We propose a non-BCS mechanism for superconductivity in hole-underdoped cuprates based on a gauge approach to the {\it t-J} model. The gluing force is an attraction between spin vortices centered on the empty sites of two opposite Néel sublattices, leading to pairing of charge carriers. In the presence of these pairs, a gauge force coming from the single occupancy constraint induces, in turn, the pairing of the spin carriers. The combination of the charge and spin pairs gives rise to a finite density of incoherent hole pairs, leading to a finite Nernst signal as precursor to superconductivity. The true superconducting transition occurs at an even lower temperature, via a 3D XY-type transition. The main features of this non-BCS description of superconductivity are consistent with the experimental results in underdoped cuprates, especially the contour plot of the Nernst signal.
Within a gauge approach to the t-J model, we propose a new, non-BCS mechanism of superconductivity for underdoped cuprates. The gluing force of the superconducting mechanism is an attraction between spin vortices on two different Néel sublattices, centered around the empty sites described in terms of fermionic holons. The spin fluctuations are described by bosonic spinons with a gap generated by the spin vortices. Due to the no-double occupation constraint, there is a gauge attraction between holon and spinon binding them into a physical hole. Through gauge interaction the spin vortex attracti…
On the basis of the observed short coherence lengths in the cuprates we argue that a BCS-Bose-Einstein condensation (BEC) crossover approach is an appropriate starting point for correcting the mean field approach of BCS and, thereby, for addressing pseudogap phenomena in these materials. Our version of the BCS-BEC approach is based on a particular Greens' function decoupling scheme which should be differentiated from others in the literature, and which yields (i) the Leggett crossover ground state (for all coupling constants g, at T=0) and (ii) BCS theory (for all $ T \leq T_c$ over a range of…
Various properties of underdoped superconducting cuprates, including the momentum-dependent pseudogap opening, indicate a behavior which is neither BCS nor Bose-Einstein condensation (BEC) like. To explain this issue we introduce a two-gap model. This model assumes an anisotropic pairing interaction among two kinds of fermions with small and large Fermi velocities representing the quasiparticles near the M and the nodal points of the Fermi surface respectively. We find that a gap forms near the M points resulting into incoherent pairing due to strong fluctuations. Instead the pairing near the …
We propose a theoretical description of the superconducting state of under- to overdoped cuprates, based on the short coherence length of these materials and the associated strong pairing fluctuations. The calculated $T_c$ and the zero temperature excitation gap $Δ(0)$, as a function of hole concentration $x$, are in semi-quantitative agreement with experiment. Although the ratio $T_c/Δ(0)$ has a strong $x$ dependence, different from the universal BCS value, and $Δ(T)$ deviates significantly from the BCS prediction, we obtain, quite remarkably, quasi-universal behavior, for the normalized supe…
The finite-frequency optical properties of the underdoped cuprates, in both the normal and superconducting state, display features which go beyond a Fermi liquid and a BCS description. We provide an understanding of these properties within a simplified analytical model, which has been evolved out of the Hubbard model and ideas based on a resonating valence bond spin liquid. We find that: 1) in underdoped samples, the missing area integrals reveal a second energy scale due to the pseudogap, not present at optimum or overdoping; 2) the real part of the optical self-energy shows a large sharp pea…
Raman and ARPES experiments have demonstrated that in superconducting underdoped cuprates nodal and antinodal regions are characterized by two energy scales instead of the one expected in BCS. The nodal scale decreases with underdoping while the antinodal one increases. Contrary to the behavior expected for an increasing energy scale, the antinodal Raman intensity decreases with decreasing doping. Using the Yang, Rice and Zhang (YRZ) model, we show that these features are a consequence of the non-conventional nature of the superconducting state in which superconductivity and pseudogap correlat…
We have considered the BCS-BEC crossover at T=0 in the framework of a lattice fermion model (the extended Hubbard model). We have analyzed the case of on-site hard core repulsion ($U=\infty$) and intersite attraction ($W<0$) in a 3D system with extended s-wave pairing symmetry. The mechanisms of density-driven and attraction-strength-driven crossover have been analyzed. We have obtained the ground state phase diagram. The analyzed quantities are: chemical potential, order parameter, coherence length and fraction of condensed particles.
