Engineering quantum phases using light is a novel route to designing functional materials, where light-induced superconductivity is a successful example. Although this phenomenon has been realized experimentally, especially for the high-$T_c$ cuprates, the underlying mechanism remains mysterious. Using the recently developed variational non-Gaussian exact diagonalization method, we investigate a particular type of photoenhanced superconductivity by suppressing a competing charge order in a strongly correlated electron-electron and electron-phonon system. We find that the $d$-wave superconductivity pairing correlation can be enhanced by a pulsed laser, consistent with recent experiments based on gap characterizations. However, we also find that the pairing correlation length is heavily suppressed by the pump pulse, indicating that light-enhanced superconductivity may be of fluctuating nature. Our findings also imply a general behavior of nonequilibrium states with competing orders, beyond the description of a mean-field framework.
A strong periodic potential generally enhances the short wavelength fluctuations of a superfluid beyond the validity of standard continuum approaches. Here we report some recent results on hard core bosons on finite lattices. We find several interesting effects of the periodic potential on the ground state, vortex dynamics, and and Hall conductivity. For example, the Magnus field on a vortex abruptly reverses direction at half filling. A rotating Bose condensate on an optical lattice may allow an experimental test of our results. Insight may also be gained about strongly fluctuating supercondu…
We analyze the form of static charge susceptibility $χ(q)$ in underdoped cuprates near axial momenta $(Q,0)$ and $(0,Q)$ at which short-range static charge order has been observed. We show that the momentum dependence of $χ(q)$ is anisotropic, and the correlation length in the longitudinal direction is larger than in the transverse direction. We show that correlation lengths in both directions decrease once the system evolves into a superconductor, as a result of the competition between superconductivity and charge order. These results are in agreement with resonant x-ray scattering data [R. C…
Twenty years of extensive research has yet to produce a general consensus on the origin of high temperature superconductivity (HTS). However, several generic characteristics of the cuprate superconductors have emerged as the essential ingredients of and/or constraints on any viable microscopic model of HTS. Besides a Tc of order 100K, the most prominent on the list include a d-wave superconducting gap with Fermi liquid nodal excitations, a d-wave pseudogap with the characteristic temperature scale T*, an anomalous doping-dependent oxygen isotope shift, nanometer-scale gap inhomogeneity, etc.. …
We study the physical property of pair density wave (PDW) and fluctuating PDW, and use it to build an effective theory of the strongly interacting pseudogap phase in cuprate high temperature superconductors. In Chapter2, we study how Fulde-Ferrell state, the simplest form of PDW, responds to incident light. The collective motion of the condensate plays a key role; gauge invariance guides us to the correct result. From Chapter 3 to Chapter 7, we construct a pseudogap metallic state by considering quantum fluctuating PDW. We analyze a recent scanning tunneling microscope (STM) discovery of perio…
Using a phenomenological lattice model of coupled spin and charge modes, we determine the spin susceptibility in the presence of fluctuating stripe charge order. We assume the charge fluctuations to be slow compared to those of the spins, and combine Monte Carlo simulations for the charge order parameter with exact diagonalization of the spin sector. Our calculations unify the spin dynamics of both static and fluctuating stripe phases and support the notion of a universal spin excitation spectrum in doped cuprate superconductors.
