The electronically nematic order has emerged as a key feature of cuprate superconductors,however, its correlation with the fundamental properties such as the electromagnetic response remains unclear. Here the nematic-order state strength dependence of the electromagnetic response in cuprate superconductors is investigated within the framework of the kinetic-energy-driven superconductivity. It is shown that a significant anisotropy of the electromagnetic response is caused by the electronic nematicity. In particular, in addition to the pure d-wave component of the superconducting gap, the pure s-wave component of the superconducting gap is generated by the electronic nematicity, therefore there is a coexistence and competition of the d-wave component and the s-wave component. This coexistence and competition leads to that the maximal condensation energy appears at around the optimal strength of the electronic nematicity, and then decreases in both the weak and strong strength regions, which in turn induces the enhancement of superconductivity, and gives rise to the dome-like shape of the nematic-order state strength dependence of the superfluid density.
The nature of the pseudogap and its relationship with superconductivity are one of the central issues of cuprate superconductors. Recently, a possible scenario has been proposed that the pseudogap state is a distinct phase characterized by spontaneous rotational symmetry breaking called "nematicity" based on transport and magnetic susceptibility measurements, where the symmetry breaking was observed below the pseudogap temperature $T^*$. Here, we report a temperature-dependent ARPES study of nematicity in slightly overdoped Bi${}_{1.7}$Pb${}_{0.5}$Sr${}_{1.9}$CaCu${}_2$O${}_{8+δ}$ triggered by…
The cuprate superconductors are characterized by numerous ordering tendencies, with the nematic order being the most distinct form of order. Here the intertwinement of the electronic nematicity with superconductivity in cuprate superconductors is studied based on the kinetic-energy-driven superconductivity. It is shown that the optimized Tc takes a dome-like shape with the weak and strong strength regions on each side of the optimal strength of the electronic nematicity, where the optimized Tc reaches its maximum. This dome-like shape nematic-order strength dependence of Tc indicates that the …
In underdoped cuprate superconductors, a rich competition occurs between superconductivity and charge density wave (CDW) order. Whether rotational symmetry breaking (nematicity) occurs intrinsically and generically or as a consequence of other orders is under debate. Here we employ resonant x-ray scattering in stripe-ordered (La,M)_2CuO_4 to probe the relationship between electronic nematicity of the Cu 3d orbitals, structure of the (La,M)_2O_2 layers, and CDW order. We find distinct temperature dependences for the structure of the (La,M)_2O_2 layers and the electronic nematicity of the CuO_2 …
We study the coexisting smectic modulations and intra-unit-cell nematicity in the pseudogap states of underdoped Bi2Sr2CaCu2O8+δ. By visualizing their spatial components separately, we identified 2πtopological defects throughout the phase-fluctuating smectic states. Imaging the locations of large numbers of these topological defects simultaneously with the fluctuations in the intra-unit-cell nematicity revealed strong empirical evidence for a coupling between them. From these observations, we propose a Ginzburg-Landau functional describing this coupling and demonstrate how it can explain the c…
To address the issues of superconducting and charge properties in high-T$_c$ cuprates, we perform a quantum Monte Carlo study of an extended three-band Emery model, which explicitly includes attractive interaction $V_{OO}$ between oxygen orbitals. In the physically relevant parameter range, we find that $V_{OO}$ acts to strongly enhance the long-range part of d-wave pairing correlation, with a clear tendency to form long-range superconducting order in the thermodynamic limit. Simultaneously, increasing $|V_{OO}|$ renders a rapid increase of the nematic charge structure factor at most of waveve…
There is now copious direct experimental evidence of various forms of (short-range) charge order in underdoped cuprate high temperature superconductors, and spectroscopic signatures of a nodal-antinodal dichotomy in the structure of the single-particle spectral functions. In this context, we analyze the Bogoliubov quasiparticle spectrum in a superconducting nematic glass. The coincidence of the superconducting "nodal points" and the nematic "cold-spots" on the Fermi surface naturally accounts for many of the most salient features of the measured spectral functions (from angle-resolved photoemi…
Nematicity has emerged as a key feature of cuprate superconductors, but its link to other fundamental properties such as superconductivity, charge order and the pseudogap remains unclear. Here we use measurements of transport anisotropy in YBa$_2$Cu$_3$O$_y$ to distinguish two types of nematicity. The first is associated with short-range charge-density-wave modulations in a doping region near $p = 0.12$. It is detected in the Nernst coefficient, but not in the resistivity. The second type prevails at lower doping, where there are spin modulations but no charge modulations. In this case, the on…
The physical properties of high-$T_c$ superconductors are affected by spatial inhomogeneities introduced by impurities. In addition, superconductivity and electronic nematicity seem intertwined in these materials. To address these questions, we apply inhomogeneous cluster dynamical mean field theory to the study of superconductivity in the Hubbard model, in the presence of a repeated impurity, at zero temperature. We find that the superconducting phase is shifted slightly away from half-filling due to the presence of the impurity. This can be explained by a competition with the Mott insulating…
The pseudogap (PG) state and its related intra-unit-cell symmetry breaking remain the focus in the research of cuprate superconductors. Although the nematicity has been studied in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, especially underdoped samples, its behavior in other cuprates and different doping regions is still unclear. Here we apply a scanning tunneling microscope to explore an overdoped (Bi, Pb)$_2$Sr$_2$CuO$_{6+δ}$ with a large Fermi surface (FS). The establishment of a nematic order and its real-space distribution is visualized as the energy scale approaches the PG.
