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By calculating dynamical structure factor of two-dimensional doped attractive Fermi-Hubbard model with Rashba spin-orbit coupling, we not only investigate collective modes and single-particle excitations of the system during the phase transition between Bardeen-Cooper-Schrieffer superfluid and topological superfluid, but also propose a universal method to measure pairing gap measurement in an optical lattice system. Our numerical results show that the area of the molecular excitation peak at the transferred momentum ${\bf q}=\left[\pi,\pi\right]$ is proportional to the square of the pairing gap in the system with Rashba SOC. In particular, this method is very sensitive to the pairing gap. This goes on verifying that this method is universal to measure the pairing gap in a doped optical lattice with Rashba SOC. These theoretical results are important for experimentally measuring the pairing gap and studying the topological superfluid in an optical lattice., Comment: 12 pages, 8 figures

We theoretically investigate a one-dimensional Fulde-Ferrell Fermi superfluid at a finite effective Zeeman field $h$, and study entire dynamical excitations related to density perturbation. By calculating the density dynamic structure factor, we find anisotropic dynamical excitations in both collective modes and single-particle excitations. Along the direction of centre-of-mass momentum $p$, there are two obvious gapless collective modes with different speed. The lower collective modes is from the usual gauge symmetry breaking and has a larger speed than the one in the negative direction of $p$. The higher one is due to the direction spontaneous symmetry breaking of centre-of-mass momentum $p$, and separates two kinds of single-particle excitations in the positive $p$ direction. However, this higher mode disappears in the opposite direction of $p$, where two single-particle excitations overlap with each other. These signals of dynamical excitations can do help to distinguish Fulde-Ferrell superfluid from the conventional Bardeen-Cooper-Schrieffer superfluid in the future experiment., Comment: 7 pages, 5 figures

We theoretically calculate the dynamic structure factor of two-dimensional Rashba-type spinorbit coupled (SOC) Fermi superfluid with random phase approximation, and analyse the main characters of dynamical excitation sh own by both density and spin dynamic structure factor during a continuous phase transition between Bardeen-Cooper-Schrieffer superfluid and topological superfluid. Generally we find three different excitations, including collective phonon excitation, two-atom molecular and atomic excitations, and pair-breaking excitations due to two-branch structure of quasi-particle spectrum. It should be emphasized that collective phonon excitation is overlapped with a gapless DD type pair-breaking excitation at the critical Zeeman field hc, and is imparted a finite width to phonon peak when transferred momentum q is around Fermi vector kF. At a much larger transferred momentum (q = 4kF ), the pair-breaking excitation happens earlier than two-atom molecular excitation, which is different from the conventional Fermi superfluid without SOC effect., Comment: 10 pages, 8 figures. arXiv admin note: text overlap with arXiv:2210.10407

By calculating the dynamical structure factor along the high symmetry directions in the Brillouin zone, the dynamical excitations of attractive Fermi-Hubbard model in a two-dimensional square optical lattice are studied with random phase approximation. {Two kinds of collective modes are investigated, including a Goldstone phonon mode at transferred momentum ${\bf q}=\left[0,0\right]$ and a roton mode at ${\bf q}=\left[\pi,\pi\right]$. The phonon origins from the spontaneously U(1) symmetry breaking of pairing gap, and its speed is suppressed by the interaction strength. The collective roton mode origins from the breaking of a global pseudospin SU(2) symmetry.} Dynamical excitations at ${\bf q}=\left[\pi,\pi\right]$ consist of a sharp roton molecular peak in the low-energy region and a broad atomic excitation band in the higher energy region. Furthermore, the weight of the roton molecular peak decreases monotonically with increasing the hopping strength, while the weight of the atomic excitations increases quickly. Interestingly we check that the area covered by the roton molecular peak scales with the square of the pairing gap, which is also true in the system with spin-orbit coupling. This conclusion paves a potential way to measure the pairing gap of lattice system experimentally by measuring the dynamical structure factor at ${\bf q}=\left[\pi,\pi\right]$., Comment: 12 pages, 9 figures

