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arXiv:1905.04617 · Physical review. B./Physical review. B

Higher-form symmetries and d -wave superconductors from doped Mott insulators

Ki‐Seok Kim, Yuji Hirono

Published Aug 27, 2019• 4 citations
arXivHTMLPDF

Abstract

One path to high-temperature cuprate superconductors is doping a Mott insulator. In this paper, we study this system from the view point of higher-form symmetries. On the introduction of slave bosons, the $t\ensuremath{-}J$ model at a finite hole doping can be written in the form of U(1) gauge theories. After a duality transformation, they can be written as a generalized $BF$ theory, in which the higher-form symmetries are more manifest. We identify the emergent continuous and discrete higher-form symmetries in both $s$-wave and $d$-wave superconducting phases, expected to be realized from a doped Mott insulator. The existence of a topological order is tested by examining if there is a spontaneously broken discrete one-form symmetry. We claim that a spontaneous breaking of discrete one-form symmetry may extend to a phase that has massless Dirac fermions in the limit of large number of flavors. We discuss the possibility of a topological phase transition inside the superconducting dome of high-${T}_{c}$ cuprates.

DOI
10.1103/physrevb.100.085142

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One path to high-temperature cuprate superconductors is doping a Mott insulator. In this paper, we study this system from the view point of higher-form symmetries. On the introduction of slave bosons, the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model at a finite hole doping can be written in the form of U(1) gauge theories. After a duality transformation, they can be written as a generalized BFBFBF theory, in which the higher-form symmetries are more manifest. We identify the emergent continuous and discrete higher-form symmetries in both sss-wave and ddd-wave superconducting phases, expected to be realized from a doped Mott insulator. The existence of a topological order is tested by examining if there is a spontaneously broken discrete one-form symmetry. We claim that a spontaneous breaking of discrete one-form symmetry may extend to a phase that has massless Dirac fermions in the limit of large number of flavors. We discuss the possibility of a topological phase transition inside the superconducting dome of high-Tc{T}_{c}Tc​ cuprates.
The electronic $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}U\text{\ensuremath{-}}J$ model for the CuO2\mathrm{Cu}{\mathrm{O}}_{2}CuO2​ plane in high-Tc{T}_{c}Tc​ superconducting cuprates is elaborated. It incorporates both charge transfer UUU and exchange correlation JJJ with direct ttt and diagonal ${t}^{\ensuremath{'}}$ hopping. Making use of the Yang concept of the off diagonal long range order (ODLRO) in the reduced density matrix of the electronic system we study the loss of quantum wave coherence (and thereby superconductivity) due to the Coulomb interaction. To this aim the second-quantized Hamiltonian of the model is translated to the phase representation with the help of the topologically constrained path integral formalism. As a result the electrons emerge as composite particles consisting of of spin-carrying neutral fermions and charged topological bosons in a form of ``flux tubes'' with the quantum phase variable dual to the local electron density. The charge carrying bose field forms a collective variable representing the correlated ``sliding'' motion of the entire electronic system. We found that the spin gap $\ensuremath{\Delta}$ which appears in one-particle spectrum is the result of valence bond pairing of neutral fermions without ODLRO and deduce the solution for $\ensuremath{\Delta}$ with ``ddd-wave'' symmetry. In the bosonic sector we derive the effective quantum rotor model along with microscopic phase stiffnesses setting the energy scale for superconductivity and point out the special role played by the diagonal hopping ${t}^{\ensuremath{'}}$. We explore the relationship of the quantum rotor phase model and the Bose-Hubbard system emphasizing the ring topology of quantum phase variable. Furthermore, we obtain the ground state phase diagrams which facilitate the Mott insulator-superconductor transition scenario. We elucidate the role of the chemical potential (doping) and the huge degeneracy of the effective bosonic system in achieving ODLRO with long-range phase coherence in the presence of large Coulomb repulsion. Finally, we discuss a number of relevant issues pertaining to the the present work which include: theoretical aspects of the hierarchy of the energy scales in cuprates, ``spin-charge separation'' concepts, ``local-pair'' and ``phase-fluctuation'' scenarios as well as experimental findings related to the role of the ``ddd-wave'' symmetry of the spin gap and diagonal hopping ${t}^{\ensuremath{'}}$ in cuprates.
Proximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step toward a quantitative theory of the competition between antiferromagnetism and ddd-wave superconductivity in the cuprates, we use cellular dynamical mean-field theory to compute zero-temperature properties of the two-dimensional square lattice Hubbard model. The ddd-wave order parameter is found to scale like the superexchange coupling JJJ for on-site interaction UUU comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping, while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second neighbor hopping ${t}^{\ensuremath{'}}$, the zero-temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third neighbor hopping ${t}^{\ensuremath{''}}$ improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping vs Tc∕Tcmax{T}_{c}∕{T}_{c}^{\mathit{max}}Tc​∕Tcmax​ phase diagram of the cuprates is universal. The calculated angle-resolved photoemission spectrum displays the observed electron-hole asymmetry. The tendency to homogeneous coexistence of the superconducting and antiferromagnetic order parameters is stronger than observed in most experiments but consistent with many theoretical results and with experiments in some layered high-temperature superconductors. Clearly, our calculations reproduce important features of ddd-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard Bardeen--Cooper--Schrieffer approach. At strong coupling, ddd-wave superconductivity and antiferromagnetism naturally appear as two equally important competing instabilities of the normal phase of the same underlying Hamiltonian.
