Pseudogap Phenomena Research Articles

Staggered Flux State in Two-Dimensional Hubbard Models

The stability and other properties of a staggered flux (SF) state or a correlated d-density wave state are studied for the Hubbard (t-t'-U) model on extended square lattices, as a low-lying state that competes with the d(x2-y2)-wave superconductivity (d-SC) and possibly causes the pseudogap phenomena in underdoped high-Tc cuprates and organic kappa-BEDT-TTF salts. In calculations, a variational Monte Carlo method is used. In the trial wave function, a configuration-dependent phase factor, which is vital to treat a current-carrying state for a large U/t, is introduced in addition to ordinary correlation factors. Varying U/t, t'/t, and the doping rate (delta) systematically, we show that the SF state becomes more stable than the normal state (projected Fermi sea) for a strongly correlated (U/t\gtrsim 5) and underdoped (delta\lesssim 0.16) area. The decrease in energy is sizable, particularly in the area where Mott physics prevails and the circular current (order parameter) is strongly suppressed. These features are consistent with those for the t-J model. The effect of the frustration t'/t plays a crucial role in preserving charge homogeneity and appropriately describing the behavior of hole- and electron-doped cuprates and kappa-BEDT-TTF salts. We argue that the SF state does not coexist with d-SC and is not a `normal state' from which d-SC arises. We also show that a spin current (flux or nematic) state is never stabilized in the same regime.

Dip-Hump Temperature Dependence of Specific Heat and Effects of Pairing Fluctuations in the Weak-Coupling Side of a P-Wave Interacting Fermi Gas

We investigate the specific heat $C_V$ at constant volume in the normal state of a $p$-wave interacting Fermi gas. Including $p$-wave pairing fluctuations within the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that, in the weak-coupling side, $C_V$ exhibits a dip-hump behavior as a function of the temperature. While the dip is associated with the pseudogap phenomenon near $T_{\rm c}$, the hump structure is found to come from the suppression of Fermi quasiparticle scattering into a $p$-wave molecular state in the Fermi degenerate regime. Since the latter phenomenon does not occur in the ordinary $s$-wave interacting Fermi gas, it may be viewed as a characteristic phenomenon associated with a $p$-wave pairing interaction.

Superconducting correlations above Tc in the pseudogap state of Bi2Sr2CaCu2O8+δ cuprates revealed by angular-dependent magnetotunneling

We present an angular-dependent magnetotunneling technique, which facilitates unambiguous separation of superconducting (supporting circulating screening currents) and nonsuperconducting (not supporting screening currents) contributions to the pseudogap phenomenon in layered ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ cuprates. Our data indicate persistence of superconducting correlations at temperatures up to $1.5{T}_{c}$ in a form of both phase and amplitude fluctuations of the superconducting order parameter. However, despite a profound fluctuations region, only a small fraction of the pseudogap spectrum is caused by superconducting correlations, while the dominating part comes from a competing nonsuperconducting order, which does not support circulating orbital currents.

Pseudogap Phenomena Near the BKT Transition of a Two-Dimensional Ultracold Fermi Gas in the Crossover Region

We investigate strong-coupling properties of a two-dimensional ultracold Fermi gas in the normal phase. In the three-dimensional case, it has been shown that the so-called pseudogap phenomena can be well described by a (non-self-consistent) $T$-matrix approximation (TMA). In the two-dimensional case, while this strong coupling theory can explain the pseudogap phenomenon in the strong-coupling regime, it unphysically gives large pseudogap size in the crossover region, as well as in the weak-coupling regime. We show that this difficulty can be overcome when one improve TMA to include higher order pairing fluctuations within the framework of a self-consistent $T$-matrix approximation (SCTMA). The essence of this improvement is also explained. Since the observation of the BKT transition has recently been reported in a two-dimensional $^6$Li Fermi gas, our results would be useful for the study of strong-coupling physics associated with this quasi-long-range order.

Quasiparticle density of states by inversion with maximum entropy method

We propose to extract the quasiparticle density of states (DOS) of the superconductor directly from the experimentally measured superconductor-insulator-superconductor junction tunneling data by applying the maximum entropy method to the nonlinear systems. It merits the advantage of model independence with minimum a priori assumptions. Various components of the proposed method have been carefully investigated, including the meaning of the targeting function, the mock function, as well as the role and the designation of the input parameters. The validity of the developed scheme is shown by two kinds of tests for systems with known DOS. As a preliminary application to a ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ sample with its critical temperature ${T}_{c}=89\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, we extract the DOS from the measured intrinsic Josephson junction current data at temperatures of $T=4.2\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, $45\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, $55\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, $95\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, and $130\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. The energy gap decreases with increasing temperature below ${T}_{c}$, while above ${T}_{c}$, a kind of energy gap survives, which provides an angle to investigate the pseudogap phenomenon in high-${T}_{c}$ superconductors. The developed method itself might be a useful tool for future applications in various fields.