Based on the two-dimensional (2D) attractive Fermi-Hubbard model with Rashba spin-orbit coupling (SOC), the SOC strength and Zeeman field dependences of the phase diagram are investigated by calculating the pairing gap self-consistently. The results reveal that the phase transition from the BCS superfluid to the topological superfluid happens under proper Zeeman field strength and SOC strength. In particular, in contrast to the BCS superfluid decreasing monotonically as the SOC strength increasing, the topological superfluid region shows a dome with the SOC strength increasing. An optimal region in the phase diagram to find the topological superfluid can be found, which is important to realize the topological superfluid in optical lattice experimentally. Then we obtain the change of both band structure and density of states (DOS) during the topological phase transition, and explain the four peaks of DOS in the topological superfluid by the topology change of the low-energy branch of quasiparticle energy spectra. Moreover, the topological superfluid can be suppressed by the doping concentration., Comment: 15 pages,9 figures

We theoretically calculate the density dynamic structure factor of one-dimensional Fermi superfluid with Raman-type spin-orbit coupling, and analyze its main dynamical character during phase transition between Bardeen-Cooper-Schrieffer superfluid and topological superfluid. Our theoretical results display four kinds of single-particle excitations induced by the two-branch structure of single-particle spectrum, and the cross single-particle excitation is much easier to be seen in the spin dynamic structure factor at a small transferred momentum. Also we find a new roton-like collective mode emerges at a fixed transferred momentum $q \simeq 2k_F$, and it only appears once the system enters the topological superfluid state. The occurrence of this roton-like excitation is related to switch of global minimum in single-particle spectrum from $k=0$ to $k \simeq 2k_F$.

We theoretically investigate dynamic structure factors of a strongly interacting Fermi superfluid near an orbital Feshbach resonance with random phase approximation, and find their dynamical characters during the phase transition between a balanced conventional Bardeen-Cooper-Schrieffer superfluid and a polarized Sarma superfluid by continuously varying the chemical potential difference of two spin components. In a BEC-like regime of the BCS superfluid, dynamic structure factors can do help to distinguish the in-phase ground state from the out-of-phase metastable state by the relative location of molecular excitation and Leggett mode, or the minimum energy to break a Cooper pair. In the phase transition between BCS and Sarma superfluid, we find the dynamic structure factor of Sarma superfluid has its own specific gapless excitation at a small transferred momentum which is mixed with the collective phonon excitation, and also a relatively strong atomic excitation at a large transferred momentum because of the existence of unpaired Fermi atoms, these signals can be used to differentiate Sarma superfluid from BCS superfluid., Comment: 9 pages, 7 figures

We theoretically generalize a systematic language to describe the phase-imprinting technique to investigate the dynamical generation of solitons in a one-dimensional Raman-type spin-orbit-coupled Fermi superfluid. We check our method with the simulation of time-dependent Bogoliubov-de Gennes equations and find that our method not only can generate stable dark and even gray solitons in a conventional Fermi superfluid by controlling the transferred phase jump but also is feasible to create a stable dark soliton in both BCS and topological states of a spin-orbit-coupled Fermi superfluid. We also discuss the physical implication of our method., Comment: 10 pages, 12 figures

Based on random phase approximation (RPA), we numerically calculate dynamical structure factors of a balanced two-dimensional (2D) Fermi superfluid, and discuss their energy, momentum and interaction strength dependence in the 2D BEC-BCS crossover. At a small transferred momentum, a stable Higgs mode is observed in the unitary 2D Fermi superfluid gas where the particle-hole symmetry is not satisfied. Stronger interaction strength will make the visibility of the dispersion of Higgs mode harder to be observed. We also discuss the dimension effect and find that the signal of the Higgs mode in two dimension is more obvious than that in 3D case. At a large transferred momentum regime, stronger interaction strength will induce the weight of the molecules excitation increasing, while in verse the atomic one decreasing, which shows the pairing information of Fermi superfluid. The theoretical results qualitatively agree with the corresponding Quantum Monte Carlo data., Comment: 15 pages and 9 figures