The mechanism that leads to high‐temperature superconductivity in cuprates remains an open question despite intense study for nearly two decades. Here, we introduce an SU(4) model for cuprate systems having many similarities to dynamical symmetries known to play an important role in nuclear structure physics and in elementary particle physics. Analytical solutions in three dynamical symmetry limits of this model are found: an SO(4) limit associated with antiferromagnetic order; an SU(2) limit that may be interpreted as a d‐wave pairing condensate; and an SO(5) limit that may be interpreted as a doorway state between the antiferromagnetic order and the superconducting order. It is demonstrated that with a slightly broken SO(5) but under constraint of the parent SU(4) symmetry, the model is capable of describing the rich physics that is crucial in explaining why cuprate systems that are antiferromagnetic Mott insulators at half filling become superconductors through hole doping.
We study the phases of doped spin S=1∕2S=1∕2S=1∕2 quantum antiferromagnets on the square lattice as they evolve from paramagnetic Mott insulators with valence bond solid (VBS) order at doping $\ensuremath{\delta}=0$ to superconductors at moderate $\ensuremath{\delta}$. The interplay between density-wave and VBS order and superconductivity is efficiently described by the quantum dimer model, which acts as an effective theory for the total spin S=0S=0S=0 sector. We extend the dimer model to include fermionic S=1∕2S=1∕2S=1∕2 excitations and show that its mean-field, static gauge-field saddle points have projective symmetries (PSG's) similar to those of ``slave''-particle U(1) and SU(2) gauge theories. We account for the nonperturbative effects of gauge fluctuations by a duality mapping of the S=0S=0S=0 dimer model. The dual theory of vortices has a PSG identical to that found in a previous paper [L. Balents et al., preceding paper, Phys. Rev. B 71, 144508 (2005)] by a duality analysis of bosons on the square lattice. The previous theory therefore also describes fluctuations across superconducting, supersolid, and Mott insulating phases of the present electronic model. Finally, with the aim of describing neutron scattering experiments, we present a phenomenological model for collective S=1S=1S=1 excitations and their coupling to superflow and density-wave fluctuations.
We study electronic structure of hole- and electron-doped Mott insulators in the two-dimensional Hubbard model to reach a unified picture for the normal state of cuprate high-Tc{T}_{c}Tc​ superconductors. By using a cluster extension of the dynamical mean-field theory, we demonstrate that structure of coexisting zeros and poles of the single-particle Green's function holds the key to understand Mott physics in the underdoped region. We show evidence for the emergence of non-Fermi-liquid phase caused by the topological quantum phase transition of Fermi surface by analyzing low-energy charge dynamics. The spectra calculated in a wide range of energy and momentum reproduce various anomalous properties observed in experiments for the high-Tc{T}_{c}Tc​ cuprates. Our results reveal that the pseudogap in hole-doped cuprates has a ddd-wavelike structure only below the Fermi level while it retains non-ddd-wave structure with a fully opened gap above the Fermi energy even in the nodal direction due to a zero surface extending over the entire Brillouin zone. In addition to the non-ddd-wave pseudogap, the present comprehensive identifications of the spectral asymmetry as to the Fermi energy, the Fermi arc, and the back-bending behavior of the dispersion, waterfall, and low-energy kink, in agreement with the experimental anomalies of the cuprates, do not support that these originate from (the precursors of) symmetry breakings such as the preformed pairing and the ddd-density-wave fluctuations, but support that they are direct consequences of the proximity to the Mott insulator. Several possible experiments are further proposed to prove or disprove our zero mechanism.
A d-wave superconducting ground state for a doped Mott insulator is obtained. It is distinguished from a Gutzwiller-projected Bardeen–Cooper–Schrieffer (BCS) superconductor by an explicit separation of Cooper pairing and resonating valence bond (RVB) pairing. Such a state satisfies the precise sign structure of the t–J model, just as a BCS state satisfies the Fermi–Dirac statistics. This new class of wavefunctions can be intrinsically characterized and effectively manipulated by electron fractionalization with neutral spinons and 'backflow' spinons forming a two-component RVB structure. While the former spinon is bosonic, originating from the superexchange correlation, the latter spinon is found to be fermionic, accompanying the hopping of bosonic holons. The low-lying emergent gauge fields associated with such a specific fractionalization are of mutual Chern–Simons type. Corresponding to this superconducting ground state, three types of elementary excitations are identified. Among them a Bogoliubov nodal quasiparticle is conventional, while the other two are neutral excitations of non-BCS type that play crucial roles in higher-energy/temperature regimes. Their unique experimental implications for the cuprates are briefly discussed.