We argue that the pseudogap phase may be an attribute of the non-BCS pairing of quantum-critical, diffusive fermions near the antiferromagnetic quantum critical point. We derive and solve a set of three coupled Eliashberg-type equations for spin-mediated pairing and show that in some $T$ range below the pairing instability, there is no feedback from superconductivity on fermionic excitations, and fermions remain diffusive despite of the pairing. We conject that in this regime, fluctuations of the pairing gap destroy the superconducting condensate but preserve the leading edge gap in the fermio…
The influence of the Zeeman magnetic field ($h$) on the ground state evolution of superfluid properties from the weak coupling (BCS like) to the strong coupling limit of tightly bound local pairs (LP) with increasing attraction has been studied. The analysis was carried out within the spin-polarized attractive Hubbard model, for a fixed number of particles and a $d=3$ simple cubic lattice. The broken symmetry Hartree approximation was used. For strong attraction and in the dilute limit, the homogeneous magnetized superconducting phase (SC$_M$) was found in the $(h-|U|)$ and ($P-|U|$) diagrams.
We consider the coexistence of superconductivity(SC) and spin-density wave(SDW). The SC is presumed to be of $d_{x^2-y^2}+id_{xy} (d_1 + i d_2) $ type whereas the SDW order parameter is of $BCS$/$d_{x y} $ symmetry. The Hamiltonian having such a structure is shown to have topological coexistence phases in addition to the conventional one. It is shown that the amplitudes of both the order parameters determine the nature of topological phases. A phase diagram characterizing different topological phases with their Chern numbers are obtained. The experimental realization of such topological phases…
Despite more than two decades of intensive investigations, the true nature of high temperature (high-$T_c$) superconductivity observed in the cuprates remains elusive to the researchers. In particular, in the so-called `underdoped' region, the overall behavior of superconductivity deviates $qualitatively$ from the standard theoretical description pioneered by Bardeen, Cooper and Schrieffer (BCS). Recently, the importance of phase fluctuation of the superconducting order parameter has gained significant support from various experiments. However, the microscopic mechanism responsible for the sur…
In the context of a simple model featuring an explicit, central interaction potential, and using a standard functional-integral technique, we study superconductivity with angular momentum quantum number l=2 as an emergent property of the many-body system. Our interaction potential is attractive at a finite distance r_0, and the breaking of the rotational symmetry is the result of an interplay between r_0 and the inter-particle distance r_s which we deem generic to interactions of this type. However such interplay, responsible for the preference of a d-wave state for a range of intermediate den…
Combining (1) the universal correlations between $T_{c}$ and $n_{s}/m^{*}$ (superconducting carrier density / effective mass) and (2) the pseudo-gap behavior in the underdoped region, we obtain a picture to describe superconductivity in cuprate systems in evolution from Bose-Einstein to BCS condensation. Overdoped and Zn-substituted cuprate systems show signatures of reduced superfluid density in a microscopic phase separation. Scaling of $T_{c}$ to the superfluid volume density $n_{s}$ in all these cases indicate importance of Bose condensation.
