Session V25: Superconductivity: HTSC Theory, Mostly Nematics and Inhomogeneous Systems

The role of nematic fluctuations in the thermal melting of pair-density-wave phases in superconductors

We study properties of phase transitions of the superconductor liquid crystal phases, and analyze the competition between the recently proposed Pair Density Wave (PDW) and nematic $4e$ superconductor (4eSC). Nematic fluctuations enhance the 4eSC and suppress the PDW phase. For a system decoupled from a lattice, the PDW state exists only at $T=0$ and the low temperature phase is a nematic $4e$SC with short ranged PDW order.   

Nematicity in 3-band Hubbard model of cuprate superconductors

The recent discovery of intra-unit-cell nematicity in STM studies of cuprate superconductors [1] underscores the importance of the role played by oxygen orbitals in CuO2 plane. Motivated by this observation we study 3-band Hubbard model using exact diagonalization. In particular, we investigate the effects various interaction parameters (Ud, Up, Vpd, Vpp) have on nematicity. Interestingly, we find that Ud, the on-site repulsion at copper sites, enhances nematicity in the strongly coupled regime.\\[4pt] [1] Lawler, M. J. \textit{et al}. Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states. \textit{Nature} \textbf{466}, 347 (2010).   

Mean-Field Nematic Phase Diagram for the Three-Band Hubbard Model

We map out the phase diagram of the three-band Hubbard model of a CuO$_2$ plane for nematic order in the parameter space of various on-site and nearest-neighbor interactions. For this, we define an intra-unit cell nematic order parameter in terms of a charge imbalance between the two oxygen sites in the unit cell and employ a self-consistent mean-field analysis. This study is motivated by recent STM experiments on high-T$_c$ cuprate superconductors pointing towards intra-unit cell nematicity.   

Dynamical electronic nematicity from Mott physics

We study the two-dimensional Hubbard model with small band anisotropy using dynamical-mean-field theory for clusters. We found that very large transport anisotropies can be induced by very small band anisotropy as in many strongly correlated materials. This happens when the interaction is large enough to yield a Mott transition. The maximum effect on conductivity anisotropy occurs in the underdoped regime as observed in high temperature superconductors. The anisotropy decreases at large frequency and is not associated with static stripe order. Thus we call the phenomenon ``dynamical electronic nematicity''. This work was supported by the Materials Sciences and Engineering Division, Office of Basic Energy Sciences, U.S. DOE (S.O.), NSERC (Canada) and the Tier I Canada Research Chair Program (A.- M.T.), with part of the computational resources by RQCHP and Compute Canada.   

Quantum Nematic Physics in the Hubbard Model of Cuprate Superconductors

Recent experiments have provided strong evidence that quantum electronic nematic order plays an important role in characterizing the pseudogap region of the cuprate superconductors. Starting from the generic Hubbard model of the cuprates, we introduce a small anisotropy in the hopping integral to model a small orthorhombic distortion. We perform a dynamic cluster quantum Monte Carlo approximation of this model, in order to study the effects of this anisotropy on various properties. In particular, we investigate the effects on superconductivity and pseudogap behavior, as well as the competition between different effects.   

On the origin of quantum criticality found at finite doping in 2D Hubbard model

To better understand the excitations responsible for quantum criticality (QC) found at finite doping in the 2D Hubbard model, we analyze the vertices for different scattering channels obtained from the Dynamical Cluster Continuous-Time Quantum Monte Carlo simulation. By decomposing these vertices using the parquet equations we find that both superconductivity and the charge instabilities responsible for the QC come from the crossed spin channel contribution, and thus are driven by the spin-fluctuations. On contrast, the spin instability comes from the fully irreducible spin vertex contribution.   

Superconductivity from purely repulsive interactions in the 2D electron gas

We present a well-controlled perturbative renormalization group (RG) treatment of superconductivity from short-ranged repulsive interactions in a variety of model two dimensional electronic systems. Our analysis applies in the limit where the repulsive interactions between the electrons are small compared to their kinetic energy.   

Effect of competing orders on superconductivity in the Hubbard model

We study the superconducting transition in the repulsive Hubbard model incorporating different competing orders at the mean field level. To the model on the square lattice with nearest and next-nearest neighbor hopping amplitudes, we add appropriate modulations of the hopping terms or onsite energies, such that they produce the desired broken symmetry. We then study the superconducting instability in the (theoretically tractable) limit in which the onsite repulsion U is small compared to the bandwidth. We obtain the pairing symmetry and strength as a function of the magnitude of the order parameter. Specific cases of broken symmetry states we study include antiferromagnetism, ferromagnetism, nematic order, d-density wave, and orbital loop order.   

$d$-wave Cooper pairing in multiband models for the high-$T_c$ cuprates

We investigate possible reasons for the significant differences of $T_c$s in high-$T_c$ cuprate compounds, based on renormalization group treatments of downfolded models for the electronic structure. Generally, cuprates with a square like Fermi surface exhibit lower critical temperatures than materials with a more rounded Fermi surface, which contradicts with many theoretical studies of the one band Hubbard model. To resolve this contradiction we study multiband models which in addition to the $d_{x2-y2}$ orbital contain $4s$ and $d_{z2}$ orbitals using different approximation levels of the functional renormalization group technique. Our results suggest that the observed material trend can be explained in parts by the influence of orbital mixing, which can dominate over the effect of the Fermi surface shape.   

