Wave Pairing Symmetry Research Articles

Anderson topological superconductor

In this paper we study the phase diagram of a disordered, spin-orbit coupled superconductor with $s$-wave or $d+id$-wave pairing symmetry in symmetry class $D$. We analyze the topological phase transitions by applying three different methods which include a disorder averaged entanglement entropy, a disorder averaged real-space Chern number, and an evaluation of the momentum space Chern number in a disorder averaged effective model. We find evidence for a disorder-induced topological state. While in the clean limit there is a single phase transition from a trivial phase with a Chern number $C=4$ to a topological phase with $C=1$, in the disordered system there is an intermediate phase with $C=3$. The phase transition from the trivial $C=4$ phase into the intermediate phase with $C=3$ is seen in the real-space calculation of the Chern number. In spite of this, this phase transition is not detectable in the entanglement entropy. A second phase transition from the disorder induced $C=3$ into the $C=1$ phase is seen in all three quantities.

Transport properties of spin-triplet superconducting monolayerMoS2

The quantum transport properties of graphene and monolayer $MoS_2$ superconductor heterostructures has been of considerable importance in the recent few years. Layered nature of molybdenum disulfide permits the superconducting correlation induction. Moreover, peculiar dynamical features of monolayer $MoS_2$, such as valence band spin-splitting in the nondegenerate $K$ and $K'$ valleys originated from strong spin-orbit coupling, and considerable direct band gap can make it potentially a useful material for electronics applications. Using the Dirac-like Hamiltonian of $MoS_2$ with taking into account the related mass asymmetry and topological contributions, we investigate the effect of spin-triplet $p$-wave pairing symmetry on the superconducting excitations, resulting in Andreev reflection process and Andreev bound state in the corresponding normal-superconductor (NS) and superconductor-normal-superconductor (SNS) structures, respectively. We study how the resulting subgap conductance and Josephson current are affected by the particular symmetry of order parameter. The signature of $p_x$-wave symmetry is found to decline the subgap superconducting energy excitations and, consequently, slightly suppress the Andreev reflection in the case of $p$-doped S region. The essential dynamical parameters $\lambda$ and $\beta$ of $MoS_2$ have significant effect on the both tunneling conductance and Josephson current. Particularly, the considered $p$-wave symmetry in the superconducting bound energies may feature the zero energy states at the interfaces. The critical current oscillations as a function of length of junction are obtained in the $p$-doped S region.

Structure of vortex-bound states in spin-singlet chiral superconductors

We investigate the structure of vortex-bound states in spin-singlet chiral superconductors with ($d_{x^2-y^2} \pm i d_{xy}$)-wave and ($d_{xz} \pm id_{yz}$)-wave pairing symmetries. It is found that vortices in the ($d_{xz} \pm id_{yz}$)-wave state bind zero-energy states which are dispersionless along the vortex line, forming a doubly degenerate Majorana flat band. Vortex-bound states of ($d_{x^2-y^2} \pm i d_{xy}$)-wave superconductors, on the other hand, exist only at finite energy. Using exact diagonalization and analytical solutions of tight-binding Bogoliubov-de Gennes Hamiltonians, we compute the energy spectrum of the vortex-bound states and the local density of states around the vortex and antivortex cores. We find that the tunneling conductance peak of the vortex is considerably broader than that of the antivortex. This difference can be used as a direct signature of the chiral order parameter symmetry.

Fragile surface zero-energy flat bands in three-dimensional chiral superconductors

We study surface zero-energy flat bands in three-dimensional chiral superconductors with $p_z (p_x +ip_y)^{\nu}$-wave pairing symmetry ($\nu$ is a nonzero integer), based on topological numbers and tunneling conductance. It is shown that the surface flat bands are fragile against (i) the misorientation angle and (ii) surface Rashba spin-orbit interaction. The fragility of (i) is specific to chiral SCs, whereas that of (ii) happens for general odd-parity SCs. We demonstrate that these flat band instabilities vanish or suppress a zero-bias conductance peak in a normal/insulator/superconductor junction, which behavior is clearly different from high-$T_c$ cuprates and noncentrosymmetric superconductors. By calculating the angle resolved conductance, we also discuss a topological surface state associated with the coexistence of line and point nodes.