In underdoped cuprates fluctuations of the phase of the superconducting order parameter play a role due to the small superfluid density. We consider the effects of phase fluctuations assuming the exchange of spin fluctuations to be the predominant pairing interaction. Spin fluctuations are treated in the fluctuation-exchange approximation, while phase fluctuations are included by Berezinskii-Kosterlitz-Thouless theory. We calculate the stiffness against phase fluctuations, ns(omega)/m*, as a function of doping, temperature, and frequency, taking its renormalization by phase fluctuations into a…
Superconducting electron systems of solids hosting flat bands are studied, with a view to improved understanding of the fundamental physics giving rise to high-temperature superconductivity. We present a modified form of the set of Gor'kov equations of BCS theory that incorporates a Mott-like gap in the single-particle spectrum. Such a quantity is emergent in systems with flat bands having interactions repulsive in the Cooper channel, provided particle-hole symmetry is broken. The equations so obtained are applied to the elucidation of features of the two-gap structure of single-particle spect…
One of the most prominent problems in high temperature superconductivity is the nature of the pseudogap phase in underdoped regimes; particularly important is the role of phase fluctuations. The Gutzwiller-projected BCS Hamiltonian is a useful model for high temperature superconductivity due to an exact mapping to the Heisenberg model at half filling and generally a very close connection to the t-J model at moderate doping. We develop the dynamical mean field theory for the d-wave BCS Hamiltonian with on-site repulsive interaction, $U$, physically imposing the partial Gutzwiller projection. Fo…
We analyze the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (LP's) in the 2D asymmetric attractive Hubbard model, in the presence of the Zeeman magnetic field ($h$). The broken symmetry Hartree approximation is used. We also apply the Kosterlitz-Thouless (KT) scenario to determine the phase coherence temperatures. We obtain that for the spin dependent hopping integrals ($t^{\uparrow}\neq t^{\downarrow}$) the homogeneous polarized superfluid (SC$_M$) phase in the ground state for the strong attraction and lower filling can be stabil…
We study disorder effects upon the temperature behavior of the upper critical magnetic field in attractive Hubbard model within the generalized $DMFT+Σ$ approach. We consider the wide range of attraction potentials $U$ - from the weak coupling limit, where superconductivity is described by BCS model, up to the strong coupling limit, where superconducting transition is related to Bose - Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures significantly higher than superconducting transition temperature, as well as the wide range of disorder - from weak to strong, when the…
We act on the suggestion that an excitonic insulator state might separate---at very low temperatures---a semimetal from a semiconductor and ask for the nature of these transitions. Based on the analysis of electron-hole pairing in the extended Falicov-Kimball model, we show that tuning the Coulomb attraction between both species, a continuous crossover between a BCS-like transition of Cooper-type pairs and a Bose-Einstein condensation of preformed tightly-bound excitons might be achieved in a solid-state system. The precursor of this crossover in the normal state might cause the transport anom…
Understanding of the puzzling phenomenon of high temperature superconductivity requires reliable spectroscopic information about temperature dependence of the bulk electronic density of states. Here I present a comprehensive analysis of $T-$evolution of bulk electronic spectra in Bi-2212 obtained by Intrinsic Tunneling Spectroscopy on small mesa structures. Unambiguous spectroscopic information is obtained by obviation of self-heating problem and by improving the spectroscopic resolution. The obtained data indicate that the superconducting transition maintains the mean-field character down to …
Tracking unconventional superconductivity in the presence of strongly correlated Fermi arcs
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Department of Materials Science and Engineering and Materials Research Institute, The Pennsylvania State University（宾夕法尼亚州立大学材料科学与工程系及材料研究所）
The BCS to Bose-Einstein condensation (BEC) crossover of electron-hole (e-h) pairs in optically excited semiconductors is studied using the two-band Hubbard model with both repulsive and attractive interactions. Applying the self-consistent t-matrix approximation combined with a local approximation, we examine the properties of a normal phase and an excitonic instability. The transition temperature from the normal phase to an e-h pair condensed one is studied to clarify the crossover from an e-h BCS-like state to an excitonic Bose-Einstein condensation, which takes place on increasing the e-h …
