Interband Coupling Research Articles

In-plane magnetic field versus temperature phase diagram of a quasi-2D frustrated multiband superconductor

Motivated by the recent discovery of iron-based superconductors, with high critical temperatures and multiple bands crossing the Fermi level, we address the conditions for the presence of chiral superconducting phases configurations in the in-plane magnetic field versus temperature phase diagram of a quasi-2D frustrated three-band superconductor. Due to Zeeman splitting, the coupled superconducting gap equations present a complex set of solutions. For weak interband couplings, chiral configurations are only attained in a narrow strip of the in-plane magnetic field versus temperature phase diagram. This strip of chiral states becomes narrower and disappears at low temperatures, giving way to a first-order transition between non-chiral superconducting states. For stronger interband couplings, the chiral strip is much broader, if the interband couplings are approximately equal; otherwise, the chiral region is expected to be completely absent of the phase diagram.

Publisher's Note: High-temperature superconductivity stabilized by electron-hole interband coupling in collapsed tetragonal phase ofKFe2As2under high pressure [Phys. Rev. B91, 060508(R) (2015)

Publisher's Note: High-temperature superconductivity stabilized by electron-hole interband coupling in collapsed tetragonal phase ofKFe2As2under high pressure [Phys. Rev. B91, 060508(R) (2015)

Tunable orbital susceptibility in α-T3 tight-binding models

We study the importance of interband effects on the orbital susceptibility of three bands α-T3 tight-binding models. The particularity of these models is that the coupling between the three energy bands (which is encoded in the wavefunctions properties) can be tuned (by a parameter α) without any modification of the energy spectrum. Using the gauge-invariant perturbative formalism that we have recently developped[1], we obtain a generic formula of the orbital susceptibility of α-T3 tight-binding models. Considering then three characteristic examples that exhibit either Dirac, semi-Dirac or quadratic band touching, we show that by varying the parameter a and thus the wavefunctions interband couplings, it is possible to drive a transition from a diamagnetic to a paramagnetic peak of the orbital susceptibility at the band touching. In the presence of a gap separating the dispersive bands, we show that the susceptibility inside the gap exhibits a similar dia to paramagnetic transition.

Orbital magnetism in coupled-bands models

We develop a gauge-independent perturbation theory for the grand potential of itinerant electrons in two-dimensional tight-binding models in the presence of a perpendicular magnetic field. At first order in the field, we recover the result of the so-called {\it modern theory of orbital magnetization} and, at second order, deduce a new general formula for the orbital susceptibility. In the special case of two coupled bands, we relate the susceptibility to geometrical quantities such as the Berry curvature. Our results are applied to several two-band -- either gapless or gapped -- systems. We point out some surprising features in the orbital susceptibility -- such as in-gap diamagnetism or parabolic band edge paramagnetism -- coming from interband coupling. From that we draw general conclusions on the orbital magnetism of itinerant electrons in multi-band tight-binding models.

Multi-Phase Physics of Multi-Condensate Superconductivity

Multi-gap superconductors exhibit interesting properties. In N-gap superconductors, the U(1)N phase invariance is spontaneously broken. When N is greater than 2, N ≥ 3, several interesting phenomena will emerge due to the multi-band effect. Among them, the time-reversal symmetry breaking and the emergence of massless modes are significant. We consider a multi-band model with inter-band frustrated-Josephson couplings for general N. The conditions for the time-reversal symmetry breaking and the existence of massless modes are reduced to a simple form for the Josephson couplings in a separable form which we propose in this paper.

Wannier-Stark states of graphene in strong electric field

We find theoretically the energy spectrum of a graphene monolayer in a strong constant electric field using a tight-binding model. Within a single band, we find quantized equidistant energy levels (Wannier-Stark ladder), separated by the Bloch frequency. Singular interband coupling results in mixing of the states of different bands and anticrossing of corresponding levels, which is described analytically near Dirac points and is related to the Pancharatnam-Berry phase. The rate of interband tunneling, which is proportional to the anticrossing gaps in the spectrum, is only inversely proportional to the tunneling distance, in a sharp contrast to conventional solids where this dependence is exponential. This singularity will have major consequences for graphene behavior in strong ultrafast optical fields, in particular, leading to nonadiabaticity of electron excitation dynamics.