One of the central issues in the recent study of cuprate superconductors is the interplay of charge order with superconductivity. Here the interplay of charge order with superconductivity in cuprate superconductors is studied based on the kinetic-energy-driven superconducting (SC) mechanism by taking into account the intertwining between the pseudogap and SC gap. It is shown that the appearance of the Fermi pockets is closely associated with the emergence of the pseudogap. However, the distribution of the spectral weight of the SC-state quasiparticle spectrum on the Fermi arc, or equivalently the front side of the Fermi pocket, and back side of Fermi pocket is extremely anisotropic, where the most part of the spectral weight is located around the tips of the Fermi arcs, which in this case coincide with the hot spots on the electron Fermi surface (EFS). In particular, as charge order in the normal-state, this EFS instability drives charge order in the SC-state, with the charge-order wave vector that is well consistent with the wave vector connecting the hot spots on the straight Fermi arcs. Furthermore, this charge-order state is doping dependent, with the charge-order wave vector that decreases in magnitude with the increase of doping. Although there is a coexistence of charge order and superconductivity, this charge order antagonizes superconductivity. The results from the SC-state dynamical charge structure factor indicate the existence of a quantitative connection between the low-energy electronic structure and collective response of the electron density. The theory also shows that the pseudogap and charge order have a root in common, they and superconductivity are a natural consequence of the strong electron correlation., Comment: 13 pages, eight figures. arXiv admin note: text overlap with arXiv:1705.11072

The correlation between the charge-order wave vector Q_{CD} and second-neighbor hopping t' in cuprate superconductors is studied based on the t-t'-J model. It is shown that the magnitude of the charge-order wave vector Q_{CD} increases with the increase of t', and then the experimentally observed differences of the magnitudes of the charge-order wave vector Q_{CD} among the different families of cuprate superconductors at the same doping concentration can be attributed to the different values of t'., Comment: 5 pages, 3 figures, accepted for publication in the special issue of Journal of Superconductivity and Novel Magnetism for the International Conference of superstripes 2017

It has become clear that the anomalous properties of cuprate superconductors are intimately related to the formation of a pseudogap. Within the framework of the kinetic-energy-driven superconducting mechanism, the effect of the pseudogap on the electronic Raman response of cuprate superconductors in the superconducting-state is studied by taking into account the interplay between the superconducting gap and pseudogap. It is shown that the low-energy spectra almost rise as the cube of energy in the B_{1g} channel and linearly with energy in the B_{2g} channel. However, the pseudogap is strongly anisotropic in momentum space, where the magnitude of the pseudogap around the nodes is smaller than that around the antinodes, which leads to that the low-energy spectral weight of the B_{1g} spectrum is suppressed heavily by the pseudogap, while the pseudogap has a more modest effect on the electronic Raman response in the B_{2g} orientation., Comment: 7 pages, 2 figures,added references and discussions, accepted for publication in Phil. Mag. Lett

Superconductivity in copper oxides emerges on doping holes or electrons into their Mott insulating parent compounds. The spin excitations are thought to be the mediating glue for the pairing in superconductivity. Here the momentum and doping dependence of the dynamical spin response in the electron-doped cuprate superconductors is studied based on the kinetic-energy-driven superconducting mechanism. It is shown that the dispersion of the low-energy spin excitations changes strongly upon electron doping, however, the hour-glass-shaped dispersion of the low-energy spin excitations appeared in the hole-doped side is absent in the electron-doped case due to the electron-hole asymmetry. In particular, the commensurate resonance appears in the superconducting-state with the resonance energy that correlates with the dome-shaped doping dependence of the superconducting gap. Moreover, the spectral weight and dispersion of the high-energy spin excitations in the superconducting-state are comparable with those in the corresponding normal-state, indicating that the high-energy spin excitations do not play an important part in the pair formation., Comment: 9 pages, 6 figures, added discussions, accepted for publication in Journal of Low Temperature Physics. arXiv admin note: text overlap with arXiv:1405.7448