We study an extended Hubbard model with on-site repulsion and nearest neighbors attraction which tries to mimic some of the experimental features of doped cuprates in the superconducting state. We draw and discuss the phase diagram as a function of the effective interactions among electrons for a wide range of doping concentrations. We locate the region which is relevant for the cuprates setting some constraints on the parameters which may be used in this kind of effective models. We also study the effects of temperature and orthorrombicity on the symmetry and magnitude of the gap function, an…
We theoretically show that a two-band system with very different masses harbors a resonant pair scattering that leads to novel pairing properties, as highlighted by the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. Most importantly, the interband pair-exchange coupling induces an effective intraband attraction in each band, enhancing the superfluidity/superconductivity. The effect, a kind of Suhl-Kondo mechanism, is specifically enhanced when the second band has a heavy mass and is incipient (lying close to, but just above, the chemical potential, $μ$), which w…
The (mean field based) BCS theory is considered one of the most successful theories in condensed matter physics. It is justified in ordinary metal superconductors the coherence length $ξ$ is large, with two important features: the order parameter (OP) and excitation gap (EG) are identical, and the pair formation and their Bose condensation take place at the same temperature Tc. It fails to explain the underdoped cuprate superconductivity: EG is finite at Tc and thus distinct from OP. Since these superconductors belong to a large class of small $ξ$ materials, this failure has the potential for …
The existence of a normal state spectral gap in underdoped cuprates raises important questions about the associated superconducting phase. For example, how does this pseudogap evolve into its below Tc counterpart? In this paper we characterize this unusual superconductor by investigating the nature of the ``residual'' pseudogap below Tc and, find that it leads to an important distinction between the superconducting excitation gap and order parameter. Our approach is based on a conserving diagrammatic BCS Bose-Einstein crossover theory which yields the precise BCS result in weak coupling at any…
We present a minimal model of a doped Mott insulator that simultaneously supports antiferromagnetic stripes and d-wave superconductivity. We explore the implications for the global phase diagram of the superconducting cuprates. At the unrestricted mean-field level, the various phases of the cuprates, including weak and strong pseudogap phases, and two different types of superconductivity in the underdoped and the overdoped regimes, find a natural interpretation. We argue that on the underdoped side, the superconductor is intrinsically inhomogeneous -- striped coexistence of of superconductivit…
Unlike the Coulomb potential that acts between all semiconductor carriers, the potential commonly used for BCS superconductors and cold atom gases acts between different fermion species only, these species differing by their spin or hyperfine index. The coboson formalism we here develop evidences that such composite bosons interact through fermion exchange only, thus rendering the structure of the Shiva diagrams that visualize their many-body effects far simpler. A separable potential is used to obtain analytical results for the $N$-coboson normalization factor and the $N$-coboson ground-state…
An array of one-dimensional conductors coupled by transverse hopping and interaction is studied with the help of a variational wave function. This wave function is devised as to account for one-dimensional correlation effects. We show that under broad conditions our system possesses the superconducting ground state even if no attraction is present. The superconducting mechanism is of many-body nature and deviates substantially from BCS. The phase diagram of the model is mapped. It consists of two ordered phases competing against each other: density wave, spin or charge, and unconventional supe…
We investigate the properties of cuprate superconductors subject to applied current, using modified Gutzwiller projected d-wave BCS states. The parent states include quasiparticle and quasihole pockets, of variationally determined size, generated by the current. We identify two different mechanisms for the destruction of superconductivity at the critical current: at high hole doping (x>0.15) the pockets grow and completely destroy the gap, in a BCS-like mechanism; in the underdoped regime, the superfluid stiffness vanishes at a maximal phase twist with pairing still intact. This result is indi…
The aim of this Ph.D. thesis was to investigate superconducting properties in the presence of Zeeman magnetic field in systems with local fermion pairing on the lattice. The study also concerned the evolution from the weak coupling (BCS-like) limit to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, both in the ground state and at finite temperatures, within the spin-polarized extended Hubbard model. The analysis was also extended to the case of spin dependent hopping integrals (mass imbalance), with special attention paid to the BCS-BEC crossover physic…
