis of the crystal structure lacks inversion symmetry along the c-axis. In 2009, Hillier et al. performed the muon spin relaxation experiment (upSR) which implied that time-reversal symmetry is broken in LaNiC2. As a weak correlation noncentrosymmetric superconductor, LaNiC2 has attracted wide research interest in recent years. Though a lot of theoretical and experimental studies have been carried out, the order parameter of this compound remains highly controversial. The measurements of specific heat and nuclear quadrupole relaxation suggest that LaNiC2 is normally BCS-like, which is further supported by theoretical calculations. But recently another study showed that the London penetration depth depends on T2 below 0.4 Tc indicative of nodes in the energy gap. Evidence of possible nodal superconductivity can also be inferred from the early measurements of specific heat given by Lee et al. However, the experimental results obtained by Chen et al. supported the existence of two-gap superconductivity in LaNiC2.Based on the above case, the two-band Ginzburg-Landau theory is used to study the temperature dependence of the upper critical field for the superconductor LaNiC2 in this paper. Choosing the Ginzburg-Landau theory for calculating the upper critical field is just because Ginzburg-Landau theoretical model is simple, easy to understand, low-calculation, and the clear physical meanings of the parameters. The theoretical results in this paper accord with the experimental data very well in the whole temperature range. The curve of Hc2 (T) has an obvious positive curvature near the critical temperature, which is typical feature of multi-gap superconductor. Therefore, our results show strong evidence that two-gap scenario is better to account for the superconductivity of LaNiC2, consistent with the results of Chen Jian et al. The influences of two different energy bands on the upper critical field are also studied. It is found that the relatively small coherent length has a grester influence on the upper critical magnetic field of LaNiC2. So if we want to improve the upper critical field of LaNiC2, reducing the relatively small coherence length can be achieved in theory.

Odd-frequency Cooper pairs in two-band superconductors and their magnetic response

We discuss odd-frequency Cooper pairs appearing in two-band superconductors by solving the Gor'kov equation analytically. We introduce the equal-time $s$-wave pair potentials as realized in MgB$_2$ and iron pnictides. Although the order parameter symmetry is conventional, the band degree of freedom enriches the symmetry variety of pairing correlations. The hybridization and the asymmetry between the two conduction bands induce odd-frequency pairs as a subdominant pairing correlation in the uniform ground state. To study the magnetic response of odd-frequency Cooper pairs, we analyze the Meissner kernel represented by the Gor'kov Green function. In contrast to the even-frequency pairs linked to the pair potential, the induced odd-frequency Cooper pairs indicate a paramagnetic property. We also discuss the relation between the amplitude of the odd-frequency pairing correlation and the stability of superconducting states in terms of the self-consistent equation for the pair potential.

Vortex in Holographic Two-band Superconductor

A single static vortex in a holographic two-band superconductor is constructed. We investigate the effect of the interband coupling to the condensate profile. We estimate the first critical magnetic field, and compute characteristic lengths like penetration and coherence lengths and conclude both bands in our superconductor behave type II.

Josephson systems based on ballistic point contacts between single-band and multi-band superconductors

The Josephson effect in ballistic point contacts between single-band and multi-band superconductors was investigated. It was found that in the case of Josephson junctions formed by a single-band and an s±-wave two-band superconductor as well as by a single-band and a three-band superconductor the junctions become frustrated, showing the φ-contact properties. Depending on the ground state of a three-band superconductor with time-reversal symmetry breaking, the Josephson junction can have from one to three energy minima, some of which can be locally stable. We also study the behavior of a dc SQUID based on the Josephson junctions between single-band and multi-band superconductors. Some features on the dependences of the critical current and the total magnetic flux on the applied flux of a dc SQUID based on the Josephson point contacts between a single-band superconductor and an s±-wave superconductor, three-band superconductor with broken time-reversal symmetry and three-band superconductor without broken time-reversal symmetry as compared to the conventional dc SQUIDs based on single-band superconductors were found. The results can be used as an experimental tool to detect the existence of multi-band structure and time-reversal symmetry breaking.

Effect of interband interactions on the pressure dependence on transition temperature of MgB2

A two-band BCS model with interactions, both phonon and non-phonon induced interactions, were employed to investigate the pressure dependence on superconducting transition temperature of two-band superconductor. We derived the transition temperature and its pressure dependence within Bogoliubov--Valatin formalism for magnesium diboride superconductor. We examined the influence of interband interactions on transition temperature at varying pressure and analyzed the relevance of this calculation in magnesium diboride, MgB2.

Fluctuation conductivity in two-band superconductor SmFeAsO0.8F0.2

Abstract In this study we have calculated the fluctuation conductivity near critical temperature of SmFeAsO0.8F0.2 superconductor using two-band Ginzburg-Landau theory. It was illustrated that in the absence of external magnetic field, the two-band model reduced to a single effective band theory with modified temperature dependences. The calculations revealed three-dimensional character of fluctuations of conductivity in the new Fe-based superconductor SmFeAsO0.8F0.2. It has been shown that such a model is in good agreement with experimental data for this compound.