One of the most intriguing puzzle is why there is a coexistence of Fermi arcs and Fermi pockets in the pseudogap phase of cuprate superconductors? This puzzle is calling for an explanation. Based on the t-J model in the fermion-spin representation, the coexistence of the Fermi arcs and Fermi pockets in cuprate superconductors is studied by taking into account the pseudogap effect. It is shown that the pseudogap induces an energy band splitting, and then the poles of the electron Green's function at zero energy form two contours in momentum space, however, the electron spectral weight on these two contours around the antinodal region is gapped out by the pseudogap, leaving behind the low-energy electron spectral weight only located at the disconnected segments around the nodal region. In particular, the tips of these disconnected segments converge on the hot spots to form the closed Fermi pockets, generating a coexistence of the Fermi arcs and Fermi pockets. Moreover, the single-particle coherent weight is directly related to the pseudogap, and grows linearly with doping. The calculated result of the overall dispersion of the electron excitations is in qualitative agreement with the experimental data. The theory also predicts that the pseudogap-induced peak-dip-hump structure in the electron spectrum is absent from the hot-spot directions., Comment: 11 pages, 8 figures, added discussions and new reference

The study of superconductivity arising from doping a Mott insulator has become a central issue in the area of superconductivity. Within the framework of the kinetic-energy-driven superconducting mechanism, we discuss the thermodynamic properties in triangular-lattice superconductors. It is shown that a sharp peak in the specific-heat appears at the superconducting transition temperature Tc, and then the specific-heat varies exponentially as a function of temperature for the temperatures T

The recently discovered charge order is a generic feature of cuprate superconductors, however, its microscopic origin remains debated. Within the framework of the fermion-spin theory, the nature of charge order in the pseudogap phase and its evolution with doping are studied by taking into account the electron self-energy (then the pseudogap) effect. It is shown that the antinodal region of the electron Fermi surface is suppressed by the electron self-energy, and then the low-energy electron excitations occupy the disconnected Fermi arcs located around the nodal region. In particular, the charge-order state is driven by the Fermi-arc instability, with a characteristic wave vector corresponding to the hot spots of the Fermi arcs rather than the antinodal nesting vector. Moreover, although the Fermi arc increases its length as a function of doping, the charge-order wave vector reduces almost linearity with the increase of doping. The theory also indicates that the Fermi arc, charge order, and pseudogap in cuprate superconductors are intimately related each other, and all of them emanates from the electron self-energy due to the interaction between electrons by the exchange of spin excitations., Comment: 10 pages, 8 figures, added comments and reference, accepted for publication in Philosophical Magazine. arXiv admin note: text overlap with arXiv:1502.02903

A long-standing unsolved problem is how a microscopic theory of superconductivity in cuprate superconductors based on the charge-spin separation can produce a large electron Fermi surface. Within the framework of the kinetic-energy driven superconducting mechanism, a full charge-spin recombination scheme is developed to fully recombine a charge carrier and a localized spin into a electron, and then is employed to study the electronic structure of cuprate superconductors in the superconducting-state. In particular, it is shown that the underlying electron Fermi surface fulfills Luttinger's theorem, while the superconducting coherence of the low-energy quasiparticle excitations is qualitatively described by the standard d-wave Bardeen-Cooper-Schrieffer formalism. The theory also shows that the observed peak-dip-hump structure in the electron spectrum and Fermi arc behavior in the underdoped regime are mainly caused by the strong energy and momentum dependence of the electron self-energy., Comment: 14 pages, 7 figures. Updated references, accepted for publication in Physica C. arXiv admin note: text overlap with arXiv:1501.02420

