Session L25: Superconductivity: Theory II

How the Mott and pseudogap states coalesce beneath the superconductor Dome

Former results of a Tight-Binding (TB) model of CuO planes in La$_{\mathrm{2}}$CuO$_{\mathrm{4}}$ are reviewed to underline their wider implications. It is noted that physical systems being appropriately described by the TB model can exhibit the main strongly correlated electron system (SCES) properties, when they are solved in the HF approximation, by also allowing crystal symmetry breaking effects and non-collinear spin orientations of the HF orbitals. In particular, it is argued how a simple 2D square lattice system of Coulomb interacting electrons can exhibit insulator gaps and pseudogap states, and quantum phase transitions as illustrated by the mentioned former works. These results allow to understand the nature of the observed quantum phase transition laying ``beneath'' the superconducting Dome. It corresponds to coalescence under hole doping increase, of an insulator ground state (with a highly degenerated spin order) with an excited pseudogap state, showing a lattice order symmetry breaking. The evolution of the band structure and Fermi surface with doping are determined.   

Scattering rates and specific heat jumps in high-$T_c$ cuprates

Inspired by recent ARPES and tunneling studies on high-$T_c$ cuprates, we examine the effect of a pair-breaking term in the self-energy on the shape of the electronic specific heat jump. It is found that the observed specific heat jump can be described in terms of a superconducting gap, that persists above the observed $T_c$, in the presence of a strongly temperature dependent pair-breaking scattering rate. An increase in the scattering rate is found to explain the non-BCS-like suppression of the specific heat jump with magnetic field. A discussion of these results in the context of other properties such as the superfluid density and Raman spectra will also be presented.   

Skyrmion-induced Bound States in Superconductors

We consider superconducting systems proximity-coupled to magnetic materials with skyrmion structures. Motivated by the progress in experiments which allows us to control the magnetic textures, we consider the case where a single skyrmion is floating in ferromagnetic background. We predict the skyrmion bound state is formed around the core of it. The results are obtained through the numerical calculation on the spin-polarized local density of states in the vicinity of the skyrmion core, which shows good agreement with T-matrix analysis. The bound states can be recognized as skyrmion-version of well-known Yu-Shiba-Rusinov states.   

Theory of quantum fluctuating superconductivity in incoherent metals

Quantum superconducting fluctuations can be important in two-dimensional, disordered thin films. They lead to the appearance of a metallic state characterized by a non-zero resistivity. We construct an effective description of superfluid hydrodynamics where the phase of the order parameter is relaxed, due to Coulomb interactions or the motion of vortices for instance. We predict there should be a Drude-like or a cyclotron-like pole in the spectrum, and corresponding sharp peaks in the optical conductivity. In some cases the finite electrical conductivity in the phase-fluctuating metallic state is found to be related in a novel way to the thermal conductivity of the normal state.   

Charge transfer insulators at half-filling in multiband models of cuprates

Self-consistent mean-field three-band and four-band Hubbard models are used to study the collapse of the Mott gap in doped cuprates. While no set of doping-independent parameters can explain the observed gaps for the entire doping range, the experimental results are consistent with a weakly doping dependent Hubbard U. A key finding is that, when the Cu-O splitting energy $\Delta$ is large, the cuprates behave as Mott insulators. However, for small $\Delta$, the cuprates become charge transfer insulators.   

Polar Kerr effect in high temperature cuprate superconductors

A mechanism is proposed for the tantalizing evidence of polar Kerr effect in a class of high temperature superconductors–the signs of the Kerr angle from two opposite faces of the same sample are identical and magnetic field training is non-existent. The mechanism does not break global time reversal symmetry, as in an antiferromagnet, and results in zero Faraday effect. It is best understood in a phenomenological model of bilayer cuprates, such as YBCO, in which intra-bilayer tunneling nucleates a chiral d-density wave such that the individual layers have opposite chirality. Although the presentation is specific to the chiral d-density wave, the mechanism may be more general to any quasi-two-dimensional orbital antiferromagnet in which time reversal symmetry is broken in each plane, but not when averaged macroscopically.   

Dirac lines in the superconducting hyper-honeycomb lattice

Motivated by the recent discovery of the hyper-honeycomb $\beta$-Li$_2$IrO$_3$ studied in the context of Kitaev spin liquids, we investigate the possibility to realize superconductivity in the hyper-honeycomb lattice. Based on a t-J model we discuss the effect of the band structure and spin-orbit coupling on the most stable superconducting state. Using group theory we construct all symmetry allowed superconducting states and show that we naturally get Dirac line nodes protected by the non-symmorphic symmetries.   

Radiation induced oscillating gap states of nonequilibrium superconductors

In recent years, non-equilibrium superconducting phenomena induced by light have drawn great interests. We study effects of a light radiation to a BCS superconductor. The phase transition are obtained from the analysis of self-oscillation conditions of the irradiated dynamical systems. We find an oscillating gap phase solution with a frequency not directly related to the radiation frequency but resulting from the asymmetry of electron density of states of the system. When such a superconductor is in contact with another superconductor, it will give rise to an alternating Josephson current. We further discuss the existence conditions and properties of this alternating gap phase solution and its interesting effects on experiments.   

Transient Dynamics of d-wave Superconductors after a Sudden Excitation

Motivated by recent ultafast pump probe experiments on high-temperature superconductors, we discuss the transient dynamics of a d-wave BCS model after a quantum quench of the interaction parameter. We find that the existence of gap nodes, with the associated nodal quasiparticles, introduces a dissipation channel which makes the dynamics much faster than in the conventional s-wave model. For every value of the quench parameters, the superconducting gap rapidly converges to a stationary value smaller than the one at equilibrium. Using a sudden approximation for the gap dynamics, we find an analytical expression for the reduction of spectral weight close to the nodes, which is in qualitative agreement with recent experiments.   