The electronic nematic order characterized by broken rotational symmetry has been suggested to play an important role in the phase diagram of the high temperature cuprates. We study the interplay between the electronic nematic order and a spin density wave order in the presence of a magnetic field. We show that a cooperation of the nematicity and the magnetic field induces a finite coupling between the spin density wave and spin-triplet staggered flux orders. As a consequence of such a coupling, the magnon gap decreases as the magnetic field increases, and it eventually condenses beyond a crit…
Overshadowing the superconducting dome in hole-doped cuprates, the pseudogap state is still one of the mysteries that no consensus can be achieved. It has been suggested that the rotational symmetry is broken in this state and may result in a nematic phase transition, whose temperature seems to coincide with the onset temperature of the pseudogap state $T^*$ around optimal doping level, raising the question whether the pseudogap results from the establishment of the nematic order. Here we report results of resistivity measurements under uniaxial pressure on several hole-doped cuprates, where t…
During the last decade, translational and rotational symmetry-breaking phases -- density wave order and electronic nematicity -- have been established as generic and distinct features of many correlated electron systems, including pnictide and cuprate superconductors. However, in cuprates, the relationship between these electronic symmetry-breaking phases and the enigmatic pseudogap phase remains unclear. Here, we employ resonant x-ray scattering in a cuprate high-temperature superconductor La$_{1.6-x}$Nd$_{0.4}$Sr$_{x}$CuO$_{4}$ (Nd-LSCO) to navigate the cuprate phase diagram, probing the rel…
In the present paper II, we will gain an understanding of the nematicity, insulating ground state (IGS), nematicity to stripe phase transition, Fermi pockets evolution, and resistivity temperature upturn, as to be metal - insulator (fermion-boson)- crossover (MIC) phenomena for the pseudogap (PG) region of cuprates. While in the paper I [1], we obtained an understanding of the observed heat conductivity downturn, anomalous Lorentz ratio, insulator resistivity boundary, nonlinear entropy as manifestations of the same MIC. The recently observed nematicity and hidden magnetic order are related to…
Surface probes such as scanning tunneling microscopy (STM) have detected complex patterns at the nanoscale, indicative of electronic inhomogeneity, in a variety of high temperature superconductors. In cuprates, the pattern formation is associated with the pseudogap phase, a precursor to the high temperature superconducting state. Symmetry breaking (i.e. from C4 to C2) in the form of electronic nematicity has recently been implicated as a unifying theme of the pseudogap phase,[1] however the fundamental physics governing the nanoscale pattern formation has not yet been identified. Here we use u…
We use coherent pump-probe spectroscopy to measure the photoinduced reflectivity \DeltaR, and complex dielectric function, δ\in, of the electron-doped cuprate superconductor Nd_{2-x}Ce_xCuO_{4+δ} at a value of x near optimal doping, as a function of time, temperature, and laser fluence. We observe the onset of a negative \DeltaR at T=85 K, above the superconducting transition temperature, T_c, of 23 K, that exhibits a form of scaling consistent with critical fluctuations in the time domain. A positive ΔR onsets at T_c that we associate with superconducting order. We find that the two signals a…
Charge order in cuprate superconductors 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 and calculate the charge susceptibility within diagrammatic perturbation theory. In this approach, the onset of charge order is signalled by a divergence of the susceptibility. Our calculations reveal three different kinds of order: a commensurate ($q=0$) nematic order, and two incommensurate nematic p…
The defining characteristic of hole-doped cuprates is $d$-wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity (D. F. Agterberg et al., Annual Review of Condensed Matter Physics 11, 231 (2020)). Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, $d$-symmetry form factor, pair density wave (PDW) state coexisting with $d$-wave superconductivity (DSC). From this PDW+DSC model, the …