A muon-spin relaxation (muSR) investigation is presented for the molecular superconductor kappa-(BEDT-TTF)2Cu[N(CN)2Br]. Evidence is found for low-temperature phase-separation, with only a fraction of the sample showing a superconducting signal, even for slow cooling. Rapid cooling reduces the superconducting fraction still further. For the superconducting phase, the in-plane penetration depth is measured to be lambda_{parallel} = 0.47(1) mu m and evidence is seen for a vortex decoupling transition in applied fields above 40 mT. The magnetic fluctuations in the normal state produce Korringa be…
A hydrodynamic theory of transport in quantum mechanically phase-disordered superconductors is possible when supercurrent relaxation can be treated as a slow process. We obtain general results for the frequency-dependent conductivity of such a regime. With time-reversal invariance, the conductivity is characterized by a Drude-like peak, with width given by the supercurrent relaxation rate. Using the memory matrix formalism, we obtain a formula for this width (and hence also the dc resistivity) when the supercurrent is relaxed by short range Coulomb interactions. This leads to a new -- effectiv…
We extend recent low temperature analyses of competing orders in the cuprate superconductors to the pseudogap regime where all orders are fluctuating. A universal continuum limit of a classical Ginzburg-Landau functional is used to characterize fluctuations of the superconducting order: this describes the crossover from Gaussian fluctuations at high temperatures to the vortex-binding physics near the onset of global phase coherence. These fluctuations induce affiliated corrections in the correlations of other orders, and in particular, in the different realizations of charge order. Implication…
Within the framework of the QED3 theory of cuprates it is argued that bulk antiferromagnetic (AF) order can coexist with d-wave superconductivity in the underdoped region, in agreement with recent experiments. The AF order arises from the phase fluctuating d-wave superconductor via the mechanism of spontaneous chiral symmetry breaking, provided that fluctuations are sufficiently strong. The phase diagram for this coexistence is mapped out by means of analytical and numerical solutions of the underlying Dyson-Schwinger equation in the large N limit.
We observe charge-order fluctuations in the quasi-two-dimensional organic superconductor $β^{\prime\prime}$-(BEDT-TTF)2 SF5 CH2 CF2 SO3 both by means of vibrational spectroscopy, locally probing the fluctuating charge order, and investigating the in-plane dynamical response by infrared reflectance spectroscopy. The decrease of effective electronic interaction in an isostructural metal suppresses both charge-order fluctuations and superconductivity, pointing on their interplay. We compare the results of our experiments with calculations on the extended Hubbard model.
Disordered thin films close to the superconducting-insulating phase transition (SIT) hold the key to understanding quantum phase transition in strongly correlated materials. The SIT is governed by superconducting quantum fluctuations, which can be revealed for example by tunneling measurements. These experiments detect a spectral gap, accompanied by suppressed coherence peaks that do not fit the BCS prediction. To explain these observations, we consider the effect of finite-range superconducting fluctuations on the density of states, focusing on the insulating side of the SIT. We perform a con…
We present a volume-sensitive high-energy x-ray diffraction study of the underdoped cuprate high temperature superconductor La2-xSrxCuO4 (x = 0.12, Tc=27 K) in applied magnetic field. Bulk short-range charge stripe order with propagation vector q_ch = (0.231, 0, 0.5) is demonstrated to exist below T_ch = 85(10) K and shown to compete with superconductivity. We argue that bulk charge ordering arises from fluctuating stripes that become pinned near boundaries between orthorhombic twin domains.
A one-dimensional model of electrons locally coupled to spin-1/2 degrees of freedom is studied by numerical techniques. The model is one in the class of $dynamic$ $Hubbard$ $models$ that describe the relaxation of an atomic orbital upon double electron occupancy due to electron-electron interactions. We study the parameter regime where pairing occurs in this model by exact diagonalization of small clusters. World line quantum Monte Carlo simulations support the results of exact diagonalization for larger systems and show that kinetic energy is lowered when pairing occurs. The qualitative physi…
Dynamic Hubbard models have been proposed as extensions of the conventional Hubbard model to describe the orbital relaxation that occurs upon double occupancy of an atomic orbital. These models give rise to pairing of holes and superconductivity in certain parameter ranges. Here we explore the changes in carrier effective mass and quasiparticle weight and in one- and two-particle spectral functions that occur in a dynamic Hubbard model upon pairing, by exact diagonalization of small systems. It is found that pairing is associated with lowering of effective mass and increase of quasiparticle we…
The two-dimensional t-J model in a staggered field is studied by exact diagonalization of small clusters. For the low-hole-density region and a realistic value of J/t, it is found that the presence of a staggered field strengthens the attraction between two holes. With increasing field, the d_{x^2-y^2}-wave superconducting correlations are enhanced while the extended-s-wave ones hardly change. This implies that coexistence of the d_{x^2-y^2}-wave superconducting order and the commensurate antiferromagnetic order occurs in a staggered field.
