D-wave Superconductors Research Articles

Specific criteria for BCS-type cuprate superconductivity and peculiar isotope effects on the critical superconducting transition temperature

So far, many researchers have been misled to believe that the Bardeen–Cooper–Schrieffer (BCS)-like (s- or d-wave) pairing theory is adequate for explaining high- $$T_\mathrm {c}$$ superconductivity in doped cuprates from underdoped to overdoped regime. We show that the doped cuprates, depending on the Fermi energy ( $$\varepsilon _\mathrm {F}$$ ) and the energy ( $$\varepsilon _\mathrm {A}$$ ) of the effective attraction between pairing carriers, might be either unconventional (non-BCS-type) superconductors (at intermediate doping) or BCS-type superconductors (at higher doping). We argue that specific criteria for BCS-type superconductivity formulated in terms of two ratios $$\varepsilon _\mathrm {A}/\varepsilon _\mathrm {F}$$ and $$\Delta /\varepsilon _\mathrm {F}$$ (where $$\Delta $$ is the BCS-like gap) must be met in these systems. We demonstrate that these criteria are satisfied only in overdoped cuprates but not in underdoped and optimally doped cuprates, where the origin of high- $$T_\mathrm {c}$$ superconductivity is quite different from the BCS-type (s- or d-wave) superconductivity. The BCS-like pairing theory is then used to calculate the critical superconducting transition temperature ( $$T_\mathrm {c}$$ ) and the peculiar oxygen and copper isotope effects on $$T_\mathrm {c}$$ in overdoped cuprates.

Spectroscopic Evidence for Electron-Boson Coupling in Electron-Doped Sr_{2}IrO_{4}.

The pseudogap, d-wave superconductivity and electron-boson coupling are three intertwined key ingredients in the phase diagram of the cuprates. Sr_{2}IrO_{4} is a 5d-electron counterpart of the cuprates in which both the pseudogap and a d-wave instability have been observed. Here, we report spectroscopic evidence for the presence of the third key player in electron-doped Sr_{2}IrO_{4}: electron-boson coupling. Akink in nodal dispersion is observed with an energy scale of ∼50 meV. The strength of the kink changes with doping, but the energy scale remains the same. These results provide the first noncuprate platform for exploring the relationship between the pseudogap, d-wave instability, and electron-boson coupling in doped Mott insulators.

Unfrustrating the t-J Model: Exact d-wave BCS Superconductivity in the t'-J_z-V Model

The t-J model is believed to be a minimal model that may be capable of describing the low-energy physics of the cuprate superconductors. However, although the t-J model is simple in appearance, obtaining a detailed understanding of its phase diagram has proved to be challenging. We are therefore motivated to study modifications to the t-J model such that its phase diagram and mechanism for d-wave superconductivity can be understood analytically without making uncontrolled approximations. The modified model we consider is a t’-J_zJz-V model on a square lattice, which has a second-nearest-neighbor hopping t’ (instead of a nearest-neighbor hopping t, an Ising (instead of Heisenberg) antiferromagnetic coupling J_zJz, and a nearest-neighbor repulsion V. In a certain strongly interacting limit, the ground state is an antiferromagnetic superconductor that can be described exactly by a Hamiltonian where the only interaction is a nearest-neighbor attraction. BCS theory can then be applied with arbitrary analytical control, from which nodeless d-wave or s-wave superconductivity can result.

Nodal superconducting exchange coupling.

A superconducting spin valve consists of a thin-film superconductor between two ferromagnetic layers. A change of magnetization alignment shifts the superconducting transition temperature (ΔΤc) due to an interplay between the magnetic exchange energy and the superconducting condensate. The magnitude of ΔΤc scales inversely with the superconductor thickness (dS) and is zero when dS exceeds the superconducting coherence length (ξ). Here, we report a superconducting spin-valve effect involving a different underlying mechanism in which magnetization alignment and ΔΤc are determined by nodal quasiparticle excitation states on the Fermi surface of the d-wave superconductor YBa2Cu3O7-δ sandwiched between insulating layers of ferromagnetic Pr0.8Ca0.2MnO3. We observe ΔΤc values that approach 2 K with the sign of ΔΤc oscillating with dS over a length scale exceeding 100ξ and, for particular values of dS, the superconducting state reinforces an antiparallel magnetization alignment. These results pave the way to all-oxide superconducting memory in which superconductivity modulates the magnetic state.

