We have studied systematically the influence of particle-hole symmetric and asymmetric kinetic terms on the ordered phases that we may observe competing or coexisting in a tetragonal system. We show that there are precise patterns of triplets of ordered phases that are accessible (i.e. it is impossible to observe two of them without the third one). We found a systematic way to predict these patterns of states and tested it by identifying at least 16 different patterns of three order parameters that necessarily coexist in the presence of the kinetic terms. We show that there are two types of general equations governing the competition of all these triplets of order parameters and we provide them.
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…
Motivated by numerical evidence of the valence bond groundstate of the two-dimensional Heisenberg pyrochlore lattice, we argue using a $t$-$J$ model that it evolves under doping into novel phases characterized by superconductivity coexisting with the underlying valence-bond solid order. A fermionic mean-field theory supplemented by exact diagonalization results provide strong arguments in favor of the stability of such supersolid phases. The resemblance with modulated superconducting patterns in high-$T_c$ cuprates as well as possible relevance to frustrated noncuprate superconductors such as …
In usual superconductors the carriers form Cooper pairs that have zero total momentum meaning that the superfluid density is homogeneous. We know for decades that it is a priori possible to observe at high fields the Fulde-Ferrel-Larkin-Ovchinikov (FFLO) state in which the superfluid density exhibits a field dependent modulation. The search for such inhomogeneous condensates in materials is the subject of tremendous excitement especially after the discovery of a promising high-field superconducting (HFSC) phase in CeCoIn$_5$. However, subsequent neutron and NMR experiments contradicted the FFL…
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 …
Relationship between the superconducting gap and the pseudogap has been the subject of controversies. In order to clarify this issue, we have studied the superconducting gap and pseudogap of the high-Tc superconductor La2-xSrxCuO4 (x=0.10, 0.14) by angle-resolved photoemission spectroscopy (ARPES). Through the analysis of the ARPES spectra above and below Tc, we have identified a superconducting coherence peak even in the anti-nodal region on top of the pseudogap of a larger energy scale. The superconducting peak energy nearly follows the pure d-wave form. The d-wave order parameter Δ_0 [defin…
We present nuclear magnetic resonance (NMR) measurements on the three distinct In sites of CeCoIn$_5$ with magnetic field applied in the [100] direction. We identify the microscopic nature of the long range magnetic order (LRO) stabilized at low temperatures in fields above 10.2 T while still in the superconducting (SC) state. We infer that the ordered moment is oriented along the $\hat c$-axis and map its field evolution. The study of the field dependence of the NMR shift for the different In sites indicates that the LRO likely coexists with a modulated SC phase, possibly that predicted by Fu…
Recent experiments on Pr$_{0.89}$LaCe$_{0.11}$CuO$_4$ observe an anisotropic spin-correlation gap and a nonmonotonic superconducting (SC) gap, which we analyze within the framework of a $t-t^{\prime}-t^{\prime\prime}-t^{\prime\prime\prime}-t^{iv}-U$ model with a $d_{x^2-y^2}$ pairing interaction including a third harmonic contribution. By introducing a realistic broadening of the quasiparticle spectrum to reflect small-angle scattering, our computations explain the experimental observations, especially the presence of a maximum in the leading edge gap in the vicinity of the hot-spots. Our anal…
We present new x-ray and neutron scattering measurements of stripe order in La(1.875)Ba(0.125)CuO(4), along with low-field susceptibility, thermal conductivity, and specific heat data. We compare these with previously reported results for resistivity and thermopower. Temperature-dependent features indicating transitions (or crossovers) are correlated among the various experimental quantities. Taking into account recent spectroscopic studies, we argue that the most likely interpretation of the complete collection of results is that an unusual form of two-dimensional superconducting correlations…
A d-wave superconducting phase with coexisting intra-unit-cell orbital current order has the remarkable property that it supports finite size Fermi pockets of Bougoliubov quasiparticles. Experimentally detectable consequences of this include a residual $T$-linear term in the specific heat in the absence of disorder and residual features in the thermal and microwave conductivity in the low disorder limit.
High resolution measurements of the dynamic magnetic susceptibility are reported for ferromagnetic re-entrant superconductor, ErRh$_{4}$B$_{4}$. Detailed investigation of the coexisting regime reveals unusual temperature-asymmetric and magnetically anisotropic behavior. The superconducting phase appears via a series of discontinuous steps upon warming from the ferromagnetic normal phase, whereas the ferromagnetic phase develops via a gradual transition. A model based on local field inhomogeneity is proposed to explain the observations.