We argue that the experimentally observed nonmonotonic gap in electron-doped cuprates at optimal doping is the lowest quasiparticle excitation energy in the coexisting antiferromagnetic (AF) and superconducting (SC) state. The idea is implemented by studying the coexistence of AF and SC orders with the t-t'-t''-J model. Although the pairing gap itself is assumed to be the simplest $d$ wave which is monotonic, we have found that the quasiparticle excitation gap in the coexisting state is nonmonotonic, with the maxima around the hot spots where the Fermi surface is missing due to the AF gap. Wit…
In correlated electrons system, quantum melting of electronic crystalline phase often gives rise to many novel electronic phases. In cuprates superconductors, melting the Mott insulating phase with carrier doping leads to a quantum version of liquid crystal phase, the electronic nematicity, which breaks the rotational symmetry and exhibits a tight twist with high-temperature superconductivity. Recently, the electronic nematicity has also been observed in Fe-based superconductors. However, whether it shares a similar scenario with its cuprates counterpart is still elusive. Here, by measuring nu…
Understanding the nature of the mysterious pseudogap phenomenon is one of the most important issues associated with cuprate high-$T_c$ superconductors. Here, we report $^{17}$O nuclear magnetic resonance (NMR) studies on two planar oxygen sites in stoichiometric cuprate YBa$_2$Cu$_4$O$_8$ to investigate the symmetry breaking inside the pseudogap phase. We observe that the Knight shifts of the two oxygen sites are identical at high temperatures but different below $T_{\rm nem} \sim$ 185 K, which is close to the pseudogap temperature $T^{\ast}$. Our result provides a microscopic evidence for int…
Compton scattering provides invaluable information on the underlying Fermi surface (FS) and is a powerful tool complementary to angle-resolved photoemission spectroscopy and quantum oscillation measurements. Here we perform high-resolution Compton scattering measurements for La_{2-x}Sr_{x}CuO_{4} with x=0.08 (Tc=20K) at 300K and 150K, and image the momentum distribution function in the two-dimensional Brillouin zone. We find that the observed images cannot be reconciled with the conventional hole-like FS believed so far. Instead, our data imply that the FS is strongly deformed by the underlyin…
We point out that unidirectional bond-centered charge-density-wave states in cuprates involve electronic order in both s- and d-wave channels, with non-local Coulomb repulsion suppressing the s-wave component. The resulting bond-charge-density wave, coexisting with superconductivity, is compatible with recent photoemission and tunneling data and as well as neutron-scattering measurements, once long-range order is destroyed by slow fluctuations or glassy disorder. In particular, the real-space structure of d-wave stripes is consistent with the scanning-tunneling-microscopy measurements on both …
The Copper-Oxygen planes in cuprates have been at the center of the search for a theory of high-temperature superconductivity. We conduct an extensive study of the ground state of the three-band Hubbard (Emery) model in the underdoped regime. We focus on the magnetic and charge orders, and present results from generalized Hartree-Fock (GHF) calculations. The ground-state properties at the thermodynamic limit are challenging to pin down because of sensitivity to computational details including the shapes and sizes of the supercells. We employ large-scale computations with various technical impr…
Multilayered cuprates possess not only the highest superconducting temperature transition but also offer a unique platform to study disorder-free CuO$_2$ planes and the interplay between competing orders with superconductivity. Here, we study the underdoped trilayer cuprate HgBa$_2$Ca$_2$Cu$_3$O$_{8+ δ}$ and we report the first quantum oscillation and Hall effect measurements in magnetic field up to 88 T. A careful analysis of the complex spectra of quantum oscillations strongly supports the coexistence of an antiferromagnetic order in the inner plane and a charge order in the outer planes. Th…
Motivated by the widespread experimental observations of nematicity in strongly underdoped cuprate superconductors, we investigate the possibility of enhanced nematic fluctuations in the vicinity of a Mott insulator that displays Néel-type antiferromagnetic order. By performing a strong-coupling expansion of an effective model that contains both Cu-$d$ and O-$p$ orbitals on the square lattice, we demonstrate that quadrupolar fluctuations in the $p$-orbitals inevitably generate a biquadratic coupling between the spins of the $d$-orbitals. The key point revealed by our classical Monte Carlo simu…