Tunable 0–π transition by interband coupling in iron-based superconductor Josephson junctions

An extended four-component Bogoliubov–de Gennes equation is applied to study the Josephson effect in ballistic limit between either two iron-based superconductors (SCs) or an iron-based SC and a conventional s-wave SC, separated by a normal metal. A 0–π transition as a function of interband coupling strength α is always exhibited, arising from the tuning of mixing between the two trajectories with opposite phases. The novel property can be experimentally used to discriminate the -wave pairing symmetry in the iron-based SCs from the -wave one in MgB2. The effect of interface transparency on the 0–π transition is also presented. The 0–π transition as a function of α is wholly distinct from that as a function of barrier strength or temperature in recent theories (Linder et al 2009 Phys. Rev. B 80 020503(R)). The possible experimental probe of the phase-shift effect in iron-based SC Josephson junctions is commented on as well.

Effect of single interstitial impurity in iron-based superconductors with sign-changed s-wave pairing symmetry

We employ the self-consistent Bogoliubov-de Gennes (BdG) formulation to investigate the effect of single interstitial nonmagnetic/magnetic impurity in iron-based superconductors with s ± -wave pairing symmetry. We find that both the nonmagnetic and magnetic impurities can induce bound states within the superconducting (SC) gap and a π phase shift of SC order parameter at the impurity site. However, different from the interstitial-nonmagnetic-impurity case characterized by two symmetric peaks with respect to zero energy, the interstitial magnetic one only induces single bound-state peak. In the strong scattering regime this peak can appear at the Fermi level, which has been observed in the recent scanning tunneling microscope (STM) experiment of Fe(Te,Se) superconductor with interstitial Fe impurities (Yin et al. 2015 [44]). This novel single in-gap peak feature also distinguishes the interstitial case from the substitutional one with two peaks. These results provide important information for comparing the different impurity effects in the iron-based superconductors.

Momentum dependence of the superconducting gap and in-gap states inMgB2multiband superconductor

We use tunable laser-based angle-resolved photoemission spectroscopy to study the electronic structure of the multiband superconductor ${\mathrm{MgB}}_{2}$. These results form the baseline for detailed studies of superconductivity in multiband systems. We find that the magnitude of the superconducting gap on both $\ensuremath{\sigma}$ bands follows a BCS-like variation with temperature with ${\mathrm{\ensuremath{\Delta}}}_{0}\ensuremath{\sim}7\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$. The value of the gap is isotropic within experimental uncertainty and in agreement with a pure $s$-wave pairing symmetry. We also observe in-gap states confined to ${k}_{F}$ of the $\ensuremath{\sigma}$ band that occur at some locations of the sample surface. The energy of this excitation, $\ensuremath{\sim}3$ meV, is somewhat larger than the previously reported gap on $\ensuremath{\pi}$ Fermi sheet and therefore we cannot exclude the possibility of interband scattering as its origin.

Anomalous proximity effect and theoretical design for its realization

We discuss the stability of zero-energy states appearing in a dirty normal metal attached to a superconducting thin film with Dresselhaus [110] spin-orbit coupling under the in-plane Zeeman field. The Dresselhaus superconductor preserves an additional chiral symmetry and traps more than one zero-energy state at its edges. All the zero-energy states at an edge belong to the same chirality in large Zeeman field due to the effective $p$-wave pairing symmetry. The pure chiral nature in the wave function enables the penetration of the zero-energy states into the dirty normal metal with keeping their high degree of degeneracy. By applying a theorem, we prove the the perfect Andreev reflection into the dirty normal metal at the zero-energy. This paper gives a microscopic understanding of the anomalous proximity effect.

Theory of nodal s ± -wave pairing symmetry in the Pu-based 115 superconductor family.

The spin-fluctuation mechanism of superconductivity usually results in the presence of gapless or nodal quasiparticle states in the excitation spectrum. Nodal quasiparticle states are well established in copper-oxide, and heavy-fermion superconductors, but not in iron-based superconductors. Here, we study the pairing symmetry and mechanism of a new class of plutonium-based high-Tc superconductors and predict the presence of a nodal s+− wave pairing symmetry in this family. Starting from a density-functional theory (DFT) based electronic structure calculation we predict several three-dimensional (3D) Fermi surfaces in this 115 superconductor family. We identify the dominant Fermi surface “hot-spots” in the inter-band scattering channel, which are aligned along the wavevector Q = (π, π, π), where degeneracy could induce sign-reversal of the pairing symmetry. Our calculation demonstrates that the s+− wave pairing strength is stronger than the previously thought d-wave pairing; and more importantly, this pairing state allows for the existence of nodal quasiparticles. Finally, we predict the shape of the momentum- and energy-dependent magnetic resonance spectrum for the identification of this pairing symmetry.