The interaction of the ionic lattice with the superconducting condensate is treated in terms of the electrostatic force in superconductors. It is shown that this force is similar but not identical to the force suggested by the volume difference of the normal and superconducting states. The BCS theory shows larger deviations than the two-fluid model.
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…
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.
We study the influence of diagonal disorder (random site energy) of local pair (LP) site energies on the superconducting properties of a system of coexisting local pairs and itinerant electrons described by the (hard-core) boson-fermion model. Our analysis shows that the properties of such a model with s-wave pairing can be very strongly affected by the diagonal disorder in LP subsystem (the randomness of the LP site energies). This is in contrast with the conventional s-wave BCS superconductors, which according to the Anderson's theorem are rather insensitive to the diagonal disorder (i.e. to…
Motivated by the recent discovery of noncentrosymmetric superconductors, such as $CePt_{3}Si$, $CeRhSi_{3}$ and $CeIrSi_{3}$, we investigate theoretically the impurity resonance states with coexisting $s$- and p-wave pairing symmetries. Due to the nodal structure of the gap function, we find single nonmagnetic impurity-induced resonances appearing in the local density of state (LDOS). In particular, we analyze the evolution of the local density of states for coexisting isotropic s-wave and p-wave superconducting states and compare with that of anisotropic s-wave and p-wave symmetries of the su…
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…
The recent discovery and subsequent developments of FeAs-based superconductors have presented novel challenges and opportunities in the quest for superconducting mechanisms in correlated-electron systems. Central issues of ongoing studies include interplay between superconductivity and magnetism as well as the nature of the pairing symmetry reflected in the superconducting energy gap. In the cuprate and RE(O,F)FeAs (RE = rare earth) systems, the superconducting phase appears without being accompanied by static magnetic order, except for narrow phase-separated regions at the border of phase bou…
Superconductivity in the cuprates is found to be intertwined with charge and spin density waves. Determining the interactions between the different types of order is crucial for understanding these important materials. Here, we elucidate the role of the charge density wave (CDW) in the prototypical cuprate La$_{1.885}$Sr$_{0.115}$CuO$_4$, by studying the effects of large magnetic fields ($H$) up to 24 Tesla. At low temperatures ($T$), the observed CDW peaks reveal two distinct regions in the material: a majority phase with short-range CDW coexisting with superconductivity, and a minority phase…
Temperature dependences of the optical spectra of La$_{2-x}$Sr$_x$CuO$_4$ with $x$=0.12 and 0.15 were carefully examined for a polarization parallel to the CuO$_2$-plane over a wide frequency range down to 8 cm$^{-1}$. Selection of well-characterized crystals enabled us to measure purely in-plane polarized spectra without any additional peak. The weight of superconducting (SC) condensate estimated from the missing area in $σ_1(ω$) well agrees with the estimate from the slope of $σ_2(ω$) vs 1/$ω$ plot, showing no evidence that the Ferrell-Glover-Tinkham sum-rule is violated in the optical spect…
We calculate within a mean-field theory the spectral signatures of various striped d-wave superconducting phases. We consider both in-phase and anti-phase modulations of the superconducting order across a stripe boundary, and the effects of coexisting inhomogeneous orders, including spin stripes, charge stripes, and modulated d-density-wave. We find that the anti-phase modulated d-wave superconductor exhibits zero-energy spectral weight, primarily along extended arcs in momentum space. Concomitantly, a Fermi surface appears and typically includes both open segments and closed pockets. When wea…
A model of a Fermi liquid with the fermion condensate (FC) is applied to the consideration of quasiparticle excitations in high temperature superconductors, in their superconducting and normal states. Within our model the appearance of the fermion condensate presents a quantum phase transition, that separates the regions of normal and strongly correlated electron liquids. Beyond the phase transition point the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other --- fermion condensate localized at the Fermi surface and characterized by almost d…
The long-studied Hubbard model is one of the simplest models of copper-oxide superconductors. However, the connection between the model and the experimental phase diagram is still under debate, in particular regarding the existence and extent of the $d$-wave superconducting phase. Recent rapid progress in improving the accuracy of numerical solvers has opened a way to answer this question reliably. Here, we study the hole-doping concentration ($δ$) dependence of the Hubbard model in the ground states on a square lattice at strong coupling $U/t=10$, for the on-site interaction $U$ and the trans…
We have measured the complex conductivity of a BSCCO(2212) thin film between 0.2 and 1.0 THz. We find the conductivity in the superconducting state to be well described as the sum of contributions from quasiparticles, the condensate, and order parameter fluctuations which draw 30% of the spectral weight from the condensate. An analysis based on this decomposition yields a quasiparticle scattering rate on the order of k_(B)*T/(hbar) for temperatures below Tc.