We study the ground-state properties of the double-chain Hubbard model coupled with ferromagnetic exchange interaction by using the weak-coupling theory, density-matrix renormalization group technique, and Lanczos exact-diagonalization method. We determine the ground-state phase diagram in the parameter space of the ferromagnetic exchange interaction and band filling. We find that, in high electron density regime, the spin gap opens and the spin-singlet $d_{xy}$-wave-like pairing correlation is most dominant, whereas in low electron density regime, the fully-polarized ferromagnetic state is st…
The compound IrTe2 is known to exhibit a transition to a modulated state featuring Ir-Ir dimers, with large associated atomic displacements. Partial substitution of Pt or Rh for Ir destabilizes the modulated structure and induces superconductivity. It has been proposed that quantum critical dimer fluctuations might be associated with the superconductivity. Here we test for such local dimer correlations and demonstrate their absence. X-ray pair distribution function approach reveals that the local structure of Ir0.95Pt0.05Te2 and Ir0.8Rh0.2Te2 dichalcogenide superconductors with compositions ju…
Cuprate materials hosting high-temperature superconductivity (HTS) also exhibit various forms of charge and/or spin ordering whose significance is not fully understood. To date, static charge-density waves (CDWs) have been detected by diffraction probes only at special doping or in an applied external field. However, dynamic CDWs may also be present more broadly and their detection, characterization and relationship with HTS remain open problems. Here, we present a new method, based on ultrafast spectroscopy, to detect the presence and measure the lifetimes of CDW fluctuations in cuprates. In …
By a novel exact diagonalization technique we show that bound pairs propagate between repulsive Hubbard clusters in a superconducting fashion. The size of the matrices that must be handled depends on the number of fermion configurations {\em per spin}, which is of the order of the square root of the overall size of the Hilbert space. We use CuO$_{4}$ units connected by weak O-O links to model interplanar coupling and c-axis superconductivity in Cuprates. The numerical evidence on Cu$_{2}$O$_{8}$ and Cu$_{3}$O$_{12}$ prompts a new analytic scheme describing the propagation of bound pairs and al…
In this talk I outline the general strategy behind the SO(5) theory of high $T_c$ superconductivity. Progress in the direction of exact SO(5) models, numerical exact diagonalization and possible experimental tests are reviewed. I also address the criticisms raised recently against the SO(5) theory and point out directions for future exploration.
The particular shape of the Fermi surface can give rise to a number of collective quantum phenomena in solids, such as density wave orderings or even superconductivity. In many new iron superconductors this shape, the 'nested' Fermi surface, is indeed observed, but its role in the formation of spin-density waves or superconductivity is not clear. We have studied the electronic structure of the non-magnetic LiFeAs (Tc~18K) superconductor using angle-resolved photoemission spectroscopy. We find a notable absence of the Fermi surface nesting, strong renormalization of the conduction bands by a fa…
We study a quasi-2D classical Landau-Ginzburg-Wilson effective field theory in the presence of quenched disorder in which incommensurate charge-density wave and superconducting orders are intertwined. The disorder precludes long-range charge-density wave order, but not superconducting or nematic order. We select three representative sets of input parameters and compute the corresponding charge-density wave structure factors using both large-$N$ techniques and classical Monte Carlo simulations. Where nematicity and superconductivity coexist at low temperature, the peak height of the charge-dens…
We compute the ground-state fidelity and various correlations to gauge the competition between different orders in two-dimensional t-J-type models. Using exact numerical diagonalization techniques, these quantities are examined for (i) the plain t-J and t-t'-J models, (ii) for the t-J model perturbed by infinite-range d-wave or extended-s-wave superconductivity inducing terms, and (iii) the t-J model, plain and with a d-wave perturbation, in the presence of non-magnetic quenched disorder. Various properties at low hole doping are contrasted with those at low electron filling. In the clean case…