The t-J model is believed to be a minimal model that may be capable of describing the low-energy physics of the cuprate superconductors. However, although the t-J model is simple in appearance, obtaining a detailed understanding of its phase diagram has proved to be challenging. We are therefore motivated to study modifications to the t-J model such that its phase diagram and mechanism for d-wave superconductivity can be understood analytically without making uncontrolled approximations. The modified model we consider is a $t'$-$J_z$-$V$ model on a square lattice, which has a second-nearest-ne…
We derive an effective Hamiltonian for spin polarons forming in weakly doped antiferromagnets and demonstrate that the system becomes superconducting at finite doping. We argue that the driving mechanism which gives rise to superconductivity is lowering of the kinetic energy by formation of mobile antiferromagnetic spin bipolarons. That source of attraction between holes is by definition effective if the antiferromagnetic correlation length is longer than the radius of forming polarons. Notwithstanding that the attraction is strongest in the undoped system with long range order, the supercondu…
Motivated by the possibility of pressure-induced exciton condensation in intermediate-valence Tm[Se,Te] compounds we study the Falicov-Kimball model extended by a finite f-hole valence bandwidth. Calculating the Frenkel-type exciton propagator we obtain excitonic bound states above a characteristic value of the local interband Coulomb attraction. Depending on the system parameters coherence between c- and f-states may be established at low temperatures, leading to an excitonic insulator phase. We find strong evidence that the excitonic insulator typifies either a BCS condensate of electron-hol…
BCS-BEC crossover driven by small Fermi pockets of a high-Tc cuprate superconductor
The University of Tokyo（东京大学）；Tokyo University of Science（东京理科大学）；Shizuoka University（静冈大学）；Diamond Light Source Ltd（钻石光源有限公司）；Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory（斯坦福同步辐射光源，SLAC国家加速器实验室）
We consider the pairing of electrons and holes due to their Coulomb attraction in two parallel, independently gated graphene layers, separated by a barrier. At weak coupling, there exist the BCS-like pair-condensed state. Despite the fact that electrons and holes behave like massless Dirac fermions, the problem of BCS-like electron-hole pairing in graphene bilayer turns out to be rather similar to that in usual coupled semiconductor quantum wells. The distinctions are due to Berry phase of electronic wave functions and different screening properties. We estimate values of the gap in one-partic…
A full Fermi surface exists in underdoped high-temperature superconductors if the temperature T lies above the pseudogap temperature T*. Below T* only arcs of Fermi surface survive, scaling with T/T* as T -> 0, with T* displaying strong doping dependence. There is no accepted explanation for this behavior. We show that generalizing the BCS theory of normal superconductivity to include d-wave pairs and antiferromagnetism leads to the origin and doping dependence of the T* scale, and a quantitative description of Fermi arcs. These results place strong constraints on viable theories of high-tempe…
With high-Tc cuprates in mind, properties of correlated dx2-y2-wave superconducting (SC) and antiferromagnetic (AF) states are studied for the Hubbard (t-t'-U) model on square lattices, using a variational Monte Carlo method. We employ simple trial wave functions including only crucial parameters, such as a doublon-holon binding factor indispensable to describe correlated SC and normal states as doped Mott insulators. U/t, t'/t and δ(doping rate) dependence of relevant quantities are systematically calculated. As U/t increases, a sharp crossover of SC properties occurs at U_co/t \sim 10 from a…
We show how, within a preformed pair scenario for the cuprate pseudogap, the nodal and antinodal responses in angle resolved photoemission spectroscopy necessarily have very different temperature $T$ dependences. We examine the behavior and the contrasting $T$ dependences for a range of temperatures both below and above $T_c$. Our calculations are based on a fully microscopic $T$-matrix approach for addressing pairing correlations in a regime where the attraction is stronger than BCS and the coherence length is anomalously short. Previously, the distinct nodal and anti-nodal responses have pro…
In conventional superconductors, the pairing energy gap (Δ) and superconducting phase coherence go hand-in-hand. As the temperature is lowered, both the energy gap and phase coherence appear at the transition temperature T_c. In contrast, in underdoped high-T_c superconductors (HTSCs), a pseudogap appears at a much higher temperature T^*, smoothly evolving into the superconducting gap at T_c. Phase coherence on the other hand is only established at T_c, signaled by the appearance of a sharp quasiparticle (QP) peak in the excitation spectrum. Another important difference between the two types o…
