Session K25: Superconductivity: Theory I

Revised phase diagram and anomalous thermal evolution of the antinodal gap and Raman response in high-temperature superconductors

The interplay of competing orders is essential to high-temperature superconductivity, which emerges upon suppression of an antiferromagnetic order typically via charge doping. However, where the zero-temperature quantum critical point (QCP) takes place --- in terms of the doping level --- is still elusive for it is hidden by the superconducting dome. The QCP has long been believed to follow the continuous extrapolation of the characteristic temperature (T*) for a normal-state order, but recently T* within the superconducting dome was found to exhibit unexpected back-bending in the cuprate Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ and the iron-pnictide BaFe$_{1-x}$Co$_{x}$As. Here we show that the original and the revised phase diagrams can be understood in terms of weak and moderate competitions, respectively, between superconductivity and a pseudogap state such as d-density-wave, based on Ginzburg-Landau theory and the microscopic extended t-J model. We further illustrate that the anomalous thermal dependences of the measured antinodal gap and Raman response in cuprates can be well understood by a two-step evolution, dominated by superconductivity and pseudogap, respectively.   

The Andreev reflection in a superconductor-normal metal junction of a doped correlated quantum spin Hall insulator

Andreev conductance across a normal metal-superconductor (N-S) junction of doped correlated quantum spin Hall insulator on honeycomb lattice is theoretically studied via Blonder-Tinkham-Klapwijk (BTK) formalism. The normal side is modeled by the doped Kane-Mele (KM) model. The superconducting side is a doped correlated KM t-J model, which has been shown to feature d+id'-wave spin singlet pairing. With increasing intrinsic spin-orbit coupling, the doped KM t-J system undergoes a topological phase transition from the chiral d-wave superconductivity to the $Z_{2}$ spin-Chern superconducting phase with helical Majorana fermions at edges. We apply a local strain on the N-S interface to generate an effective Dirac-delta barrier and study the transport near the chiral-helical phase transition in the weak tunneling limit. We explore the Andreev conductance at the K and K’ Dirac points, respectively and find the distinctive behaviors across the transition. Relevance of our results for the adatom-doped graphene is discussed. Reference: S.J. Sun, C.H. Chung, Y.Y. Chang, W.F. Tsai, and F.C. Zhang, arxiv:1506.02584."   

Macroscopic character of composite high temperature superconducting wires

The ``d-wave'' symmetry of the superconducting order in the cuprate high temperature superconductors is a well established fact, and one which identifies them as ``unconventional.'' However, in macroscopic contexts -- including many potential applications ({\it i.e.} superconducting ``wires'') -- the material is a composite of randomly oriented superconducting grains in a metallic matrix, in which Josephson coupling between grains mediates the onset of long-range phase coherence. Here, we analyze the physics at length scales large compared to the size of such grains, and in particular the macroscopic character of the long-range order that emerges. While XY-superconducting glass order and macroscopic d-wave superconductivity may be possible, we show that under many circumstances -- especially when the d-wave superconducting grains are embedded in a metallic matrix -- the most likely order has global s-wave symmetry.   

Random field disorder and charge order driven quantum oscillations in cuprates

In the pseudogap regime of the cuprates, charge order breaks a $\mathbb{Z}_{2}$ symmetry. Therefore, the interaction of charge order and quenched disorder due to potential scattering, can, in principle, be treated as a random field Ising model. A numerical analysis of the ground state of such a random field Ising model reveals local, glassy dynamics in both $2D$ and $3D$. The glassy dynamics are treated as a heat bath which couple to the itinerant electrons, leading to an unusual electronic non-Fermi liquid. If the dynamics are strong enough, the electron spectral function has no quasiparticle peak and the effective mass diverges at the Fermi surface, precluding quantum oscillations. In contrast to charge density, $d$-density wave order (reflecting staggered circulating currents) does not directly couple to potential disorder, allowing it to support quantum oscillations. At fourth order in Landau theory, there is a term consisting of the square of the $d$-density wave order parameter, and the square of the charge order. This coupling could induce parasitic charge order, which may be weak enough for the Fermi liquid behavior to remain uncorrupted. Here, we argue that this distinction must be made clear, as one interprets quantum oscillations in cuprates.   

