Competition between superconductivity and charge order is a recurring theme in contemporary condensed matter physics. This is quintessentially captured in the attractive Hubbard model, a simple theoretical model where the competition can be directly tuned. In previous studies by the current authors, it has been suggested that the Hubbard model maps to an $SO(3)$ non-linear sigma model, where the phase competition becomes manifest. In this article, we rigorously demonstrate this mapping and use it to study thermal disordering of a supersolid. Starting with the attractive Hubbard model in the presence of an orbital field, we take the limit of strong coupling where a pseudospin description emerges. The in-plane pseudospin components represent superconducting pairing while the out-of-plane component encodes charge density wave order. We obtain an effective spin-$1/2$ Hamiltonian with ferromagnetic in-plane couplings and antiferromagnetic z-z couplings. In addition, the orbital field gives rise to a textured Dzyaloshinskii-Moriya interaction that has the same periodicity as the magnetic unit cell. In order to examine the nature of ordering in this spin model, we consider it in the classical limit. We assume slowly varying fields, leading to the $SO(3)$ non-linear sigma model description. As an application of these ideas, we study the nature of ordering using simulated annealing and classical Monte Carlo simulations. The ground state represents a supersolid with coexisting superconductivity and charge order. It can be viewed as a `meron crystal', a regular arrangement of superconducting vortices with charge-ordered cores. The coherent overlap of core regions gives rise to coherent long-ranged charge order. As the temperature is raised, this charge order is lost via a sharp phase transition in the Ising universality class.
We use quantum Monte Carlo simulations to determine the finite temperature phase diagram and to investigate the thermal and quantum melting of stripe phases in a two-dimensional hard-core boson model. At half filling and low temperatures the stripes melt at a first order transition. In the doped system, the melting transitions of the smectic phase at high temperatures and the superfluid smectic (supersolid) phase at low temperatures are either very weakly first order, or of second order with no clear indications for an intermediate nematic phase.
Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex superso…
We calculate the phase diagram of the Bose-Fermi Hubbard model on the 3d cubic lattice at fermionic half filling and bosonic unit filling by means of single-site dynamical mean-field theory. For fast bosons, this is equivalent to the Cooper problem in which the bosons can induce s-wave pairing between the fermions. We also find miscible superfluid and canted supersolid phases depending on the interspecies coupling strength. In contrast, slow bosons favor fermionic charge density wave structures for attractive fermionic interactions. These competing instabilities lead to a rich phase diagram wi…
Several material families show competition between superconductivity and other orders. When such competition is driven by doping, it invariably involves spatial inhomogeneities which can seed competing orders. We study impurity-induced charge order in the attractive Hubbard model, a prototypical model for competition between superconductivity and charge density wave order. We show that a single impurity induces a charge-ordered texture over a length scale set by the energy cost of the competing phase. Our results are consistent with a strong-coupling field theory proposed earlier in which supe…
We develop a theory for light-induced superconductivity in underdoped cuprates in which the competing bond-density wave order is suppressed by driving phonons with light. Close to a bond-density wave instability in a system with a small Fermi surface, such as a fractionalized Fermi liquid, we show that the coupling of electrons to phonons is strongly enhanced at the bond-density wave ordering wavevectors, leading to a strong softening of phonons at these wavevectors. For a model of classical phonons with anharmonic couplings, we show that the combination of strong softening and driving can lea…
Using large scale quantum Monte Carlo simulations and dual vortex theory we analyze the ground state phase diagram of hard-core bosons on the kagome lattice with nearest neighbor repulsion. In contrast to the case of a triangular lattice, no supersolid emerges for strong interactions. While a uniform superfluid prevails at half-filling, two novel solid phases emerge at densities $ρ=1/3$ and $ρ=2/3$. These solids exhibit an only partial ordering of the bosonic density, allowing for local resonances on a subset of hexagons of the kagome lattice. We provide evidence for a weakly first-order phase…
Comment on "Light-induced melting of competing stripe orders without introducing superconductivity in La$_{1.875}$Ba$_{0.125}$CuO$_4$" (arXiv:2306.07869v1)
Using a novel differential magneto-optical imaging technique we investigate the phenomenon of vortex lattice melting in crystals of Bi_2Sr_2CaCu_2O_8 (BSCCO). The images of melting reveal complex patterns in the formation and evolution of the vortex solid-liquid interface with varying field (H) or temperature (T). We believe that the complex melting patterns are due to a random distribution of material disorder or inhomogeneities across the sample, which create fluctuations in the local melting temperature or field value. To study the fluctuations in the local melting temperature / field, we h…
We use femtosecond resonant soft x-ray diffraction to measure the optically stimulated ultrafast changes of charge density wave correlations in underdoped YBa2Cu3O6.6. We find that when coherent interlayer transport is enhanced by optical excitation of the apical oxygen distortions, at least 50% of the in-plane charge density wave order is melted. These results indicate that charge ordering and superconductivity may be competing up to the charge ordering transition temperature, with the latter becoming a hidden phase that is accessible only by nonlinear phonon excitation.