Recent scanning tunnelling spectroscopy measurements [Y. Koksaka et al., Nature 454, 1072 (2008)] have shown that dispersing quasiparticle interference peaks in Fourier transformed conductance maps disappear as the bias voltage exceeds a certain threshold corresponding to the coincidence of the contour of constant quasiparticle energy with the antiferromagnetic zone boundary. Here we argue that this is caused by quasistatic short-range coexisting order present in the d-wave superconducting phase, and that the most likely origin of this order is disorder-induced incommensurate antiferromagnetis…
The pseudogap regime of the cuprate high-temperature superconductors is characterized by a variety of competing orders, the nature of which are still widely debated. Recent experiments have provided evidence for electron nematic order, in which the electron fluid breaks rotational symmetry while preserving translational invariance. Raman spectroscopy, with its ability to symmetry resolve low energy excitations, is a unique tool that can be used to assess nematic fluctuations and nematic ordering tendencies. Here, we compare results from determinant quantum Monte Carlo simulations of the Hubbar…
In light of recent experimental evidence of density wave order in the cuprates, we consider a phenomenological model of a d-wave superconductor with coexisting charge, spin or pair density wave order of various form and wave vector. We study the evolution of the nodal structure of the quasiparticle energy spectrum as a function of the amplitude of the coexisting order and perform diagrammatic linear response calculations of the low-temperature (universal-limit) thermal conductivity. The work described herein expands upon our past studies, which focused on a particular unit-cell-doubling charge…
The pseudogap phenomenon in cuprates is the most mysterious puzzle in the research of high-temperature superconductivity. In particular, whether the pseudogap is associated with a crossover or phase transition has been a long-standing controversial issue. The tetragonal cuprate HgBa$_2$CuO$_{4+δ}$, with only one CuO$_2$ layer per primitive cell, is an ideal system to tackle this puzzle. Here, we measure the anisotropy of magnetic susceptibility within the CuO$_2$ plane with exceptionally high-precision magnetic torque experiments. Our key finding is that a distinct two-fold in-plane anisotropy…
Unconventional symmetry-breaking phenomena due to nontrivial order parameters attract increasing attention in strongly correlated electron systems. Here, we predict theoretically the occurrence of nanoscale spontaneous spin-current, called the spin loop-current (sLC) order, as a promising origin of the pseudogap and electronic nematicity in cuprates. We reveal that the sLC is driven by the odd-parity electron-hole condensation that are mediated by transverse spin fluctuations around the pseudogap temperature $T^*$. At the same temperature, odd-parity magnon pair condensation occurs. The sLC or…
The spontaneous appearance of nematicity, a state of matter that breaks rotation but not translation symmetry, is one of the most intriguing property of the iron based superconductors (Fe SC), and has relevance for the cuprates as well. Establishing the critical electronic modes behind nematicity remains however a challenge, because their associated susceptibilities are not easily accessible by conventional probes. Here using FeSe as a model system, and symmetry resolved electronic Raman scattering as a probe, we unravel the presence of critical charge nematic fluctuations near the structural …
Within a model that supports stripe spin and charge order coexisting with a d$_{x^2-y^2}$-wave superconducting phase, we study the self-consistently obtained electronic structure and the associated transverse dynamical spin susceptibility. In the coexisting phase of superconducting and static stripe order, the resulting particle-hole continuum can strongly damp parts of the low-energy spin wave branches. This provides insight into recent inelastic neutron scattering data revealing the dispersion of the low-energy collective magnetic modes of lanthanum based cuprate superconductors.