Inhomogeneity and d-wave superconductivity in the Hubbard model

Whether or not inhomogeneity plays a significant role in determining the superconducting properties of the cuprate high-Tc superconductors remains an open issue, in spite of extensive theoretical and experimental focus. To this end, we study d-wave superconductivity in the checkerboard Hubbard model on a square lattice. We employ the Cellular Dynamical Mean Field theory method with an exact diagonalization solver at zero temperature. The d-wave order parameter is computed for various inhomogeneity levels over the entire doping range of interest. We find a monotonic decrease in the maximum amplitude of the superconducting order parameter with inhomogeneity. However, the order parameter increases with inhomogeneity in a small doping interval lying in the extreme overdoped regime. For any doping, an inhomogeneity-induced change in the height of the lowest energy peak in the antiferromagnetic spin susceptibility correlates with the change in amplitude of the order parameter.   

Disorder effects on pair binding in the checkerboard Hubbard model

The checkerboard Hubbard model is an inhomogeneous fermionic Hubbard model in which hopping on plaquettes takes a different value to hopping between plaquettes. The pair binding energy in the clean checkerboard Hubbard model, interpreted as a tendency towards superconducting order, is positive over a wide part of the zero temperature phase diagram. We perform exact diagonalization studies of the checkerboard Hubbard model with on-site disorder. For systems up to twelve sites, we study the distribution of pair binding energies that results from the introduction of potential disorder and find that weak disorder enhances the region of the phase diagram over which there is a non-zero probability of pair binding, without greatly changing the average pair binding energy. We also study how stronger disorder destroys pair binding.   

Theoretical investigation of superconductivity and antiferromagnetism in trilayer cuprate superconductors

Recent ARPES experiment on the optimally doped trilayer cuprate superconductors Bi2223 has revealed a layer variation of both doping density and d-wave gap. In particular, the two outer layers are overdoped with a gap which is larger than the gap for optimally doped single layer cuprates while the inner layer is underdoped with an even larger gap. Here we propose a minimal model composed of three layer t-J model, single particle interlayer tunneling as well as Cooper pair tunneling terms. By using renormalized mean field method, both the superconducting (SC) and antiferromagnetic (AFM) properties are theoretically investigated. Both tunneling effects may influence the phase configurations of both d-wave SC and AFM order parameters on each layer which plays a crucial role in determining the electronic structures of trilayer cuprates. In particular, the inphase state for both SC and AFM phases is found to be relevant to the Bi2223 trilayer system. In such a state, the superconducting order parameter of inner plane will be further enhanced due to the constructive proximity effect from the two outer planes and the hole density of inner plane will be much suppressed. Furthermore we predict that the appearance of interlayer ferromagnetic correlations for such system which could be tested by future NMR experiments. **This work is in collaboration with Chun Chen and A. Fujimori.   

Confinement-deconfinement interplay in quantum phases of doped Mott insulators

It is generally accepted that doped Mott insulators can be well described by the t-J model. In the latter, the electron fractionalization is dictated by the phase string effect. We found that in underdoped regime, the antiferromagnetic and superconducting phases are dual: in the former, holons are confined while spinons are deconfined, and vice versa in the latter. These two phases are separated by a novel phase, the so- called Bose-insulating phase, where both holons and spinons are deconfined. A pair of Wilson loops was found to constitute a complete set of order parameters determining this zero- temperature phase diagram. The quantum transitions between these phases are suggested to be of non-Landau-Ginzburg-Wilson type.   

FLEX calculation of the pairing state symmetry and quasiparticle excitations for SrRu$_2$O$_4$

We calculate the superconducting phase diagram for a two-dimensional, three-band tight-binding model of SrRu$_2$O$_4$ using the fluctuation exchange approximation (FLEX). Electron interactions are modeled by an atomically-local interaction with intra-band, inter-band and exchange terms and an atomically-local spin-orbit interaction is included as well. Preliminary results suggest that FLEX produces a singlet-pairing state with d$_{x^2 - y^2}$ orbital symmetry, a result that is not in agreement with many experimental results. However, we do find that the values for the interaction strengths that are required to generate $T_c \simeq 1.5\,K$ lead to normal state quasiparticle line widths that are in reasonable agreement with experimental results.   

Diagrammatic Quantum Monte Carlo Solution of Two dimensional Cooperon-Fermion model

We investigate the two-dimensional Cooperon-fermion model in the strong coupling limit with continuous-time diagrammatic determinant quantum monte carlo (DDQMC). We obtained the same Kosterlitz-Thouless transition temperature $T_{c}$ for the fermion's off-diagonal long range order $\chi_{OD}$ ({\boldmath $k$}=0,$\omega=0)$ and cooperon's Greens function $G^{b}$({\boldmath $k$}=0,$\omega=0)$ as expected. The renormalized cooperon's band (band gap and mass) is examined carefully. The delocalization of the cooperons enhances the diamagnetism. When applied to study the diamagnetism of pseudogap state in high-T$_{c}$ cuprate, the results we obtained is in good agreement with recent torque magnetization measurements.