Vortices in a type-II superconductor form a lattice structure that melts when the thermal displacement of the vortices is an appreciable fraction of the distance between vortices. In an anisotropic high-Tc superconductor, such as YBa2Cu3Oy, the magnetic field value where this melting occurs can be much lower than the mean-field critical field Hc2. We examine this melting transition in YBa2Cu3Oy with oxygen content y from 6.45 to 6.92, and fit the data to a theory of vortex-lattice melting. The quality of the fits indicates that the transition to a resistive state is indeed the vortex lattice m…
The electronic phase diagram of the weak spin-orbit Mott insulator (Sr(1-x)Lax)3Ir2O7 is determined via an exhaustive experimental study. Upon doping electrons via La substitution, an immediate collapse in resistivity occurs along with a narrow regime of nanoscale phase separation comprised of antiferromagnetic, insulating regions and paramagnetic, metallic puddles persisting until x~0.04. Continued electron doping results in an abrupt, first-order phase boundary where the Neel state is suppressed and a homogenous, correlated, metallic state appears with an enhanced spin susceptibility and loc…
Superconductivity occurs in the proximity of other competing orders in a wide variety of materials. Such competing phases may reveal themselves when superconductivity is locally suppressed by a magnetic field in the core of a vortex. We explore the competition between superconductivity and charge density wave order in the attractive Hubbard model on a square lattice. Using Bogoliubov-deGennes mean field theory, we study how vortex structures form and evolve as the magnetic flux is tuned. Each vortex seeds a CDW region whose size is determined by the energy cost of the competing phase. The vort…
In two-dimensional (2D) systems, the melting from a solid to an isotropic liquid can occur via an intermediate phase that retains orientational order. However, in 2D superconducting vortex lattices, the effect of orientational correlations on transport, and their interplay with disorder remain open questions. Here we study a 2D weakly pinned vortex system in amorphous MoGe films over an extensive range of temperatures ($\bm{T}$) and perpendicular magnetic fields ($\bm{H}$) using linear and nonlinear transport measurements. We find that, at low fields, the resistivity obeys the Vogel-Fulcher-Ta…
We study the phases of doped spin S=1/2 quantum antiferromagnets on the square lattice, as they evolve from paramagnetic Mott insulators with valence bond solid (VBS) order at zero doping, to superconductors at moderate doping. The interplay between density wave/VBS order and superconductivity is efficiently described by the quantum dimer model, which acts as an effective theory for the total spin S=0 sector. We extend the dimer model to include fermionic S=1/2 excitations, and show that its mean-field, static gauge field saddle points have projective symmetries (PSGs) similar to those of `sla…
Copper-oxide high TC superconductors possess a number of exotic orders co-existing with or proximal to superconductivity, whose quantum fluctuations may account for the unusual behaviors of the normal state, even affecting superconductivity. Yet, spectroscopic evidence about such quantum fluctuations remains elusive. Here, we reveal spectroscopic fingerprints for such fluctuations associated with a charge order (CO) in nearly optimally-doped Bi2Sr2CaCu2O8+d, using resonant inelastic x-ray scattering (RIXS). In the superconducting state, while the quasi-elastic CO signal decreases with temperat…
Vortex lattices, arising from repulsive inter-vortex interactions, are a canonical example of emergent phenomena. Recent studies on the cuprates have drawn attention to the appearance of competing correlations within vortex cores. This gives internal structure to each vortex and changes the nature of inter-vortex interactions, especially at short range. This can have significant consequences for vortex lattices wherein vortices are in close proximity to one another. We consider the attractive Hubbard model, a prototypical model for phase competition, with checkerboard charge density wave order…
Superconductivity in the vicinity of a competing electronic order often manifests itself with a superconducting dome, centred at a presumed quantum critical point in the phase diagram. This common feature, found in many unconventional superconductors, has supported a prevalent scenario that fluctuations or partial melting of a parent order are essential for inducing or enhancing superconductivity. Here we present a contrary example, found in IrTe2 nanoflakes of which the superconducting dome is identified well inside the parent stripe charge ordering phase in the thickness-dependent phase diag…
Nonlinear optical excitation of infrared active lattice vibrations has been shown to melt magnetic or orbital orders and to transform insulators into metals. In cuprates, this technique has been used to remove charge stripes and promote superconductivity, acting in a way opposite to static magnetic fields. Here, we show that excitation of large-amplitude apical oxygen distortions in the cuprate superconductor YBa2Cu3O6.5 promotes highly unconventional electronic properties. Below the superconducting transition temperature (Tc = 50 K), interbilayer coherence is transiently enhanced at the expen…
Superconductivity often emerges in proximity of other symmetry-breaking ground states, such as antiferromagnetism or charge-density-wave (CDW) order. However, the subtle inter-relation of these phases remains poorly understood, and in some cases even the existence of short-range correlations for superconducting compositions is uncertain. In such circumstances, ultrafast experiments can provide new insights, by tracking the relaxation kinetics following excitation at frequencies related to the broken symmetry state. Here, we investigate the transient terahertz conductivity of BaPb1-xBixO3 - a m…