Dirac-fermion-induced parity mixing in superconducting topological insulators

We self-consistently study surface states of superconducting topological insulators. We clarify that, if a topologically trivial bulk $s$-wave pairing symmetry is realized, parity mixing of the pair potential near the surface is anomalously enhanced by surface Dirac fermions, opening an additional surface gap larger than the bulk one. In contrast to classical $s$-wave superconductors, the resulting surface density of state hosts an extra coherent peak at the induced gap besides a conventional peak at the bulk gap. We also find that no such extra peak appears for odd-parity superconductors with a cylindrical Fermi surface. Our calculation suggests that the simple U-shaped scanning tunneling microscope spectrum in ${\mathrm{Cu}}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ does not originate from $s$-wave superconductivity, but can be explained by odd-parity superconductivity with a cylindrical Fermi surface.

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.

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.

Vortex core properties in iron pnictides

The mechanism of unconventional superconductivity in recently discovered Fe-based superconductors has been intensively discussed. A plausible candidate is the superconducting (SC) pairing mediated by antiferromagnetic (AFM) interactions. There are two different approaches predicting the s ± pairing state, in which the SC gap shows an s -wave symmetry that changes sign between different Fermi-surface (FS) sheets. The first one is based on the itinerant spin fluctuations promoted by FS nesting, and the second is based on the local AFM exchange couplings. We apply quasiclassical Eilenberger approach to the vortex state to calculate the cutoff parameter, ξh , at different levels of impurity scattering rates and to compare results with experimental data for iron pnictides. The s ± -wave pairing symmetry is considered as a presumable state for these materials. Magnetic field dependence of ξh /ξ c 2 is found to be nonuniversal for s ± pairing: depending on the chosen parameter set it can reside both below and above analytical Ginzburg-Landau curve. It is also found that normalized ξ 2 /ξ c 2 (B/B c 2 ) dependence is increasing with pair-breaking (interband) impurity scattering, and the intraband scattering results in decreasing of the ξ 2 /ξ c 2 value. Here, ξ 2 is the vortex core size and ξ c 2 is the Ginzburg-Landau coherence length determined from the upper critical field. The ξ 2 /ξ c 2 (B/B c 2 ) curve has a minimum at low temperatures and small scattering evolving into monotonously decreasing function at strong scattering and high temperatures.

Nonmagnetic impurity resonance states as a test of superconducting pairing symmetry in CeCoIn5

We theoretically study the effect of a nonmagnetic impurity in heavy fermion superconductor CeCoIn$_{5}$ within a realistic band model and the T-matrix approximation approach. By considering two known possible pairing symmetry candidates $d_{x^{2}-y^{2}}$ and $d_{xy}$, we find that although both total density of states exhibit a similar V-shaped gaplike feature, only the $d_{x^{2}-y^{2}}$-wave pairing symmetry gives rise to robust intragap impurity resonance states reflected by the resonance peaks near the Fermi energy in the local density of states. These features can be readily probed by scanning tunneling microscopy experiments, and are proposed to shed light on the pairing symmetry and provide hints on the microscopic mechanism of unconventional superconductivity in the Ce-based heavy fermion superconductors.

Small and nearly isotropic hole-like Fermi surfaces in LiFeAs detected through de Haas–van Alphen effect

LiFeAs is unique among the arsenic based Fe-pnictide superconductors because it is the only nearly stoichiometric compound which does not exhibit magnetic order. This is at odds with electronic structure calculations which find a very stable magnetic state and predict cylindrical hole- and electron-like Fermi surface sheets whose geometry suggests spin fluctuations and a possible instability toward long-range ordering at the nesting vector. In fact, a complex magnetic phase diagram is indeed observed in the isostructural NaFeAs compound. Previous angle-resolved photoemission (ARPES) experiments revealed the existence of both hole and electron-like surfaces, but with rather distinct cross-sectional areas and an absence of the nesting that is thought to underpin both magnetic order and superconductivity in the pnictide family of superconductors. These ARPES observations were challenged by subsequent de Haas--van Alphen (dHvA) measurements which detected a few, electron-like Fermi surface sheets in rough agreement with the original band calculations. Here, we show a detailed dHvA study unveiling additional, small and nearly isotropic Fermi surface sheets in LiFeAs single crystals, which ought to correspond to hole-like orbits, as previously observed by ARPES. Therefore, our results reconcile the apparent discrepancy between ARPES and the previous dHvA results. The small size of these Fermi surface pockets suggests a prominent role for the electronic correlations in LiFeAs. The absence of gap nodes, in combination with the coexistence of quasi-two-dimensional and three-dimensional Fermi surfaces, favor an $s$-wave pairing symmetry for LiFeAs. But similar electron-like Fermi surfaces combined with very different hole pockets between LiFeAs and LiFeP suggest that the nodes in the gap function of LiFeP might be located on the hole pockets. This would be difficult to reconcile with the current understanding of the $s\ifmmode\pm\else\textpm\fi{}$ scenario.