Interplay between interband coupling and ferromagnetism in iron pnictide superconductor/ferromagnet/iron pnictide superconductor junctions

An extended eight-component Bogoliubov-de Gennes equation is applied to study the Josephson effect between iron-based superconductors (SCs) with s±-wave pairing symmetry, separated by an ferromagnet (FM). The feature of damped oscillations of critical Josephson current as a function of FM thickness, the split of the peaks induced by the interband coupling is much different from that for the junction with the s±-wave SCs replaced by s++-wave ones. In particular, a 0−π transition as a function of interband coupling strength α is found to always exhibit with the corresponding dip shifting toward the larger α due to enhancing the spin polarization in the FM, while there exits no 0−π transition for the SC with s++-wave pairing symmetry. The two features can be used to identify the pairing symmetry in the iron pnictide SC different from the s++-wave one in MgB2. Experimentally, by adjusting the doping level in the s±-wave SCs, one can vary α.

Tunable optical properties of multilayer black phosphorus thin films

Black phosphorus thin films might offer attractive alternatives to narrow gap compound semiconductors for optoelectronics across mid- to near-infrared frequencies. In this work, we calculate the optical conductivity tensor of multilayer black phosphorus thin films using the Kubo formula within an effective low-energy Hamiltonian. The optical absorption spectra of multilayer black phosphorus are shown to vary sensitively with thickness, doping, and light polarization. In conjunction with experimental spectra obtained from infrared absorption spectroscopy, we also discuss the role of interband coupling and disorder on the observed anisotropic absorption spectra.

The Franz–Keldysh effect revisited: Electroabsorption including interband coupling and excitonic effects

We study the linear optical absorption of bulk semiconductors in the presence of a uniform and constant (dc) electric field with an approach suitable for including excitonic effects while working with many-band models. The absorption coefficient is calculated from the time evolution of the interband polarization excited by an optical pulse. We apply the formalism to a numerical calculation for GaAs using a 14-band k·p model, which allows us to properly include interband coupling, and the exchange self-energy to account for the excitonic effects due to the electron–hole interaction. The Coulomb interaction enhances the features of the absorption coefficient captured by the k·p model; the enhancement depends on the strength of the dc field and the polarization of the optical field. With respect to the polarization dependence, we find that the anisotropy described by the independent particle approximation can be modified significantly by the Coulomb interaction.

Beyond the standard model of Ginzburg–Landau theory: multiband superconductors

The recently discovered multiband superconductors have created a new class of novel superconductors. In these materials multiple superconducting gaps arise due to the formation of Cooper pairs on different sheets of the Fermi surfaces. An important feature of these superconductors is the interband couplings, which not only change the individual gap properties, but also create new collective modes. Here we investigate the effect of the interband couplings in the Ginzburg–Landau theory. We produce a general τ(2n + 1)/2 expansion (τ = 1 − T/Tc) and show that this expansion has unexpected behaviour for n ⩾ 2. This point emphasises the weaker validity of the GL theory for lower temperatures and gives credence to the existence of hidden criticality near the critical temperature of the uncoupled subdominant band. We apply this theory to a range of material parameters fitted to experimental measurements and find that for some cases the theory performs very well at all temperatures, but for other materials the range of applicability can be very limited.

Spin-Fluctuation-Driven Superconductivity in the Kondo Lattice Model

Superconductivity in solids usually arises due to the generation of an attractive effective interaction between fermions close to the Fermi energy by some bosonic fluctuations. In the conventional theory, these are phonons, but in correlated electron systems like the cuprates or heavy fermions, one believes that the relevant bosonic degrees of freedom are the spin fluctuations. In this context, one usually argues that standard s-wave superconductivity cannot be formed as these spin fluctuations in general lead to a repulsive local interaction. Recently, we observed s-wave superconductivity in the Kondo lattice model using the dynamical mean-field approach. We can indeed show that this superconducting (SC) solution is due to local spin fluctuations arising from the Kondo effect. The reason for these fluctuations mediating an effective attractive interaction lies in the special properties of the heavy electron ground state, i.e., the formation of hybridized bands. Using a simple model, we can show that it is indeed an interband coupling that is largely responsible for the observed SC state. Such an observation is possibly rather interesting also concerning the situation in the pnictide superconductors.