In the last few years evidence has been accumulating that there are a multiplicity of energy scales which characterize superconductivity in the underdoped cuprates. In contrast to the situation in BCS superconductors, the phase coherence temperature Tc is different from the energy gap onset temperature T*. In addition, thermodynamic and tunneling spectroscopies have led to the inference that the order parameter $Δ_{sc}$ is to be distinguished from the excitation gap $Δ$; in this way, pseudogap effects persist below Tc. It has been argued by many in the community that the presence of these dist…
The emergence of the coherent quasiparticle peak and the development of the peak-dip-hump structure in the anti-nodal region below $T_{c}$ is the most prominent non-BCS signature of the underdoped high-$T_{c}$ cuprates, in which no coherent quasiparticle can be defined in the anti-nodal region above $T_{c}$. The peak-dip-hump structure has been commonly interpreted as the result of the coupling of the electron to some Bosonic mode. However, such an electron-Boson coupling picture does not answer the question of \textit{why the quasiparticle dispersion is so flat in the anti-nodal region}, a be…
A quantum spin liquid (QSL) would be an exotic stage for superconductivity. A promising candidate for a doped QSL is the organic triangular-lattice system, kappa-(BEDT-TTF)4Hg2:89Br8, which hosts a non-Fermi liquid and magnetism of a QSL nature and shows superconductivity upon cooling. Here, we report that its superfluid density is anomalously reduced, indicating the existence of substantial incoherent spectral weight and weak superconducting phase stiffness. Moreover, the ratio of the superconducting transition temperature to the nominal Fermi temperature is as large as 0.1, orders of magnitu…
Finite temperature quantum Monte Carlo simulations are performed on the anisotropic t-J model and in particular on its Ising limit. Straight site-centered stripes are imposed by an on-site potential representing external mechanisms of stripe formation. In this model, we show that, even though charge inhomogeneity exists at a high temperature, the anti-phase ordering of the spin domains between stripes occurs at a much lower temperature. The magnetic correlations at this spin ordering crossover are analyzed. The stripes show metallicity, with absence of hole attraction. Comparison between this …
Microscopic mechanism of high-temperature superconductivity revealed by ab initio studies on hole-doped multilayer cuprates HgBa$_2$Ca$_2$Cu$_3$O$_8$ under pressure
Sophia University（上智大学）；The University of Tokyo（东京大学）
It has gone almost unquestioned that superexchange in the t-J (or Hubbard) model, and not phonons, is responsible for the unconventional ("d-wave") pairing symmetry of cuprate superconductors. However a number of advanced numerical studies have not found superconductivity in the Hubbard model. On the other hand compelling experimental evidence for a strong electron-phonon interaction (EPI) has currently arrived. Here I briefly review some phonon-mediated unconventional pairing mechanisms. In particular the anisotropy of sound velocity makes the phonon-mediated attraction of electrons non-local…
We study a two-dimensional t-J model close to the Ising limit in which charge inhomogeneity is stabilized by an on-site potential e_s, by using diagonalization in a restricted Hilbert space and finite temperature Quantum Monte Carlo. Both site and bond centered stripes are considered and their similitudes and differences are analyzed. The amplitude of charge inhomogeneity is studied as e_s -> 0. Moreover, we show that the anti-phase domain ordering occurs at a much lower temperature than the formation of charge inhomogeneities and charge localization. Hole-hole correlations indicate a metallic…
The mechanism of high-Tc superconductivity is investigated with interests on the microscopic aspects of the condensation energy. The theoretical analysis is performed on the basis of the FLEX approximation which is a microscopic description of the spin-fluctuation-induced-superconductivity. Most of phase transitions in strongly correlated electron system arise from the correlation energy which is copmetitive to the kinetic energy. However, we show that the kinetic energy cooperatively induces the superconductivity in the underdoped region. This unusual decrease of kinetic energy below T_c is i…
Motivated by a scarcity of simple and analytically tractable models of superconductivity from strong repulsive interactions, we introduce a simple tight-binding lattice model of fermions with repulsive interactions that exhibits unconventional superconductivity (beyond BCS theory). The model resembles an idealized conductor-dielectric-conductor trilayer. The Cooper pair consists of electrons on opposite sides of the dielectric, which mediates the attraction. In the strong coupling limit, we use degenerate perturbation theory to show that the model reduces to a superconducting hard-core Bose-Hu…
Observing Spatial Charge and Spin Correlations in a Strongly-Interacting Fermi Gas
Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France（卡斯勒-布罗塞尔实验室，巴黎高等师范学院-巴黎文理研究大学，法国国家科学研究中心，索邦大学，法兰西公学院）；Institute of Modern Physics, Northwest University（西北大学现代物理研究所）；JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado（科罗拉多大学物理系，美国国家标准与技术研究院JILA实验室）；Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS（碰撞与聚集体反应实验室，图卢兹第三大学，法国国家科学研究中心）