Superconductivity in cuprate superconductors occurs upon charge-carrier doping Mott insulators, where a central question is what mechanism causes the loss of electrical resistance below the superconducting (SC) transition temperature? In this review, we attempt to summarize the basic idea of the kinetic-energy driven SC mechanism in the description of superconductivity in cuprate superconductors. The mechanism of the kinetic-energy driven superconductivity is purely electronic without phonons, where the charge-carrier pairing interaction arises directly from the kinetic energy by the exchange of spin excitations in the higher powers of the doping concentration. This kinetic-energy driven d-wave SC-state is controlled by both the SC gap and quasiparticle coherence, which leads to that the maximal SC transition temperature occurs around the optimal doping, and then decreases in both the underdoped and overdoped regimes. In particular, the same charge-carrier interaction mediated by spin excitations that induces the SC-state in the particle-particle channel also generates the normal-state pseudogap state in the particle-hole channel. The normal-state pseudogap crossover temperature is much larger than the SC transition temperature in the underdoped and optimally doped regimes, and then monotonically decreases upon the increase of doping, eventually disappearing together with superconductivity at the end of the SC dome. This kinetic-energy driven SC mechanism also indicates that the strong electron correlation favors superconductivity, since the main ingredient is identified into a charge-carrier pairing mechanism not from the external degree of freedom such as the phonon but rather solely from the internal spin degree of freedom of the electron. The typical properties of cuprate superconductors discussed within the framework of the kinetic-energy driven SC mechanism are also reviewed., Comment: 81 pages, 30 figures, Review article, Updated references

The asymmetric tunneling in cuprate superconductors is studied based on the kinetic energy driven superconducting mechanism. By taking into account the interplay between the superconducting gap and normal-state pseudogap, the essential feature of the evolution of the asymmetric tunneling with doping and temperature is qualitatively reproduced. In particular, the asymmetry of the tunneling spectrum in the underdoped regime weakens with increasing doping, and then the symmetric tunneling spectrum recovers in the heavily overdoped regime. The theory also shows that the asymmetric tunneling is a natural consequence due to the presence of the normal-state pseudogap., Comment: 6 pages, 4 figures, added discussions and references, accepted for publication in Physica C

A long-standing puzzle is why there is a difference between the optimal doping \delta_{optimal}=0.15 for the maximal superconducting (SC) transition temperature Tc and the critical doping \delta_{critical}=0.19 for the highest superfluid density \rho_s in cuprate superconductors? This puzzle is calling for an explanation. Within the kinetic energy driven SC mechanism, it is shown that except the quasiparticle coherence, \rho_s is dominated by the bare pair gap, while Tc is set by the effective pair gap. By calculation of the ratio of the effective and the bare pair gaps, it is shown that the coupling strength decreases with increasing doping. This doping dependence of the coupling strength induces a shift from the critical doping for the maximal value of the bare pair gap parameter to the optimal doping for the maximal value of the effective pair gap parameter, which leads to a difference between the optimal doping for the maximal Tc and the critical doping for the highest \rho_s., Comment: 5 pages, 4 figures

The particle-hole asymmetry electronic state of cuprate superconductors and the related doping and temperature dependence of the Fermi arc length are studied based on the kinetic energy driven superconducting mechanism. By taking into account the interplay between the SC gap and normal-state pseudogap, the essential feature of the evolution of the Fermi arc length with doping and temperature is qualitatively reproduced. It is shown that the particle-hole asymmetry electronic state is a natural consequence due to the presence the normal-state pseudogap in the particle-hole channel. The Fermi arc length increases with increasing temperatures below the normal-state pseudogap crossover temperature $T^{*}$, and it covers the full length of the Fermi surface for $T>T^{*}$. In particular, in analogy to the temperature dependence of the Fermi arc length, the low-temperature Fermi arc length in the underdoped regime increases with increasing doping, and then it evolves into a continuous contour in momentum space near the end of the superconducting dome. The theory also predicts an almost linear doping dependence of the Fermi arc length., Comment: 9 pages, 8 figures