Exporting superconductivity across the gap: Proximity effect for semiconductor valence-band states due to contact with a simple-metal superconductor

The proximity effect refers to the phenomenon whereby superconducting properties are induced in a normal conductor that is in contact with an intrinsically superconducting material. In particular, the combination of nano-structured semiconductors with bulk superconductors is of interest because these systems can host unconventional electronic excitations such as Majorana fermions when the semiconductor's charge carriers are subject to a large spin-orbit coupling. The latter requirement generally favors the use of hole-doped semiconductors. On the other hand, basic symmetry considerations imply that states from typical simple-metal superconductors will predominantly couple to a semiconductor's conduction-band states and, therefore, in the first instance generate a proximity effect for band electrons rather than holes. In this article, we show how the superconducting correlations in the conduction band are transferred also to hole states in the valence band by virtue of inter-band coupling. A general theory of the superconducting proximity effect for bulk and low-dimensional hole systems is presented. The interplay of inter-band coupling and quantum confinement is found to result in unusual wave-vector dependencies of the induced superconducting gap parameters. One particularly appealing consequence is the density tunability of the proximity effect in hole quantum wells and nanowires, which creates new possibilities for manipulating the transition to nontrivial topological phases in these systems.

Twofold Andreev reflections and coherent transport in ferromagnetic semiconductor/d-wave superconductor/ferromagnetic semiconductor double tunneling junctions

Coherent transport in a ferromagnetic semiconductor (FS)/d-wave superconductor (SC)/FS structure with {110} interfaces is studied by extending Bogoliubov-de Gennes equation into eight components, in which the interband coupling of heavy and light hole bands in the FS, the strengths of potential scattering at the interfaces, and the mismatches in the effective mass and Fermi vector between the FS and SC are taken into account. Twofold Andreev reflections exist due to the existence of two bands in the FS, in which the incident hole and the two Andreev-reflected electrons, belonging to the different spin subbands, form twofold spin-singlet pairing states near the FS/SC interface. It is shown that due to the interplay of the SC with unconventional d-wave pairing symmetry and FS, the differential conductance and tunneling magnetoresistance exhibit an abundant dependence on not only the interband coupling in the FS but also the strengths of potential scattering at the interfaces. More importantly, the properties are found to be quite different from those in the FS/s-wave SC/FS structure with conventional pairing symmetry for the SC.

Josephson effects in three-band superconductors with broken time-reversal symmetry

In superconductors with three or more bands, time-reversal symmetry (TRS) may be broken in the presence of repulsive interband couplings, resulting in a pair of degenerate states characterized by opposite chiralities. We consider a Josephson junction between a three-band superconductor with broken TRS and a single-band superconductor. Phenomena such as asymmetric critical currents, subharmonic Shapiro steps, and symmetric Fraunhhofer patterns are revealed theoretically. Existing experimental results are discussed in terms of the present work.

Doping influence on Sm1 − x Th x OFeAs superconducting properties: Observation of the effect of intrinsic multiple Andreev reflections and determination of the superconducting parameters

We studied SNS and S-N-S-N-...-S contacts (where S is a superconductor and N is a normal metal) formed by “break-junction” technique in polycrystalline Sm1 − xThxOFeAs superconductor samples with critical temperatures TC = 34–45 K. In such contacts (intrinsic) multiple Andreev reflections effects were observed. Using spectroscopies based on these effects, we detected two independent bulk order parameters and determined their magnitudes. Theoretical analysis of the large and the small gap temperature dependences revealed superconducting properties of Sm1 − xThxOFeAs to be driven by intraband coupling, and \(\sqrt {V_{11} V_{22} } /V_{12} \approx 14\) (where Vij are the electron-boson interaction matrix elements), whereas the ratio between density of states for the bands with the small and the large gap, N2/N1, correspondingly, was roughly of an order. We estimated “solo” BCS-ratio values in a hypothetic case of zero interband coupling (Vi ≠ j = 0) for each condensate as 2ΔL, S/kBTCL,S ≤ 4.5. The values are constant within the range of critical temperatures studied, and correspond to a case of strong intraband electron-phonon coupling.