We provide analytical and numerical evidence of a spin-triplet FFLO superconductivity in the itinerant Kitaev-Heisenberg model (anti-ferromagnetic Kitaev coupling and ferromagnetic Heisenberg coupling) on the honeycomb lattice around quarter filling. The strong spin-orbit coupling in our model leads to the emergence of 6 inversion symmetry centers for the Fermi surface at non zero momenta in the first Brillouin zone. We show how the Cooper pairs condense into these non-trivial momenta, causing the spatial modulation of the superconducting order parameter. Applying a Ginzburg-Landau expansion a…
In quantum materials, electrons that have strong correlations tend to localize, leading to quantum spins as the building blocks for low-energy physics. When strongly correlated electrons coexist with more weakly-correlated conduction electrons, multiple channels of effective interactions develop and compete with each other. The competition creates quantum fluctuations having a large spectral weight, with the associated entropies reaching significant fractions of $R\ln 2$ per electron. Advancing a framework to understand how the fluctuating local moments influence unconventional superconductivi…
We study the low temperature tunneling density of states of thin wires where superconductivity is destroyed through quantum phase-slip proliferation. Although this regime is believed to behave as an insulator, we show that for a large temperature range this phase is characterized by a conductivity falling off at most linearly with temperature, and has a gapless excitation spectrum. This novel conducting phase results from electron-electron interaction induced pair breaking. Also, it may help clarify the low temperature metallic features found in films and wires whose bulk realization is superc…
Fluctuating Pair Density Wave in Finite-temperature Phase Diagram of the $t$-$t^\prime$ Hubbard Model
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；State Key Laboratory of Surface Physics and Department of Physics, Fudan University（复旦大学表面物理国家重点实验室和物理系）；Hefei National Laboratory（合肥国家实验室）
An exact-diagonalization technique on finite-size clusters is used to study the ground state and excitation spectra of the two-dimensional effective fermion model, a fictious model of hole quasiparticles derived from numerical studies of the two-dimensional t-J model at low doping. We show that there is actually a reasonable range of parameter values where the $d_{x^2-y^2}$-wave pairing of holes occurs and the low-lying excitation can be described by the picture of Bogoliubov quasiparticles in the BCS pairing theory. The gap parameter of a size $Δ_d\simeq 0.13|V|$ (where $V$ is the attractive …
The possible ground states of the undoped and doped Kitaev-Heisenberg model on a triangular lattice are studied. For the undoped system, a combination of the numerical exact diagonalization calculation and the four-sublattice transformation analysis suggests one possible exotic phase and four magnetically ordered phases including a collinear stripe pattern and a noncollinear spiral pattern in the global phase diagram. The exotic phase near the antiferromagnetic (AF) Kitaev point is further investigated by using the Schwinger-fermion mean-field method, and we obtain an energetically favorable $…
Solid 4He may acquire superfluid characteristics due to the frustration of the solid phase at grain boundaries. Here, we show that an analogous effect occurs in systems with competition among charge-density-waves (CDWs) and superconductivity in the presence of disorder, as cuprate or dichalcogenide superconductors. The CDWs breaks apart in domains with topologically protected filamentary superconductivity (FSC) at the interfaces. Transport experiments carried out in underdoped cuprates with the magnetic field acting as a control parameter are shown to be in excellent agreement with the theoret…
When a superconductor is warmed above its critical temperature $T_c$, long range order is destroyed by fluctuations in the order parameter. These fluctuations can be probed by measurements of conductivity, diamagnetism, and of the Nernst effect. Here, we study a regime where superconductivity is destroyed by phase fluctuations arising from a dilute liquid of mobile vortices. We find that the Nernst effect and diamagnetic response differ significantly from Gaussian fluctuations -- in particular, a much sharper decay with temperature is obtained. We predict a rapid onset of Nernst signal at a te…