The coexisting state of the staggered flux and d-wave superconducting order in a t-J type model

We study the quasiparticle structures in the coexisting phase of the d-wave superconductivity (dSC) and the staggered flux state using the renormalized mean-field theory for the t-J type model with additional nearest-neighbor Coulomb repulsion V, based on the Gutzwiller approximation. We find that this coexisting state exhibits the dome-like behavior of dSC in the phase diagram and also the so-called two-gap structure found in ARPES experiments, both of which are quite consistent with the experimental results.

Odd-parity superconductivity driven by octahedra rotations in iridium oxides

Iridium oxides have provided a playground to study novel phases originating from spin-orbit coupling and electron-electron interactions. Among them, the d-wave singlet superconductor was proposed for electron-doped Sr$_2$IrO$_4$, containing two Ir atoms in a unit cell due to the staggered rotation of oxygen octahedra about the c-axis. It was also noted that such oxygen octahedra rotation affects electronic transports. Here we study the role of octahedra tilting away from the c-axis, in determining superconducting pairing symmetry. We show that the octahedra tilting changes the large Fermi surface to a Dirac point, which strongly suppresses the conventional d-wave pairing. Furthermore, it also promotes effective spin-triplet interactions in the strong Hubbard interaction limit, leading to a transition from the even-parity to odd-parity superconducting phase. Thus, tuning octahedra distortions can be used as a tool to engineer a spin triplet superconductor in strongly correlated systems with strong spin-orbit coupling.

π-Loops With ds Josephson Junctions

We fabricated Josephson junctions (JJs) between the d-wave superconductor (SC) YBa 2 Cu 3 O 7 -x (YBCO) and the swave SC Nb (ds-JJs) on graphoepitaxially buffered MgO substrates, studied ds-JJs at temperatures down to 30 mK and employed these JJs in π-loops. Current-voltage characteristics of dsJJs oriented along the [100] axis of YBCO exhibited up to a factor of 200 higher critical current densities than ds-JJs oriented along the [110] axis of YBCO. The critical current I and the IcRn product of [100]-oriented 3 μm wide ds-JJs are ~70 μA and ~200 μV, respectively, at 4.2 K. Rectangular arrays of up to 40 000 π-loops based on such ds-JJs were investigated using a low temperature scanning superconducting quantum interference device (SQUID) microscope. We observed ordering of spontaneously generated half integer magnetic flux quanta in the π-loops correlated with minute spurious background magnetic fields, as well as with configurations and mutual coupling of the π-loops. We manipulated the magnetic states of the π-loops by the local application of magnetic fields using nearby planar coils. This paper paves the way for the use of π-loops in computations that are based on annealing processes.

Fate of a strongly correlated d -wave superconductor in a Zeeman field: The Fulde-Ferrel-Larkin-Ovchinnikov perspective

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is an unconventional superconducting state found under the influence of strong Zeeman field. This phase is identified by finite center-of-mass momenta in the Cooper pairs, causing the pairing amplitude to oscillate in real space. Repulsive correlations, on the other hand, smear out spatial inhomogeneities in d-wave superconductors. We investigate the FFLO state in a strongly correlated d-wave superconductor within a consolidated framework of Hartree-Fock-Bogoliubov theory and Gutzwiller approximation. We find that the profound effects of strong correlations lie in shifting the BCS-FFLO phase boundary towards a lower Zeeman field and thereby enlarging the window of the FFLO phase. In the FFLO state, our calculation features a sharp mid-gap peak in the density of states, indicating the formation of strongly localized Andreev bound states. We also find that the signatures of the FFLO phase survive even in the presence of an additional translational symmetry breaking competing order in the ground state. This is demonstrated by considering a broken symmetry ground state with a simultaneous presence of the d-wave superconducting order and a spin-density wave order, often found in unconventional superconductors.