Direct measurement of the temperature dependence of the magnetic penetration depth in Ba(Fe1−xNix)2As2 superconductors

The temperature dependence of the in-plane magnetic penetration depth λab of Ba(Fe1−xNix)2As2 single crystals is determined directly from the shielding magnetic susceptibility, measured in the Meissner region with the field parallel to the ab layers. The doping levels studied cover the underdoped, optimally doped and overdoped regimes. At temperatures below 0.5Tc a well-defined power-law behavior λab(T) − λab(0) = ATn (with n ≈ 2.5) is observed. At lower temperatures (T < 0.3Tc) the data are still consistent with n = 2 and , as predicted by the strong pair-breaking scenario proposed by Gordon et al (2010 Phys. Rev. B 81, 180501(R)). The temperature dependence of the superfluid density presents a marked positive curvature just below Tc, which is a sign of two-gap superconductivity. The analysis of ρs(T) in terms of a two-gap model allowed estimation of parameters like the in-band and inter-band couplings, the relative weight of each band, and their dependence on the doping level. A comparison with ρs(T) data obtained by using other techniques in compounds with a similar composition is also presented.

Controllable 0 − π transition in iron pnictide superconductor junctions with a spacer of strong ferromagnet

We investigate the control of 0−π transition in Josephson junctions consisting of a highly spin-polarized ferromagnet coupled to two iron pnictide superconductors (SCs). It is shown that, a 0−π transition as a function of interband coupling strength is always exhibited, which can be experimentally used to discriminate the s±-wave pairing symmetry in the iron pnictide SCs from the s++-wave one in MgB2. By tuning the doping level in the s±-wave SCs, one can vary the interband coupling strength so as to obtain the controllable 0−π transition. This device may be realized with current technologies and has practical use in Cooper pair spintronics and quantum information.

H–T Phase Diagram of Multi-component Superconductors with Frustrated Inter-component Couplings

Multi-band superconductors in which frustrated inter-band couplings yield a time-reversal-symmetry breaking (TRSB) state are investigated. Stability condition for the TRSB state are derived based on the Bardeen-Cooper-Schrieffer (BCS) theory. With the time-dependent Ginzburg-Landau (GL) method, vortex states are investigated first at the vicinity of critical temperature $T_\text{c}$ where the GL theory is valid, and the results are extended to compose the $H$-$T$ phase diagram. When material parameters satisfy the condition that the nucleation field is slightly larger than the thermodynamic field ($H_\text{n} \gtrsim H_\text{tc}$) derived in a previous work (X. Hu and Z. Wang, Phys. Rev. B 85, 064516 (2012)), an unconventional intermediate state characterized by clustering vortices appears. Calculation of interface energy reveals that the clustering vortices are associated with positive interface energy.

Multiple andreev reflections spectroscopy of superconducting LiFeAs single crystals: Anisotropy and temperature behavior of the order parameters

The superconducting state of LiFeAs single crystals with the maximum critical temperature T c ≈ 17 K in the 111 family has been studied in detail by multiple Andreev reflections (MAR) spectroscopy implemented by the break-junction technique. The three superconducting gaps, ΔΓ = 5.1–6.5 meV, ΔL = 3.8–4.8 meV, and ΔS = 0.9–1.9 meV (at T ≪ T c), as well as their temperature dependences, have been directly determined in a tunneling experiment with these samples. The anisotropy degrees of the order parameters in the k space have been estimated as <8, ∼12, and ∼20%, respectively. Andreev spectra have been fitted within the extended Kummel-Gunsenheimer-Nikolsky model with allowance for anisotropy. The relative electron-boson coupling constants in LiFeAs have been determined by approximating the Δ(T) dependences by the system of the two-band Moskalenko and Suhl equations. It has been shown that the densities of states in bands forming ΔΓ and ΔL are approximately the same, intraband pairing dominates in this case, and the interband coupling constants are related as λΓL ≈ λLΓ ≪ λSΓ, λSL.

Erratum: Independent-particle theory of the Franz-Keldysh effect including interband coupling: Application to calculation of electroabsorption in GaAs [Phys. Rev. B 82, 075206 (2010)

Received 29 November 2013DOI:https://doi.org/10.1103/PhysRevB.88.239906©2013 American Physical Society