We model the underdoped cuprates using fermions moving in a background with local antiferromagnetic order. The antiferromagnetic order fluctuates in orientation, but not in magnitude, so that there is no long-range antiferromagnetism, but a 'topological' order survives. The normal state is described as a fractionalized Fermi liquid (FL*), with electron-like quasiparticles coupled to the fractionalized excitations of the fluctuating antiferromagnet. The electronic quasiparticles reside near pocket Fermi surfaces enclosing total area x (the dopant density), centered away from the magnetic Brillo…
The reflectivity $R (ω)$ of both the $ab$ plane and the c axis of two single crystals of La$_{1.875}$Ba$_{0.125-y}$Sr$_{y}$CuO$_4$ has been measured down to 5 cm$^{-1}$, using coherent synchrotron radiation below 30 cm$^{-1}$. For $y$ = 0.085, a Josephson Plasma Resonance is detected at $T \ll T_c$ = 31 K in $R_{c} (ω)$, and a far-infrared peak (FIP) appears in the optical conductivity below 50 K, where non-static charge ordering (CO) is reported by X-ray scattering. For $y$ = 0.05 ($T_c$ = 10 K), a FIP is observed in the low-temperature tetragonal phase below the ordering temperature $T_{CO}$…
We develop a weak coupling approach to superconductivity in twisted bilayer graphene, starting from the Fermi liquid regime. A key observation is that near half filling, the fermiology consists of well nested Fermi pockets derived from opposite valleys, leading to enhanced valley fluctuation, which in turn can mediate superconductivity. This scenario is studied within the random phase approximation. We find that inter-valley electron pairing with either chiral ($d+i d$ mixed with $p-i p$) or helical form factor is the dominant instability. An approximate SO(4) spin-valley symmetry implies a ne…
Intercalated Fe chalcogenide K$_2$Fe$_4$Se$_5$ family exhibits high Tc ($\sim$ 30 K) superconductivity and spin-8 high T$_{\rm N}$ ($\sim$ 560 K) antiferromagnetism (AFM). We present a model Hamiltonian and suggest \textit{Skyrmion superconductivity}. A doped electron creates an orbitally non degenerate S=7\half state in a F$_4$Se$_9$ cluster and moves in a single correlated band, exchange coupled to a robust S=8 AFM order. Skyrmion, a topological excitation of 2 dimensional AFM order acquires an \textit{induced charge -2e} through a quantum anomaly and becomes a Cooper pair. Superconductivity…
Effects of the magnetic impurity Ni on the Cu-spin dynamics and superconductivity have been studied in La_2-x_Sr_x_Cu_1-y_Ni_y_O_4_ with x = 0.13 changing y finely up to 0.10. Compared with the case of the nonmagnetic impurity Zn, it has been found from the muon-spin-relaxation measurements that a large amount of Ni is required to stabilize a magnetic order of Cu spins. However, the evolution toward the stabilization of the magnetic order with increasing impurity concentration is qualitatively similar to each other. The area of the non-superconducting and slowly fluctuating or static region of…
The effects of a single non-magnetic impurity on superconducting states in the Penson-Kolb-Hubbard model have been analyzed. The investigations have been performed within two steps: (i) the homogeneous system is analysed using the Bogoliubov transformation, whereas (ii) the inhomogeneous system is investigated self-consistent Bogoliubova-de Gennes equations (by exact diagonalization and the kernel polynomial method). We analysed both signs of pair hopping, which correspond to s-wave and $η$-wave superconductivity. Our results show that an enhancement of the local superconducting gap at the imp…
Quantum spin liquids (QSLs), in which spins are highly entangled, have been considered a groundwork for generating exotic superconductivity.Despite numerous efforts, superconductivity emerging from QSLs has been unrealized in actual materials due to the difficulties in stabilizing QSL states with metallic conductivity.Recently, an organic compound, $κ$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$, with a nearly regular triangular lattice of molecular dimers was recognized as a candidate for doped QSLs. In this study, we report an unusual superconducting phase of $κ$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$: unexpec…