Pseudogap and Fermi arcs in underdoped cuprates

The proposed loop-current order in cuprates cannot give the observed pseudogap and the Fermi-arcs because it preserves translation symmetry. A modification to a periodic arrangement of the four possible orientations of the order parameter with a large period of between about 12 to 30 lattice constants is proposed and shown in a simple and controlled calculation to give one-particle spectra with every feature as in the ARPES experiments. The results follow from (1) the currents at the boundaries of the periodic domains with similar topology as the Affleck-Marston flux phase, and (2) the mixing introduced by the boundary currents between the states near the erstwhile Fermi-surface and the ghost Fermi-surfaces which are displaced from it by mini-reciprocal vectors. The proposed idea can be ruled out or verified by high resolution diffraction or imaging experiments. It does not run afoul of the variety of different experiments consistent with the loop-current order as well as the theory of the marginal Fermi-liquid and d-wave superconductivity based on quantum-critical fluctuations of the loop current order.

Superconductivity and Jahn–Teller effect in bilayer cuprate superconductors

We have proposed a model Hamiltonian describing the interlayer tunnelling in d-wave bilayer cuprate superconductors in the coexistence of superconductivity and Jahn–Teller effect with the on-site non-magnetic impurity. The Hamiltonian is solved for the quasi-particle energy bands, the superconducting and the Jahn–Teller gap parameters by using Zubarev’s technique of double time electron Green’s functions. The effects of interlayer tunnelling and the strength of non-magnetic potential are studied for superconducting and Jahn–Teller gap parameters. The density of states for both the layers of the bi-layer system is studied and the results are compared with others.

Evidence for d-Wave Superconductivity in Single Layer FeSe/SrTiO3 Probed by Quasiparticle Scattering Off Step Edges.

The de Gennes extrapolation length is a direction dependent measure of the spatial evolution of the pairing gap near the boundary of a superconductor and thus provides a viable means to probe its symmetry. It is expected to be infinite and isotropic for plain s-wave pairing, and finite and anisotropic for d-wave. Here, we synthesize single-layer FeSe films on SrTiO3(001) (STO) substrates by molecular beam epitaxy and measure the de Gennes extrapolation length by scanning tunneling microscopy/spectroscopy. We find a 40% reduction of the superconducting gap near specular [110]Fe edges, yielding an extrapolation length of 8.0 nm. However, near specular [010]Fe edges, the extrapolation length is nearly infinite. These findings are consistent with a phase changing pairing with 2-fold symmetry, indicating d-wave superconductivity. This is further supported by the presence of in-gap states near the specular [110]Fe edges, but not the [010]Fe edges. This work provides direct experimental evidence for d-wave superconductivity in single-layer FeSe/STO and demonstrates quasiparticle scattering at boundaries to be a viable phase sensitive probe of pairing symmetry in Fe-based superconductors.

Tunneling spectroscopy in normal/ferromagnetic d-wave superconductor silicene junctions

The tunneling conductance in normal/ferromagnetic d-wave superconductor (N/FdS) silicene junction is studied based on Blonder-Tinkham-Klapwijk (BTK) theory. It is demonstrated that the amplitude of the normalized conductance strongly depends on the applied electric field (EZ) and the exchange field(h) in FdS, the crystal orientation of the dS (α) and the relative orientation of EZ and h. When α=π/4, a dip appears in the conductance spectrum at eV=h for 0<lEz−λSO<h with λSO the spin obit coupling term. In the case of lEz−λSO≥h, however, double dips appear at eV=h and eV=lEz−λSO, respectively. When α=0, the zero-bias conductance peak splits into two peaks as increasing h for anti-parallel configuration. Thus, the obtained result can serve as a method to identify the pairing symmetry of FdS.