The intra-unit-cell nematic phase is studied within the three-band Emery model of the cuprates with the use of the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF). According to our analysis the spontaneous $C_4$ symmetry breaking of the electronic wave function, leading to the nematic behavior, can appear due to electron correlations induced mainly by the onsite Coulomb repulsion, even in the absence of the corresponding intersite oxygen-oxygen repulsion term. The latter has been considered as the triggering factor of the nematic state formation in a numbe…
The electronic nematic phase is characterized as an ordered state of matter with rotational symmetry breaking, and has been well studied in the quantum Hall system and the high-$T_c$ superconductors, regardless of cuprate or pnictide family. The nematic state in high-$T_c$ systems often relates to the structural transition or electronic instability in the normal phase. Nevertheless, the electronic states below the superconducting transition temperature is still an open question. With high-resolution scanning tunneling microscope measurements, direct observation of vortex core in FeSe thin film…
Strongly interacting electrons can exhibit novel collective phases, among which the electronic nematic phases are perhaps the most surprising as they spontaneously break rotational symmetry of the underlying crystal lattice. The electron nematicity has been recently observed in the iron-pnictide and cuprate high-temperature superconductors. Whether such a tendency of electrons to self-organise unidirectionally has a common feature in these superconductors is, however, a highly controversial issue. In the cuprates, the nematicity has been suggested as a possible source of the pseudogap phase, w…
Motivated by the recent experiments suggesting the importance of nematicity in the phase diagrams of ironbased and cuprate high-Tc superconductors, we study the influence of nematicity on the collective modes inside the superconducting state in a non-equilibrium. In particular, we consider the signatures of collective modes in short-time dynamics of a system with competing nematic and s- and d-wave superconducting orders. In the rotationally symmetric state, we show that the Bardasis-Schrieffer mode, corresponding to the subdominant pairing, hybridizes with the nematic collective mode and merg…
We present a study of the dynamical spin susceptibility in the pseudogap region of the high-T$_c$ cuprate superconductors. We analyze and compare the formation of the so-called resonance peak, in three different ordered states: the $d_{x^2-y^2}$-wave superconducting (DSC) phase, the $d$-density wave (DDW) state, and a phase with coexisting DDW and DSC order. An analysis of the resonance's frequency and momentum dependence in all three states reveals significant differences between them. In particular, in the DDW state, we find that a nearly dispersionless resonance excitation exists only in a …
Using Monte Carlo techniques, we study a three-orbital CuO$_2$ spin-fermion model for copper-based high critical temperature superconductors that captures the charge-transfer properties of these compounds. Our studies reveal the presence of spin order in the parent compound and, more importantly, stripe spin and charge order under hole doping. Due to the $p$-$d$ orbital hybridizati on, the added holes are approximately equally distributed among the two $p$ orbitals of the oxygen atoms and the $d$ orbital of the copper atoms in the unit cell. In rectangular clusters of dimension $16\times 4$ %t…
A hallmark of the phase diagrams of quantum materials is the existence of multiple electronic ordered states, which, in many cases, are not independent competing phases, but instead display a complex intertwinement. In this review, we focus on a particular realization of intertwined orders: a primary phase characterized by a multi-component order parameter and a fluctuation-driven vestigial phase characterized by a composite order parameter. This concept has been widely employed to elucidate nematicity in iron-based and cuprate superconductors. Here we present a group-theoretical framework tha…
We discuss how stripes in cuprates can be compatible with a Fermi-liquid-like Fermi surface and, at the same time, they give rise to a one-dimensional-like pseudo Fermi surface in the momentum distribution function.
The experimentally measured phase diagram of cuprate superconductors in the temperature-applied magnetic field plane illuminates key issues in understanding the physics of these materials. At low temperature, the superconducting state gives way to a long-range charge order with increasing magnetic field; both the orders coexist in a small intermediate region. The charge order transition is strikingly insensitive to temperature, and quickly reaches a transition temperature close to the zero-field superconducting $T_c$. We argue that such a transition along with the presence of the coexisting ph…
To understand the interplay of d-wave superconductivity and antiferromagnetism in the cuprates, we consider a two-dimensional extended Hubbard model with nearest neighbor attractive interaction. Free energy of the homogeneous (coexisting superconducting and antiferromagnetic) state calculated a s a function of the band filling shows a region of of phase separation. The phase separation caused by the intersite attractive force leads to novel insights into salient features of the pseudogap phase diagram. In particular, the upper crossover curve can be identified with the phase separation boundar…