Ab initiotheory of magnetic-field-induced odd-frequency two-band superconductivity inMgB2

We develop the anisotropic Eliashberg framework for superconductivity in the presence of an applied magnetic field. Using as input the ab initio calculated electron and phonon band structures and electron-phonon coupling, we solve self-consistently the anisotropic Eliashberg equations for the archetypal superconductor ${\mathrm{MgB}}_{2}$. We find two self-consistent solutions, time-even two-band superconductivity, as well as unconventional time-odd $s$-wave spin triplet two-band superconductivity emerging with applied field. We provide the full momentum, frequency, and spin-resolved dependence and magnetic field-temperature phase diagrams of the time-even and time-odd superconducting pair amplitudes and predict fingerprints of this novel odd-frequency state in tunneling experiments.

Analysis of experimental data for two-band superconductors at T ≈ Tc using the GL theory in the presence of a self-consistent vortex line

We study the two-component Ginzburg–Landau (GL) theory, in the presence of a self-consistent vortex line, to obtain the penetration depth (λ) and the effective healing length (ξ), in the asymptotic limit r → ∞. All these parameters versus T/Tc are analyzed for the materials MgB 2, V 3 Si and LiFeAs in the interval 0.88 ≤ T/Tc ≤ 1.0, where the GL theory is assumed to be valid. We find that κ ≡ λ/ξ, which is another parameter not related to the GL parameter, is T-independent for V 3 Si and LiFeAs , while is T-dependent for the compound MgB 2. This result suggests that even though all these three materials display two-gap superconductivity overall, near Tc superconductivity in V 3 Si and LiFeAs seems to be different from the one in MgB 2. The use of this parameter, κ, as a new way to "study" the superconducting materials, under the presence of a single vortex, is valid for 0.88Tc≲ T ≤ Tc, namely, in the GL formalism.

Possible Field–Temperature Phase Diagrams of Two-Band Superconductors with Paramagnetic Pair-Breaking

Possible field-temperature superconducting (SC) phase diagrams in two-band quasi-two-dimensional materials with a strong paramagnetic pair-breaking (PPB) are considered theoretically. Attention is paid to the case under a magnetic field $perpendicular$ to the SC layers and to essential differences from the counterpart in the ordinary single-band material. It is found by examining the $H_{c2}(T)$ curve and the vortex lattices to be realized close to $H_{c2}$ that a PPB-induced SC phase with a spatial modulation parallel to the field tends to occur more easily than in the single-band case, and that a crisscrossing vortex lattice proposed previously can occur in place of the conventional Fulde-Ferrell-Larkin-Ovchinnikov state within a parameter range. The relevance of the obtained results to FeSe and other iron-based superconductors is discussed.

Current-induced massless mode of the interband phase difference in two-band superconductors

There is a current-induced massless mode of an interband phase difference in two-band superconductors. For a thin wire, the externally applied current always invokes a finite interband phase difference when the end of the wire is terminated by a natural boundary condition, i.e., where the total current is specified but the other parameters are left as free and a finite interband phase difference is allowed. This condition can be realized by the normal state region formed by the shrinking of a cross section of the wire where the critical current density is lower than that of the other region of the wire. The interband interaction in the wire cannot completely prevent the emergence of the interband phase difference, though it reduces it somewhat. Instead, boundary conditions determine the presence of the interband phase difference. By reverting the normal state into the superconducting state at the shrunken region by decreasing the current, we may trap a rotation of integral multiples of 2π radians of the interband phase difference in the wire. After switching off the current, this rotation of integral multiples of 2π radians, which continuously spreads over the whole wire, is separated into several interband phase difference solitons (i-solitons), where one i-soliton locally generates a 2π interband phase difference.

Finite temperature effective field theory and two-band superfluidity in Fermi gases

We develop a description of fermionic superfluids in terms of an effective field theory for the pairing order parameter. Our effective field theory improves on the existing Ginzburg-Landau theory for superfluid Fermi gases in that it is not restricted to temperatures close to the critical temperature. This is achieved by taking into account long-range fluctuations to all orders. The results of the present effective field theory compare well with the results obtained in the framework of the Bogoliubov-de Gennes method. The advantage of an effective field theory over Bogoliubov-de Gennes calculations is that much less computation time is required. In the second part of the paper, we extend the effective field theory to the case of a two-band superfluid. The present theory allows us to reveal the presence of two healing lengths in the two-band superfluids, to analyze the finite-temperature vortex structure in the BEC-BCS crossover, and to obtain the ground state parameters and spectra of collective excitations. For the Leggett mode our treatment provides an interpretation of the observation of this mode in two-band superconductors.