Superconductivity and strong intrinsic defects in LaPd1−xBi2

Two new phases LaPd${}_{1\ensuremath{-}x}$Bi${}_{2}$ and CePd${}_{1\ensuremath{-}x}$Bi${}_{2}$ were obtained by growing single crystals in Bi flux. They adopt the tetragonal ZrCuSi${}_{2}$-type structure and feature Bi-square nets and PbO-type PdBi layers with significant partial Pd occupancy. Bulk superconductivity at 2.1 K and metallic behavior above ${T}_{c}$ are observed in LaPd${}_{1\ensuremath{-}x}$Bi${}_{2}$. A small residual resistance ratio (RRR) indicates a strong scattering effect induced by the Pd vacancies, which implies an $s$-wave pairing symmetry in LaPd${}_{1\ensuremath{-}x}$Bi${}_{2}$. The broadening of the resistivity transition was measured under different magnetic fields demonstrating a high upper critical field of 3 T. Hall effect measurements reveal dominantly electron-like charge carriers and single-band transport behavior in LaPd${}_{1\ensuremath{-}x}$Bi${}_{2}$. The paramagnetic CePd${}_{1\ensuremath{-}x}$Bi${}_{2}$ is nonsuperconducting but shows antiferromagnetic ordering below 6 K.

Functional renormalization group study of pairing symmetry and pairing mechanism in iron-selenide superconductors

In iron selenide superconductors only electron-like Fermi pockets survive, challenging the $S^{\pm}$ pairing based on the quasi-nesting between the electron and hole Fermi pockets (as in iron arsenides). By functional renormalization group study we show that an in-phase $S$-wave pairing on the electron pockets ($S^{++}_{ee}$) is realized. The pairing mechanism involves two competing driving forces: The strong C-type spin fluctuations cause attractive pair scattering between and within electron pockets via Cooperon excitations on the virtual hole pockets, while the G-type spin fluctuations cause repulsive pair scattering. The latter effect is however weakened by the hybridization splitting of the electron pockets. The resulting $S^{++}_{ee}$-wave pairing symmetry is consistent with experiments. We further propose that the quasiparticle interference pattern in scanning tunneling microscopy and the Andreev reflection in out-of-plane contact tunneling are efficient probes of in-phase versus anti-phase $S$-wave pairing on the electron pockets.

Calculated phase diagram of doped BaFe2As2 superconductor in a C4-symmetry breaking model

We develop a minimal multiorbital tight-binding model with realistic hopping parameters. The model breaks the symmetry of the tetragonal point group by lowering it from C4 to D2d, which accurately describes the Fermi surface evolution of the electron-doped BaFe2−xCoxAs2 and hole-doped Ba1−yKyFe2As2 compounds. An investigation of the phase diagram with a mean-field Bogoliubov-de Gennes Hamiltonian results in agreement with the experimentally observed electron- and hole-doped phase diagram with only one set of t, U and V parameters. Additionally, the self-consistently calculated superconducting order parameter exhibits -wave pairing symmetry with a small d-wave pairing admixture in the entire doping range, which is the subtle result of the weakly broken symmetry and competing interactions in the multiorbital mean-field Hamiltonian.

The Finite Temperature Effect on Josephson Junction between an s-Wave Superconductor and an s±-Wave Superconductor

We investigate a Josephson junction between a one-band and a multi-band s-wave superconductor. When the multi-band lead is an s±-wave superconductor, we find that the critical Josephson current may change its sign when the temperature changes. Our result confirms that this is a widespread effect of the s±-wave superconductor, independent of the type of the junction, the ratios of the gaps and superconducting transition temperatures, as long as the tunneling matrix elements have suitable values. This novel effect comes directly from the opposite gap signs. We propose that the observation of this phenomena can be used to detect the s±-wave pairing symmetry in iron-based superconductors.

Evidence for ans-wave superconducting gap in KxFe2−ySe2from angle-resolved photoemission

Although a nodeless superconducting gap has been observed on the large Fermi pockets around the zone corner in K${}_{x}$Fe${}_{2\ensuremath{-}y}$Se${}_{2}$, whether its pairing symmetry is $s$ wave or nodeless $d$ wave is still under intense debate. Here we report an isotropic superconducting gap distribution on the small electron Fermi pocket around the $Z$ point in K${}_{x}$Fe${}_{2\ensuremath{-}y}$Se${}_{2}$, which favors the $s$-wave pairing symmetry.