Multiple Electronic Components and Lifshitz Transitions by Oxygen Wires Formation in Layered Cuprates and Nickelates

There is growing compelling experimental evidence that a quantum complex matter scenario made of multiple electronic components and competing quantum phases is needed to grab the key physics of high critical temperature (Tc) superconductivity in layered cuprates. While it is known that defect self-organization controls Tc, the mechanism remains an open issue. Here we focus on the theoretical prediction of the multiband electronic structure and the formation of broken Fermi surfaces generated by the self-organization of oxygen interstitials Oi atomic wires in the spacer layers in HgBa2CuO4+δ, La2CuO4+δ and La2NiO4+δ, by means of self-consistent Linear Muffin-Tin Orbital (LMTO) calculations. The electronic structure of a first phase of ordered Oi atomic wires and of a second glassy phase made of disordered Oi impurities have been studied through supercell calculations. We show the common features of the influence of Oi wires in the electronic structure in three types of materials. The ordering of Oi into wires leads to a separation of the electronic states between the Oi ensemble and the rest of the bulk. The wire formation first produces quantum confined localized states near the wire, which coexist with, Second, delocalized states in the Fermi surface (FS) of doped cuprates. A new scenario emerges for high Tc superconductivity, where Kitaev wires with Majorana bound states are proximity-coupled to a 2D d-wave superconductor.

Impurity-induced tunneling-mediated superconducting gap in bilayer cuprate superconductors

We have proposed a model Hamiltonian describing the interlayer tunneling in d-wave bilayer cuprate superconductors. The Hamiltonian is solved for the quasi-particle energy bands and the superconducting (SC) order parameter by using Zubarev’s technique of double time Green’s functions. The effects of interlayer tunneling and the strength of non-magnetic potential are studied for SC order parameter, density of states (DOS), electronic specific heat and quasi-particle energy bands, and the results are compared with others.

Locating the Missing Superconducting Electrons in the Overdoped Cuprates La_{2-x}Sr_{x}CuO_{4}.

Overdoped high-temperature cuprate superconductors have often been understood within the standard BCS framework of superconductivity. However, measurements in a variety of overdoped cuprates indicate that the superfluid density is much smaller than expected from BCS theory and decreases smoothly to zero as the doping is increased. Here, we combine time-domain THz spectroscopy with kHz range mutual inductance measurements on the same overdoped La_{2-x}Sr_{x}CuO_{4} films to determine the total, superfluid, and uncondensed spectral weight as a function of doping. A significant fraction of the carriers remains uncondensed in a wide Drude-like peak as T→0, while the superfluid density remains linear in temperature. These observations are seemingly inconsistent with existing, realistic theories of impurity scattering suppressing the superfluid density in a BCS-like d-wave superconductor. Our large measurement frequency range gives us a unique look at the low frequency spectral weight distribution, which may suggest the presence of quantum phase fluctuations as the critical doping is approached.

Low-energy effective theory at a quantum critical point of the two-dimensional Hubbard model: Mean-field analysis

We complement previous functional renormalization group (fRG) studies of the two-dimensional Hubbard model by mean-field calculations. The focus falls on Van Hove filling and the the hopping amplitude t'/t=0.341. The fRG data suggest a quantum critical point (QCP) in this region and in its vicinity a singular fermionic self-energy, Im $\Sigma(\omega)/\omega \sim |\omega|^{-\gamma}$ with $\gamma\approx 0.26$. Here we start a more detailed investigation of this QCP using a bosonic formulation for the effective action, where the bosons couple to the order parameter fields. To this end, we use the channel decomposition of the fermionic effective action developed in [Phys. Rev. B 79, 195125 (2009)], which allows to perform Hubbard-Stratonovich transformations for all relevant order parameter fields at any given energy scale. We stop the flow at a scale where the correlations of the order parameter field are already pronounced, but the flow is still regular, and derive the effective boson theory. It contains d-wave superconducting, magnetic, and density-density interactions. We analyze the resulting phase diagram in the mean-field approximation. We show that the singular fermionic self-energy suppresses gap formation both in the superconducting and magnetic channel already at the mean-field level, thus rounding a first-order transition (without self-energy) to a quantum phase transition (with self-energy). We give a simple effective model that shows the generality of this effect. In the two-dimensional Hubbard model, the effective density-density interaction is peaked at a nonzero frequency, so that solving the mean-field equations already involves a functional equation instead of simply a matrix equation (on a technical level, similar to incommensurate phases). Within a certain approximation, we show that such an interaction leads to a short quasiparticle lifetime.