Within the framework of the kinetic energy driven superconducting mechanism, the doping dependence of the electromagnetic response in the electron-doped cuprate superconductors is studied. It is shown that although there is an electron-hole asymmetry in the phase diagram, the electromagnetic response in the electron-doped cuprate superconductors is similar to that observed in the hole-doped cuprate superconductors. The superfluid density depends linearly on temperature, except for the strong deviation from the linear characteristics at the extremely low temperatures., Comment: 6 pages, 2 figures

The doping and temperature dependence of the thermodynamic properties in cuprate superconductors is studied based on the kinetic energy driven superconducting mechanism. By considering the interplay between the superconducting gap and normal-state pseudogap, the some main features of the doping and temperature dependence of the specific-heat, the condensation energy, and the upper critical field are well reproduced. In particular, it is shown that in analogy to the domelike shape of the doping dependence of the superconducting transition temperature, the maximal upper critical field occurs around the optimal doping, and then decreases in both underdoped and overdoped regimes. Our results also show that the humplike anomaly of the specific-heat near superconducting transition temperature in the underdoped regime can be attributed to the emergence of the normal-state pseudogap in cuprate superconductors., Comment: 8 pages, 7 figures, typos corrected and added reference, accepted for publication in Physica C

The interplay between the superconducting gap and normal-state pseudogap in cuprate superconductors is studied based on the kinetic energy driven superconducting mechanism. It is shown that the interaction between charge carriers and spins directly from the kinetic energy by exchanging spin excitations in the higher power of the doping concentration induces the normal-state pseudogap state in the particle-hole channel and superconducting state in the particle-particle channel, therefore there is a coexistence of the superconducting gap and normal-state pseudogap in the whole superconducting dome. This normal-state pseudogap is closely related to the quasiparticle coherent weight, and is a necessary ingredient for superconductivity in cuprate superconductors. In particular, both the normal-state pseudogap and superconducting gap are dominated by one energy scale, and they are the result of the strong electron correlation., Comment: 7 pages, 3 figures, added discussions and references, accepted for publication in Phys. Rev. B

The weak magnetic field induced reduction of the low-temperature superfluid density in cuprate superconductors is studied based on the kinetic energy driven superconducting mechanism. The electromagnetic response kernel is evaluated by considering both couplings of the electron charge and electron magnetic momentum with a weak magnetic field and employed to calculate the superfluid density, then the main features of the weak magnetic field induced reduction of the low-temperature superfluid density are well reproduced. The theory also shows that the striking behavior of the weak magnetic field induced reduction of the low-temperature superfluid density is intriguingly related to both depairing due to the Pauli spin polarization and nonlocal response in the vicinity of the d-wave gap nodes on the Fermi surface to a weak magnetic field., Comment: 7 pages, 3 figures, added discussions and references, accepted for publication in Phys. Rev. B

Within the t-t'-J model, the doping dependence of the Meissner effect in cuprate superconductors is studied based on the kinetic energy driven superconducting mechanism. Following the linear response theory, it is shown that the electromagnetic response consists of two parts, the diamagnetic current and the paramagnetic current, which exactly cancels the diamagnetic term in the normal state, and then the Meissner effect is obtained for all the temperature $T\leq T_{c}$ throughout the superconducting dome. By considering the two-dimensional geometry of cuprate superconductors within the specular reflection model, the main features of the doping and temperature dependence of the local magnetic field profile, the magnetic field penetration depth, and the superfluid density observed on cuprate superconductors are well reproduced. In particular, it is shown that in analogy to the domelike shape of the doping dependent superconducting transition temperature, the maximal superfluid density occurs around the critical doping $\delta\approx 0.195$, and then decreases in both lower doped and higher doped regimes., Comment: 13 pages, 5 figures