Onsager rule, quantum oscillation frequencies, and the density of states in the mixed-vortex state of cuprates

Onsager rule that determines the frequencies of quantum oscillations in high magnetic fields serves as an anchor point. In its absence it would be very difficult to interpret the experimental results, because for each instance the problem would have to be considered anew. In the mixed-vortex state of the underdoped cuprates where, major consequential discoveries have recently taken place, its validity has been recently questioned. Here we show that this rule remains intact to an excellent approximation. The models we consider are fairly general, consisting of a variety of density wave states combined with $d$-wave superconductivity. Another exceptionally interesting result from our model calculations is that the oscillations ride on top of a field independent density of states, $\rho(B)$, for higher fields. This feature appears to be consistent with the recent specific heat measurements.   

Collective modes in non-uniform superconductors

We study dynamics of a superconducting condensate in the presence of a domain wall defect in the order parameter. We find that broken translation and reflection symmetries result in new collective excitations, bound to the domain wall region. Two additional amplitude/Higgs modes lie below the bulk pairbreaking edge $2\Delta$; one of them is a Goldstone mode with vanishing excitation energy. Spectrum of bound collective modes is related to the topological structure and stability of the domain wall. The `unbound' bulk collective modes and transverse gauge field mostly propagate across the domain wall, but the longitudinal component of the gauge field is completely reflected. Softening of the amplitude mode suggests reduced damping and possible route to its detection in geometrically confined superfluids or in superconductor-ferromagnetic heterostructures.   

Quasiclassical approach to magnetic suceptibility

Quasiclassical theory is a powerful technique that allows calculation of physical observables using just the low-energy states of the system. It is especially useful in studying properties of the non-uniform superfluid phases. We extend this approach to calculate response functions that involve high-energy correlations. Using example of Pauli magnetic susceptibility we employ Andreev approximation to express the spin-spin correlation function near a pairbreaking surface, in terms of low-energy, high-energy and mixed state contributions. This provides a convenient way to calculate response of a non-uniform superconductor at finite $q$-vectors.   

Boosted one dimensional superconductors on a lattice

We study the effect of a boost (that engenders a current-carrying state) on one dimensional systems of lattice fermions with short-ranged attractive interactions. In the absence of a boost such systems possess algebraic superconducting order. Naively, one might expect a boost to weaken and ultimately destroy superconductivity, as in higher dimensions. However, we show that for one dimensional systems its effect is to {\em strengthen} the algebraic superconducting order by making correlation functions fall off more slowly with distance. We explain the physical underpinnings of these findings.   

The superconducting state of Holstein model using dynamical mean field theory

To enhance the superconducting temperature within the conventional superconductors, we solve the Holstein model, where conduction electrons are coupled to some boson field, using dynamical mean field theory (DMFT) with the configuration interaction impurity solver. Thanks to the non-perturbative nature of DMFT, we determine the zero-temperature order parameter for a wide range of boson energies to find the optimal range for superconductivity. This is beyond the Migdal-Eliashberg theory where the boson energy is assumed to be small compared to the Fermi energy. The effect of Hubbard on-site repulsion will be also discussed.   

Unconventional superconductivity and interaction induced Fermi surface reconstruction in the two-dimensional Edwards model

We study the possibility of unconventional superconducting pairing in the framework of a novel two-dimensional quantum transport model, where the charge carriers are strongly affected by the correlations and fluctuations of a background medium, described by bosonic degrees of freedom. Using the projective renormalization method (PRM) we find in the half-filled band case an interplay between stable superconducting solutions and a charge-density wave order parameter which determines the ground state in the limit of large bosonic energies. The superconducting pairing mainly appears on a new hole-like Fermi surface, which is formed nearby the center of the Brillouin zone due to strong renormalization of the original fermionic band. In the superconducting state, the Fermi surface splits into two disconnected parts, which are characterized by different sign of the superconducting order parameter.   