Nodeless High-T_{c} Superconductivity in the Highly Overdoped CuO_{2} Monolayer.

We study the electronic structure and superconductivity in a CuO_{2} monolayer grown recently on the d-wave cuprate superconductor Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}. Density functional theory calculations indicate a significant charge transfer across the interface such that the CuO_{2} monolayer is heavily overdoped into the hole-rich regime yet inaccessible in bulk cuprates. We show that both the Cu d_{x^{2}-y^{2}} and d_{3z^{2}-r^{2}} orbitals become important and the Fermi surface contains one electron and one hole pocket associated with the two orbitals, respectively. Constructing a minimal correlated two-orbital model for the e_{g} complex, we show that the spin-orbital exchange interactions produce a nodeless superconductor with extended s-wave pairing symmetry and a pairing energy gap comparable to the bulk d-wave gap, in agreement with recent experiments. The findings point to a direction of realizing new high-T_{c} superconductors in ozone grown transition-metal-oxide monolayer heterostructures.

Surface states of gapped electron systems and semi-metals

With a generic lattice model for electrons occupying a semi-infinite crystal with a hard surface, we study the eigenstates of the system with a bulk band gap (or the gap with nodal points). The exact solution to the wave functions of scattering states is obtained. From the scattering states, we derive the criterion for the existence of surface states. The wave functions and the energy of the surface states are then determined. We obtain a connection between the wave functions of the bulk states and the surface states. For electrons in a system with time-reversal symmetry, with this connection, we rigorously prove the correspondence between the change of Kramers degeneracy of the surface states and the bulk time-reversal Z2 invariant. The theory is applicable to systems of (topological) insulators, superconductors, and semi-metals. Examples for solving the edge states of electrons with/without the spin–orbit interactions in graphene with a hard zigzag edge and that in a two-dimensional d-wave superconductor with a () edge are given in appendices.

Superconductivity in the doped t−J model: Results for four-leg cylinders

We report a density-matrix renormalization group study of the lightly doped $t$-$J$ model on a 4-leg cylinder with doped hole concentrations per site $\delta=5\%\sim 12.5\%$. By keeping an unusually large number of states and long system sizes, we are able to accurately document the interplay between d-wave superconductivity (SC) and spin and charge-density-wave (CDW) orders. The long-distance behavior is consistent with that of a Luther-Emery liquid with a spin-gap, power-law CDW correlations with wave-length $\lambda =1/2\delta$, and power-law SC correlations. This is the widest (most nearly 2D) such system for which power law SC correlations have been established.

A Bogoliubov-de Gennes study of d-wave Hubbard superconductors under magnetic field

The formation of magnetic vortices and their effects on the electronic specific heat (Cel) of d-wave superconductors are studied within the generalized Hubbard model and the Bogoliubov-de Gennes (BdG) formalism. The BdG equations provide the local superconducting gaps as a function of the electron-electron interaction and carrier concentration. The electron hopping parameters of the generalized Hubbard model for the ceramic superconductor La2-xSrxCuO4 are determined by using angle-resolved photoemission spectroscopy (ARPES) data. The BdG results show that the d-wave superconducting states, induced by the correlated hopping interactions, possess an upper-critical-magnetic-field temperature dependence consistent with the generalized Ginzburg-Landau model for type II superconductors. Furthermore, the electronic specific heat reveals a square-power-law temperature behavior observed in d-wave superconductors. When an external magnetic field is applied, such behavior becomes linear at the low-temperature limit. The coefficient of this linear behavior confirms the square-root dependence with the external magnetic field predicted by the Volovik thermodynamic model and its trend is consistent with experimental data obtained from La1.85Sr0.15CuO4.