Session A36: Theory and Computation of Novel Superconductivity

Superconductivity at the onset of spin-density-wave order in a metal

We revisit the issue of superconductivity at the quantum-critical point between a 2D paramagnet and a spin-density-wave (SDW) metal with ordering momentum $(\pi,\pi)$. This problem is highly non-trivial because the system at criticality displays a non-Fermi liquid behavior and because the effective coupling constant $\lambda$ for the pairing is generally of order one, even when the actual interaction is smaller than fermionic bandwidth. Previous study [M. A. Metlitski, S. Sachdev, Phys.Rev.B 82, 075128 (2010)] has found that the leading renormalization of the pairing vertex contains $\log^2$, like in color superconductivity. We analyze the full gap equation and argue that summing up $\log^2$ term does not lead to a pairing instability. Yet, superconductivity has no threshold, even if $\lambda$ is set to be small: the subleading $\log$ terms give rise to BCS-like $T_c \propto e^{-1/\lambda}$. We argue that the analogy with BCS is not accidental as superconductivity at a QCP is a Fermi liquid phenomenon -- it comes from fermions which retain Fermi liquid behavior at criticality. We compute $T_c$ for the actual $\lambda$ and find consistency with the numerical results.   

Coexistence of Antiferromagnetism and Superconductivity in Bilayer Cuprates and Iron Arsenides

The coexistence of antiferromagnetism (AFM) and superconductivity (SC) is one of important issues in strongly correlated electron systems. One example is seen in multilayered cuprate superconductors, and another one is in iron-arsenide superconductors. In cuprates, motivated by the recent experiment reporting the enhancement of AFM order below the SC transition temperature, we study the proximity effect of the AFM correlation in a bilayer system and also examine the possibility of the coexistence. We present the result of mean-field theory that is consistent with the experiment and supports the proximity-effect picture [1]. In iron arsenides, we study possible coexistence of AFM with Dirac dispersions and SC with the same and different phase of pairing potential, based on the knowledge of the cuprates. [1] Y. Yoshizumi, T. Morinari, and T. Tohyama, Phys. Rev. B $\mathbf{85}$, 184523 (2012).   

Robust nodal $d$-wave spectrum in simulations of strongly fluctuating competing order in underdoped cuprates

While many experiments suggest that the pseudogap in cuprate superconductors originates from some nonsuperconducting broken-symmetry phase, clear spectral signatures of such a phase have not been observed in angle resolved photoemission experiments. We report on numerical simulations of the spectral function, in which competing superconducting and nonsuperconducting phases experience strong thermal fluctuations. In our work, we consider the competition between $d$-wave superconductivity and a low temperature spin density wave (SDW) phase that is widely observed in underdoped cuprates. Because of this competition, our simulations sample highly inhomogeneous states that are far from the mean-field saddle point configurations. We find that the computed spectral function is, in many cases, almost indistinguishable from that of the pure $d$-wave superconductor, and that there is no sign of the Fermi surface reconstruction generically expected for SDW phases. We argue that this work explains the absence of any clear experimental signature of such a reconstruction. We find that signatures of the fluctuating competing order can be found mainly in a splitting of the antinodal band and, for strong magnetic order, in small induced nodal gaps similar to those found in recent experiments   

Theory of nonequilibrium superconductivity in cuprates

Recently, nonequilibrium properties of Hi Tc superconductors are attracting much interest. This is because new experimental methods such as time resolved ARPES has been applied to cuprates and succeeded in observing the dynamics of photo-excited quasiparticles as well as the temporal evolution of the d-wave superconducting order parameter (e.g., [1]). One can also realize nonequilibrium states in interfaces between cuprates and metal electrodes and control the superconducting order by changing the applied bias [2]. In order to study the dynamics of superconductivity in strongly correlated systems, we developed a novel numerical method by combining the quantum kinetic equation with the fluctuation exchange approximation (FLEX, self-consistent T-matrix approximation) [3]. This method enables us to study the interplay between pair mediating fluctuations, e.g., antiferromagnetic and charge fluctuations, and the dynamics of quasiparticles and superconducting order parameter. In the presentation, we explain the physical insights we obtain by applying this method to nonequilibrium dynamics in d-wave superconductors.\\[4pt] [1] C. L. Smallwood, et al., Science 336, 1137 (2012).\\[0pt] [2] T. Oka, and H. Aoki, Phys. Rev. B 82, 064516 (2010).\\[0pt] [3] T. Oka, and V. Pietilä, in progress.   

Pair density wave superconducting state in a Nematic Liquid Crystal Phase

We consider the problem of the superconducting states that arise in a fermionic system in a nematic-like $l=2$ state in the spin-triplet channel. This nematic state is invariant under a $\pi/2$ rotation followed by a spin flip. Under these circumstances the only infinitesimal superconducting instability is in the p-wave channel. However, close enough to the nematic transition both a uniform d-wave superconducting state and a pair density wave (PDW) state (also with d-wave symmetry) can arise. We compute the phase diagram and study the competition between an uniform (BCS type) superconducting state, the PDW state and the non-superconducting state.   