A comprehensive model for high-$T_c$ based on pair-pair interactions.

The superconducting (SC) state of cuprates is characterized by a dome-shaped $T_c$ versus carrier density and an unconventional {\it pseudogap} (PG) state above $T_c$ - basic properties remain highly debated. We have recently proposed a mechanism [1] based on the mutual interaction between incoherent Cooper pairs existing above $T_c$. At the critical temperature, this interaction induces a Bose-like condensation leading to the coherent SC state. \\ Absent in the conventional BCS case, the mutual pair-pair interaction is proportional to the condensate density $n_{oc}(T)$ but is also related to the quasiparticle excitations. It gives an excellent fit to the DOS as measured by electron tunneling for a wide range of samples and carrier concentration. We conclude that long-range order is achieved by a direct quasiparticle - Cooper-pair coupling. \\ We then focus on the {\it temperature dependence} of the thermodynamic functions (condensation energy, entropy, etc.) and of the quasiparticle DOS. We show that these quantities depend on the unique combination of pair (boson) and quasiparticle (fermion) excitations, allowing a qualitative understanding of the phase diagram.\\ [1] W. Sacks, A. Mauger, Y. Noat, Superconduct. Sci.Technol. {\bf 28} 105014, 2015   

Two types of superconducting domes in unconventional superconductors

In this talk, we present a comprehensive analysis of the SC properties and phase diagrams across several families of unconventional superconductors within the copper-oxides, heavy-fermions, organics, and the recently discovered iron-pnictides, iron-chalcogenides, and oxybismuthides. We find that there are two types of SC domes present in all families of SC materials, arising sometimes as completely isolated, or merged into one, or in some materials only any one of them appears. One of the SC dome appearing at or near a possible QCP usually possesses a lower transition temperature ($T_{\mathrm{c}})$. The other SC dome appearing at a different value of the tuning parameter around a non-Fermi liquid (NFL) state often has higher $T_{\mathrm{c}}$. Both SC domes are not necessarily linked to each other, and so does the QCP and NFL state. In materials, where both domes are present, they can be isolated by multiple tuning (such as such as disorder, or pressure, or magnetic field in addition to doping, and vice versa), giving a unique opportunity to decouple the relationship between QCP, NFL, and their role on superconductivity. The systematic study the NFL state might be a generic route to higher-$T_{\mathrm{c}}$ superconductivity.   

Theory of pump-probe photoemission from a d-wave superconductor

Motivated by recent tr-ARPES experiments on high-temperature superconductors, we use the nonequilibrium Keldysh formalism to study the time-resolved photoemission spectra of a model electron-boson coupled system out of equilibrium. We introduce a momentum dependence to the electron-boson coupling to produce a superconducting state with d-wave symmetry. We investigate the nature of quasiparticle relaxation and recombination as well as the signatures of amplitude mode oscillations of the superconducting order parameter. We interpret our results in terms of existing experiments in the cuprates.   

First principles calculations of La$_2$CuO$_4$

We use the DFT+DCA method for a high-end study of the electronic structure properties of La$_2$CuO$_4$. The parameters of a tight-binding model are created using the first-principles electronic structure calculations. The all-electron full-potential linearised augmented plane-wave method is used to solve the non-interacting band problem. Then the set of physically relevant Wannier functions is chosen as a basis for the underlying Hubbard model. The Wannier functions and the corresponding non-interacting Hamiltonian $H_{nm}^{0}({\bf k})$ are created using the well-established downfolding approach. The screened Coulomb interaction parameters $U_{nm}$ of the model are computed using the constrained random-phase approximation technique. The double counting term is assumed to be a constant multiplied by the identity operator in the correlated subspace and it is determined based on first-principles considerations. The resulting {\it ab-initio} parameterisation of the Hubbard model is solved within dynamical cluster approximation (DCA).