A study of the dependence of the heat capacity Cp(alpha) on field angle in LuNi2B2C reveals an anomalous disorder effect. For pure samples, Cp(alpha) exhibits a fourfold variation as the field H < Hc2 is rotated in the [001] plane, with minima along <100> (alpha = 0). A slightly disordered sample, however, develops anomalous secondary minima along <110> for H > 1 T, leading to an 8-fold pattern. The anomalous pattern is discussed in terms of coexisting superconducting gap anisotropy and non-local effects.
We study the interplay of nematic and superconducting order in the two-dimensional Hubbard model and show that they can coexist, especially when superconductivity is not the energetically dominant phase. Due to a breaking of the $C_4$ symmetry, the coexisting phase inherently contains admixture of the $s$-wave pairing components. As a result, the superconducting gap exhibits very non-standard features including changed nodal directions. Our results also show that in the optimally doped regime the superconducting phase is typically unstable towards developing nematicity (breaking of the $C_4$ s…
The implications of the spin exciton mechanism are exposed in the context of a Spin Density Wave (SDW) instability occurring inside the superconducting phase of a layered heavy electron compound. In this model a magnetic field serves as a tuning parameter bringing the system to the point where the transverse spin correlations are enhanced due to dx2 -y2 -wave superconductivity and induces an instability to a phase with coexisting superconductivity and SDW order. The model considers electrons in a crystal with antiferromagnetic interactions and provides restrictions on the Fermi surface charact…
Recently, it has been reported that the low-temperature high-magnetic field phase in CeCoIn5 (Q-phase), has spin-density wave (SDW) order that only exists within this phase. This indicates that the SDW order is the result of the development of pair density wave (PDW) order in the superconducting phase that coexists with d-wave superconductivity. Here we develop a phenomenological theory for these coexisting orders. This provides selection rules for the PDW order and further shows that the detailed structure of this order is highly constrained. We then apply our theory to the the vortex phase. …
We study the single-particle spectral properties of a model for coexisting AFM and ICDW critical fluctuations coupled to electrons, which naturally arises in the context of the stripe-quantum-critical-point scenario for high-Tc superconducting materials. Within a perturbative approach, we show that the on-shell inverse scattering time deviates from the normal Fermi-liquid behavior near the points of the Fermi surface connected by the characteristic wave-vectors of the critical fluctuations (hot spots). The anomalous behavior is stronger when the hot spots are located near singular points of th…
We provide a quasi-one-dimensional model which can support a pair-density-wave (PDW) state, in which the superconducting (SC) order parameter modulates periodically in space, with gapless Bogoliubov quasiparticle excitations. The model consists of an array of strongly-interacting one-dimensional systems, where the one-dimensional systems are coupled to each other by local interactions and tunneling of the electrons and Cooper pairs between them. Within the interchain mean-field theory, we find several SC states from the model, including a conventional uniform SC state, PDW SC state, and a coex…
Intrinsic magnetization of the superconducting condensate in Fe(Te,Se)
State University of New York, Albany（纽约州立大学奥尔巴尼分校）；City College of the City University of New York（纽约市立学院）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Stony Brook University（石溪大学）；National Institute for Materials Science（国立材料研究所）
It is shown that exciton condensates exhibit an incredible richness in the role that fundamental symmetries play whether manifest or broken. We investigate the appearance of the singlet and the triplet excitonic condensates under spin-orbit coupling (SOC) and consider realistic couplings to the radiation field as manipulated by the fundamental symmetries related to spin, time, orbital and particle degrees of freedom. The role of the strong SOC in inducing a ground state with coexisting singlet and triplet components is shown. It is also shown that the ground state of an excitonic condensate, i…
Thinning crystalline materials to two dimensions (2D) creates a rich playground for electronic phases, including charge, spin, superconducting, and topological order. Bulk materials hosting charge density waves (CDWs), when reduced to ultrathin films, have shown CDW enhancement and tunability. However, charge order confined to only 2D remains elusive. Here we report a distinct charge ordered state emerging in the monolayer limit of $1T$-VSe$_2$. Systematic scanning tunneling microscopy experiments reveal that bilayer VSe$_2$ largely retains the bulk electronic structure, hosting a tri-directio…
Interplay of Rashba spin-orbit coupling and Coulomb interaction in topological spin-triplet excitonic condensates
Natural faculty of Science, Langson college of education（朗山师范学院自然科学系）；Department of Theoretical Physics, VNUHCM-University of Science（越南国立大学胡志明市理工大学理论物理系）；Institute of Research and Development, Duy Tan University（戴南大学研发院）；Faculty of Natural Sciences, Duy Tan University（戴南大学自然科学学院）