Incommensurate Nematic Charge Order in the Three Band Model for Cuprate Superconductors

Recent experimental evidence for charge order in cuprates is a possible source of anomalous electronic properties in the underdoped regime. Intra-unit cell charge ordering tendencies point to electronic nematic order involving oxygen orbitals. In this context we investigate charge instabilities in the Emery model. The charge susceptibilities reveal three different kinds of nematic order. The first is an intra-unit cell ($q=0$) nematic order. The second and the third are incommensurate charge orders with wavevectors that are either uniaxial or oriented along the Brillouin zone diagonal. The two latter charge patterns correspond to a spatially modulated nematic phase. The selection of the leading instability depends on the filling, the interaction parameters, and details of the band structure. For these candidate charge orderings we discuss their possible relevance for the charge ordering signatures in X-ray and STM experiments.   

Orbital Nematic Instability in Two-Orbital Hubbard Model: A Renormalization-Group Study

Motivated by the nematic electronic fluid phase in Sr$_3$Ru$_2$O$_7$, we analyze the ($d_{xz}$, $d_{yz}$)-orbital Hubbard model by the one-loop renormalization-group method [1]. We find that, in the weak-interaction case, the $q=0$ component of the orbital susceptibility $\chi^{\mathrm{q}}(q)$ is critically enhanced by the Aslamazov-Larkin (AL) type vertex correction due to the superconducting fluctuations. In the strong-interaction case, we also find the development of $\chi^{\mathrm{q}}(q)$ driven by the AL-type vertex correction due to spin fluctuations, consistently with the perturbation analysis [2]. Thus the strong orbital nematic fluctuation, i.e., orbital Pomeranchuk instability, emerges near the magnetic or superconducting quantum criticality. This mechanism of orbital nematic order presents a natural explanation for the nematic order in Sr$_3$Ru$_2$O$_7$, and is expected to be realized in various multiorbital systems, such as Fe-based superconductors [3]. \\ \noindent [1] M. Tsuchiizu, S. Onari, and H. Kontani, arXiv:1209.3664. \\ \noindent [2] Y. Ohno, M. Tsuchiizu, S. Onari, and H. Kontani, arXiv:1209.3629. \\ \noindent [3] S. Onari and H. Kontani, Phys. Rev. Lett. \textbf{109}, 137001 (2012).   

Superconductivity in CuCl/Si superlattices: excitonic pairing?

Two-dimensional (2D) hetero-bonded semiconductor interfaces have been suggested as candidate geometries where excitonic superconductivity \footnote{V.L. Ginzburg, Sov. Phys. JETP {\bf 20},1549 (1965)} -- and the greatly enhanced where $T_C$ compared to phonon mechanisms mediation -- can be realized. Among experimental efforts, epitaxially grown CuCl on Si (111) has reportedly exhibited excitonic superconductivity at 60$\sim$150 K. Our first-principles calculations confirm 2D metallicity at the interfaces due to charge transfer by valence mismatch. \footnote{S.H. Rhim {\em et al.}, Phys. Rev. B {\bf 76}, 184505 (2007).} The excitonic mechanism is investigated by calculating the kernel function, $K(\omega)$, for the average of the electronic contributions to the effective interaction.\footnote{Zakharov {\em et al.}, J.Phys.Condes.Matter {\bf 9} 8501 (1997)} The attractive interaction found in the CuCl/Si superlattice indicates the feasibility of excitonic pairing for a certain frequency range.   

Real-Space Holon Pairing in Underdoped Cuprates

We examine the behavior of a recently developed model for underdoped cuprates [1] in the fluctuation regime above $T_c$. It is characterized by a spin gap and describes sublattice preserving hopping by holons and holon pairs, accompanied by a backflow of spin singlets. The singlets form a short-range valence-bond state which is continuously connected to the correct spin state at half filling. The theory, thus constrained, leads to the correct phase diagram and also explains the two-dimensionality of the metallic states. Superconductivity is due to pair hopping, as holons form real-space pairs at low densities and undergo a Bose-Einstein condensation below $T_c$. The pairs exist up to a temperature $T_p > T_c$, which is consistent with the observed Nernst effect and diamagnetism above $T_c$. The pair spectrum is calculated by identifying poles of the pair Green's function. Here we show that the specific heat of this system is in qualitative agreement with recent measurements [2].\\[4pt] [1] S. K. Sarker and T. Lovorn, Phys. Rev. B {\bf 82}, 014504 (2010); ibid {\bf 85}, 144502 (2012)\\[0pt] [2] H.-H. Wen \textit{et al.}, Phys. Rev. Lett. {\bf 103}, 067002 (2009)   

Analyses of High-Temperature Superconductivity in Doped Hubbard Model --High-Precision Variational Monte Carlo Study--