We present Raman scattering experiments in ${\rm La_{2-x}Sr_xCuO_4}$ single crystals at various doping levels x and compare the results with theoretical predictions obtained assuming an interaction mediated by spin and charge fluctuations. The light-scattering selection rules allow us to disentangle their respective contributions. We find that the glue spectral function is spin-dominated at low doping while the contribution of charge fluctuations becomes dominant around optimal doping. This indicates that the fluctuations of a nearly ordered state with coexisting spin and charge order support …
An unidentified quantum fluid designated as the pseudogap (PG) phase is produced by electron-density depletion in the CuO$_2$ antiferromagnetic insulator. Current theories suggest that the PG phase may be a pair density wave (PDW) state characterized by a spatially modulating density of electron pairs. Such a state should exhibit a periodically modulating energy gap $Δ_P(\pmb r)$ in real-space, and a characteristic quasiparticle scattering interference (QPI) signature $Λ_P(\pmb q)$ in wavevector space. By studying strongly underdoped Bi$_2$Sr$_2$CaDyCu$_2$O$_8$ at hole-density ~0.08 in the sup…
One of the most essential aspects of cuprate superconductors is a large pseudogap coexisting with a superconducting gap, then some anomalous properties can be understood in terms of the formation of the pseudogap. Within the kinetic energy driven superconducting mechanism, the effect of the pseudogap on the infrared response of cuprate superconductors in the superconducting-state is studied. By considering the interplay between the superconducting gap and pseudogap, the electron current-current correlation function is evaluated based on the linear response approach and it then is employed to c…
We present scanning tunneling spectroscopic and high-field thermodynamic studies of hole- and electron-doped (p- and n-type) cuprate superconductors. Our experimental results are consistent with the notion that the ground state of cuprates is in proximity to a quantum critical point (QCP) that separates a pure superconducting (SC) phase from a phase comprised of coexisting SC and a competing order, and the competing order is likely a spin-density wave (SDW). The effect of applied magnetic field, tunneling current, and disorder on the revelation of competing orders and on the low-energy excitat…
We generalize the theory of Cooper pairing by spin excitations in the metallic antiferromagnetic state to include situations with electron and/or hole pockets. We show that Cooper pairing arises from transverse spin waves and from gapped longitudinal spin fluctuations of comparable strength. However, each of these interactions, projected on a particular symmetry of the superconducting gap, acts primarily within one type of pocket. We find a nodeless $d_{x^2-y^2}$-wave state is supported primarily by the longitudinal fluctuations on the electron pockets, and both transverse and longitudinal flu…
Given the experimental evidence of charge order in the underdoped cuprate superconductors, we consider the effect of coexisting charge order on low-temperature thermal transport in a d-wave superconductor. Using a phenomenological Hamiltonian that describes a two-dimensional system in the presence of a Q=(π,0) charge density wave and d-wave superconducting order, and including the effects of weak impurity scattering, we compute the self-energy of the quasiparticles within the self-consistent Born approximation, and calculate the zero-temperature thermal conductivity using linear response forma…
In the framework of the slave-boson approach to the $t-t'-t''-J$ model, it is found that for electron-doped high-$T_c$ cuprates, the staggered antiferromagnetic (AF) order coexists with superconducting (SC) order in a wide doping level ranged from underdoped to nearly optimal doping at the mean-field level. In the coexisting phase, it is revealed that the spin response is commensurate in a substantial frequency range below a crossover frequency $ω_{c}$ for all dopings considered, and it switches to the incommensurate structure when the frequency is higher than $ω_{c}$. This result is in agreem…
We establish a condition for the perturbative stability of zero energy nodal points in the quasi-particle spectrum of superconductors in the presence of coexisting \textit{commensurate} orders. The nodes are found to be stable if the Hamiltonian is invariant under time reversal followed by a lattice translation. The principle is demonstrated with a few examples. Some experimental implications of various types of assumed order are discussed in the context of the cuprate superconductors.
Quasi-low-dimensional type II superconductors in parallel magnetic fields are studied when singlet pairing interactions and relatively weak triplet pairing interactions coexist. Singlet and triplet components of order parameter are mixed at high fields, and at the same time an inhomogeneous superconducting state called a Fulde-Ferrell-Larkin-Ovchinnikov state occurs. As a result, the triplet pairing interactions enhance the upper critical field of superconductivity remarkably even at temperatures far above the transition temperature of parallel spin pairing. It is found that the enhancement is…
We investigate the issues of competing orders and quantum criticality in cuprate superconductors via experimental studies of the high-field thermodynamic phase diagrams and the quasiparticle tunneling spectroscopy. Our results suggest substantial field-induced quantum fluctuations in all cuprates investigated, and their correlation with quasiparticle spectra implies that both electron- (n-type) and hole-doped (p-type) cuprate superconductors are in close proximity to a quantum critical point that separates a pure superconducting (SC) phase from a phase consisting of coexisting SC and a competi…