Chern mosaic: topology of chiral superconductivity in ferromagnetic adatom lattices

Recent experiments have demonstrated signatures of Majorana bound states in ferromagnetic atomic chains. We show that similar systems, extended to two dimensional geometry, may support chiral topological superconductivity with large Chern numbers. Our observation is based on the fact that magnetic adatoms on an s-wave superconductor bind subgap Shiba states, which can hybridize and form subgap energy bands with nontrivial topology. Such a Shiba lattice supports long-range hopping, leading to a complex, mosaic-like phase diagram with large Chern numbers. We analyze the incidence of different Chern numbers phases and the size of their energy gaps for various lattice geometries. Our findings reveal the studied system as one of the riches platforms of topological matter known to date.   

Weak phase stiffness and nature of the quantum critical point in underdoped cuprates

We demonstrate that the zero-temperature superconducting phase diagram of underdoped cuprates can be quantitatively understood in the strong binding limit, using only the experimental spectral function of the ``normal'' pseudo-gap phase without any free parameter. In the prototypical (La$_{1-x}$Sr$_x$)$_2$CuO$_4$, a kinetics-driven $d$-wave superconductivity is obtained above the critical doping $\delta_c\sim 5.2\%$, below which complete loss of superfluidity results from local quantum fluctuation involving local $p$-wave pairs. Near the critical doping, a enormous mass enhancement of the local pairs is found responsible for the observed rapid decrease of phase stiffness. Finally, a striking mass divergence is predicted at $\delta_c$ that dictates the occurrence of the observed quantum critical point and the abrupt suppression of the Nernst effects in the nearby region. * Phys. Rev. B 92, 180501(R) (2015); Phys. Rev. X 1, 011011 (2011).   

p-Orbital Density Wave with d Symmetry in High-Tc Cuprate Superconductors

Emergence of the nematic density wave is a fundamental unsolved problem in cuprate superconductors. To understand the origin of the nematicity, we employ the recently-developed functional renormalization-group method with high numerical accuracy, and discover the critical development of the $p$-orbital-density-wave ($p$-ODW) instability in the strong-spin-fluctuation region [1]. The obtained $p$-ODW state possesses the key characteristics of the charge ordering pattern in Bi- and Y-based superconductors, such as the wavevector parallel to the nearest Cu-Cu direction, and the $d$-symmetry form factor with the antiphase correlation between $p_x$ and $p_y$ orbitals in the same unit cell. From the beautiful scaling relation between the spin susceptibility and the $p$-ODW susceptibility, we conclude that the $p$-ODW is driven by the strong interference between spin and charge fluctuations. It is clarified that the strong charge-spin interference, which is the origin of the nematicity, is the hidden but significant characteristics of the electronic states in cuprate superconductors. \\ \ [1] M. Tsuchiizu, Y. Yamakawa, and H. Kontani, arXiv:1508.07218.   

Spectral properties of the two-dimensional $t$-$J$ model near the Mott transition

The single-particle spectral function of the two-dimensional $t$-$J$ model near the Mott transition is studied using cluster perturbation theory to clarify how the spectral-weight distribution transforms to that of the Mott insulator as the doping concentration decreases. Various anomalous features observed in cuprate high-temperature superconductors are collectively explained in the two-dimensional $t$-$J$ model near the Mott transition [1] as in the two-dimensional Hubbard model [2]. The results imply that the spectral features are primarily related to the proximity of the antiferromagnetic Mott insulator, which has a low-energy spin-wave mode but no low-energy charge excitation, and to the presence of states characterized by different energy scales rather than to the presence of double occupancy, which is completely removed in the $t$-$J$ model. The results are confirmed to remain almost unchanged as the cluster size is increased from 4$\times$4 to 6$\times$6 sites in cluster perturbation theory by using the non-Abelian dynamical density-matrix renormalization group method [1]. [1] M. Kohno, Phys. Rev. B 92, 085128 (2015). [2] M. Kohno, Phys. Rev. Lett. 108, 076401 (2012).   

Monte Carlo Study of Competing Orders in a Nearly Antiferromagnetic Metal

We study a two-dimensional lattice model of a metal on the verge of an antiferromagnetic transition. The model can be simulated using the quantum Monte Carlo technique with no sign problem. We compute the antiferromagnetic, superconducting, charge density wave, and pair density wave susceptibilities, as well as the superfluid density, across the phase diagram. Near the putative antiferromagnetic quantum critical point, we find a dome-shaped d-wave superconducting phase. The electronic density of states displays an opening of a gap at temperatures moderately above the superconducting T$_c$. Our results provide insights into the interplay of antiferromagnetism and unconventional superconductivity at intermediate to strong coupling.   

TYPICAL MEDIUM DYNAMICAL CLUSTER APPROXIMATION FOR DISORDERED SUPERCONDUCTORS

We study the effect of disorder on a three dimensional attractive Hubbard model using the typical medium dynamical cluster approximation with the Bogoliubov-de Gennes approach as a cluster solver. We explore the effects of disorder for a fixed interaction strength (U) on the diagonal and off-diagonal typical density of states. Using our results we construct a complete phase diagram in the disorder vs interaction (U) parameter space. As the disorder strength is increased, the pairing parameter or the off-diagonal typical density of states decreases and vanishes at a critical disorder strength while the spectral gap remains finite. This indicates the transition from a superconducting to a super-resistive phase. We observe that at small U the superconductor to super-resistive phase line bends down in the disorder vs interaction (U) parameter space. Also, we find that the superconducting order parameter first rises and then falls with increasing disorder in the small U regime. A further increase in the disorder strength causes the diagonal typical density of states to vanish at a critical value, indicating a transition from a super-resistive to the Anderson insulator phase.