Two-dimensional Hubbard model, which only includes the on-site Coulomb interaction $U$ and the nearest hopping $t$, is one of the simplest models proposed for describing the high-T$_{\rm c}$ superconductivity. Although numerically unbiased methods such as auxiliary-field quantum Monte Carlo(QMC)[1] and Gaussian-basis QMC [2] do not find an indication for the superconductivity for intermediate coupling region($U/t<8$), several approaches such as the variational Monte Carlo(VMC) method[3,4] suggest that the $d$-wave superconductivity appears in the doped Hubbard model. To quantitatively resolve the origin of the controversy and to reveal the superconducting mechanism, by using a high-precision VMC[5], we present results which successfully reproduces the results of previous unbiased calculations[1,2], while finds the superconductivity in a strong coupling region. We focus on the relation of the superconductivity to proximity of phase separation with charge fluctuations as its mechanism. [1]N.Furukawa and M.Imada, J. Phys. Soc. Jpn. 61, 3331 (1992). [2]T.Aimi and M.Imada, J. Phys. Soc. Jpn. 76, 113708 (2007). [3]H.Yokoyama $et$ $al$. J. Phys. Soc. Jpn. 73, 1119(2004). [4]D.Baeriswyl $et$ $al$. New J. Phys. 11 075010 (2009). [5]D.Tahara and M.Imada,J. Phys. Soc. Jpn. 77,114701(2008).   

Superconductivity in two-leg ladder iron selenides

Recently, evidence of superconductivity has been discovered in the single-layer potassium-doped iron selenide that consists of weakly coupled two-leg iron ladders (Wei Li {\it et al.}, arXiv:1210.4619). Using a self-consistent mean-field approximation, we analyze the pairing symmetry and structure of the multi-orbital $t$-$J$ model defined in these two-leg ladder systems. Similar to the case of the iron pnictides, a modified $s$-wave pairing state is stabilized by the next-nearest-neighbor superexchange $J_2$. The presence of competing states will be discussed. Our result demonstrates the potential importance of the local magnetic couplings in iron-based superconductors.   

Magnetic States of the Two-Leg Ladder Iron Selenides

Neutron scattering experiments have unveiled a dominant spin arrangement in the two-leg ladder selenide compound BaFe$_2$Se$_3$, involving ferromagnetically ordered 2$\times$2 iron-superblocks, that are antiferromagnetically coupled among them (the ``block-AFM'' state). Our numerical study of the electronic five-orbital Hubbard model, within the Hartree-Fock approximation and using first principles techniques for the hopping amplitudes, has shown that the exotic block-AFM state is indeed stable at realistic electronic densities $n \sim 6.0$. Another state with wavevector $(\pi,0)$ becomes stable in other portions of the phase diagrams, including $n \sim 5.5$, as found experimentally in KFe$_2$Se$_3$. In addition, our study unveils several competing magnetic phases that could be experimentally stabilized varying either $n$ chemically or the electronic bandwidth by pressure. Similar results were obtained using two-orbital models, studied here via Lanczos and DMRG techniques [1]. [1] Qinlong Luo, et al, arXiv: 1205.3239, and references therein.   

Second Corollary to the Five Principles of Photoemission Via Dipolon Theory of High Temperature Superconductivity

Recently, we presented theory of dipolon-phonon interaction to explan the isotope shift in HTSC. Also we deduced five principles with one corollary [1] of photoemission (PE) from the dipolon theory [2,3] which not only explained the peak-dip-hump phenomenon [4] and low energy kink in quasiparticle energy dispersion (QED) but also predicted two more high energy kinks [1,4] that have now been observed. Here we present second corollary to the five principles of PE which states: ``As one changes dipolon density of states by changing or creating interactions with the factors such as doping, occupation number of ions, vacancies, defects, impurities, phononS with and without different isotope exchange, lattice structure, lattice distortion etc. there appear corresponding changes (shifts) in PE spectra, $T_C$, QED and the kink structure (predictably, one may observe the apparent isotope shift negative as well as zero or positive depending on the simultaneous action of the other factors).''\\[4pt] [1] R. R. Sharma, ``Dipolon Theory..'', in ``.. Cuprates'', Ed. K. N. Courtlandt, P. 81-100, Nova Sc, Pub., New York, 2009.\\[0pt] [2] R. R. Sharma, Phy. Rev. {\bf B 63}, 054506 (2001).\\[0pt] [3] R. R. Sharma, Physica {\bf C 439}, 47 (2006).\\[0pt] [4] R. R. Sharma, Physica {\bf C 468}, 190 (2008)   

Different roles of Zn$^{2+}$ and Li$^{+}$ impurities in the CuO2 plane in undoped cuprate compounds

A planar Mott insulator with easy plane Neel order can be mapped unto a Gutzwiller projected topological insulator model. Under the assumption that the projection operator can be permuted, Zn$^{2+}$ and Li$^{+}$ impurities can be represented as vacancies introducing a zero mode, which has a local spin moment for Zn$^{2+}$ and a charged hole for Li$^{+}$, respectively. While the local spin moment for Zn$^{2+}$ is screened by the long-range spin correlations, the active charge degree of freedom for Li$^{+}$ impurity twists the spin background. This proposal explains the very different roles of the Zn$^{2+}$ and Li$^{+}$ impurities in the CuO2 plane in the undoped cuprate compounds.