Zero-field muon-spin-relaxation (muSR) and magnetic-susceptibility measurements have been carried out in La_2-x_Sr_x_Cu_1-y_Zn_y_O_4_ with x = 0.10, 0.115 and 0.13 changing the Zn-concentration y finely up to 0.10, with the aim to clarify effects of the nonmagnetic impurity Zn on the Cu-spin dynamics and superconductivity. The muSR measurements have revealed that, in each x, a magnetic order of Cu spins is observed at y ~ 0.0075, while it disappears and Cu spins turn into a fast fluctuating state for y > 0.03. From the magnetic-susceptibility measurements, on the other hand, it has been found …
Motivated by the possibility of superconductivity in doped graphene sheets, we investigate superconducting order in the extended Hubbard model on the two-dimensional graphene lattice using the variational cluster approximation (VCA) and the cellular dynamical mean-field theory (CDMFT) with an exact diagonalization solver at zero temperature. The nearest-neighbor interaction is treated using a mean-field decoupling between clusters. We compare different pairing symmetries, singlet and triplet, based on short-range pairing. VCA simulations show that the real (nonchiral), triplet $p$-wave symmetr…
We studied the effects of nonmagnetic impurities on high-temperature superconductors by solving the Bogoliubov-de Gennes equations on a two-dimensional lattice via exact diagonalization technique in a fully self-consistent way. We found that s-wave order parameter is almost unaffected by impurities at low concentrations while $d_{x^2-y^2}$-wave order parameter exhibits a strong linear decrease with impurity concentration. We evaluated the critical impurity concentration $n_i^c$ at which superconductivity ceases to be 0.1 which is in good agreement with experimental values. We also investigated…
It has been argued that inhomogeneity generally can enhance superconductivity in the cuprate high-Tc materials. To check the validity of this claim, we study d-wave superconductivity on the checkerboard Hubbard model on a square lattice using 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 in both strong and weak coupling regimes. At a given doping, the size of the d-wave order parameter manifests itself directly in the heigh…
The high-temperature superconducting cuprates are governed by intertwined striped magnetic and charge orders in addition to superconductivity. Remarkably similar behavior has also been seen in numerical calculations for the Hubbard model describing the copper-oxygen layers in these materials. Finite cluster methods typically find that spin and charge stripe order dominates, while embedded quantum cluster methods, which access the thermodynamic limit, often conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in an embedded cluster calcula…
We use exact diagonalization techniques to study the interplay between strong correlations, superconductivity, and disorder in a model system. We study an extension of the t-J model by adding an infinite-range d-wave superconductivity inducing term and disorder. Our work shows that in the clean case the magnitude of the order parameter is surprisingly small for low-hole filling, thus implying that mean-field theories might be least accurate in that important regime. We demonstrate that substantial disorder is required to destroy a d-wave superconducting state for low-hole doping. We provide th…
We investigate a two-orbital model for iron-based superconductors to elucidate the effect of interplay between electron correlation and Jahn-Teller electron-phonon coupling by using the dynamical mean-field theory combined with the exact diagonalization method. When the intra- and inter-orbital Coulomb interactions, $U$ and $U'$, increase with $U=U'$, both the local spin and orbital susceptibilities, $χ_{s}$ and $χ_{o}$, increase with $χ_{s}=χ_{o}$ in the absence of the Hund's rule coupling $J$ and the electron-phonon coupling $g$. In the presence of $J$ and $g$, there are distinct two regimes…
We investigate the electronic states of a one-dimensional two-orbital Hubbard model with band splitting by the exact diagonalization method. The Luttinger liquid parameter $K_ρ$ is calculated to obtain superconducting (SC) phase diagram as a function of on-site interactions: the intra- and inter-orbital Coulomb $U$ and $U'$, the Hund coupling $J$, and the pair transfer $J'$. In this model, electron and hole Fermi pockets are produced when the Fermi level crosses both the upper and lower orbital bands. We find that the system shows two types of SC phases, the SC \Roman{u'-large} for $U>U'$ and …