Underlying mechanisms of pseudogap phenomena and Bose-liquid superconductivity in high-Tc cuprates

We show that the high-Tc cuprates are non-BCS superconductors exhibiting distinct pseudogap (PG) behaviors (related to real and momentum space excitations) and other anomalies above Tc, novel Bose-liquid superconductivity below Tc, and also a λ-like superconducting (SC) transition at Tc similar to the λ transition in liquid 4He. In these materials, the relevant charge carriers are polarons which are bound into bosonic Cooper pairs above Tc followed by condensing into a Bose superfluid at Tc. We found that the polaronic effects and related PG weaken with increasing of the doping level and disappear in the overdoped region, where the crossover from Bose-liquid to Fermi-liquid (BCS-type) superconductivity occurs at the quantum critical point. We identify the real phase diagrams of the cuprates, the PG and vortex-like states above Tc, the novel SC state and two distinct SC phases below Tc like two superfluid phases of 3He, and explain the rich cuprate phenomenology from lightly doped to overdoped region.

Commensurate antiferromagnetic excitations as a signature of the pseudogap in the tetragonal high-Tc cuprate HgBa2CuO(4+δ).

Antiferromagnetic correlations have been argued to be the cause of the d-wave superconductivity and the pseudogap phenomena exhibited by the cuprates. Although the antiferromagnetic response in the pseudogap state has been reported for a number of compounds, there exists no information for structurally simple HgBa2CuO4+δ. Here we report neutron-scattering results for HgBa2CuO4+δ (superconducting transition temperature Tc≈71 K, pseudogap temperature T*≈305 K) that demonstrate the absence of the two most prominent features of the magnetic excitation spectrum of the cuprates: the X-shaped ‘hourglass' response and the resonance mode in the superconducting state. Instead, the response is Y-shaped, gapped and significantly enhanced below T*, and hence a prominent signature of the pseudogap state.

Pairing mechanism of the high temperature superconductors

The pairing mechanism of the high temperature superconductors is one of the most important issues in the study of the high temperature superconductivity. After the intensive investigation in the past three decades, it is now commonly accepted that the d-wave pairing in the high temperature superconductors is driven by the exchange of the antiferromagnetic spin fluctuation in the system. However, an open problem remains: how to understand the complex phase diagram of the high temperature superconductors, especially the anomalous behaviors related to the pseudogap phenomena in the under- doped regime. The key to the answer of this question lies in the local-itinerant dualism of the electron in these systems.

Pairing fluctuations and an anisotropic pseudogap phenomenon in an ultracold superfluid Fermi gas with pluralp-wave superfluid phases

We investigate superfluid properties of a one-component Fermi gas with a uniaxially anisotropic $p$-wave pairing interaction, $U_x>U_y=U_z$ (where $U_i$ ($i=x,y,z)$ is a $p_i$-wave pairing interaction). This type of interaction is considered to be realized in a $^{40}$K Fermi gas. Including pairing fluctuations within a strong-coupling $T$-matrix theory, we determine the $p_x$-wave superfluid phase transition temperature $T^{p_x}_{\rm c}$, as well as the other phase transition temperature $T_{\rm c}^{p_x+ip_y}$ ($<T_{\rm c}^{p_x}$), below which the superfluid order parameter has the $p_x+ip_y$-wave symmetry. In the normal state near $T^{p_x}_{\rm c}$, $p_x$-wave pairing fluctuations are shown to induce an anisotropic pseudogap phenomenon, where a dip structure in the angle-resolved density of states around $\omega=0$ is the most remarkable in the $p_x$ direction. In the $p_x$-wave superfluid phase ($T_{\rm c}^{p_x+ip_y}<T\le T_{\rm c}^{p_x}$), while the pseudogap in the $p_x$ direction continuously changes to the superfluid gap, the pseudogap in the perpendicular direction to the $p_x$ axis is found to continue developing, because of enhanced $p_y$-wave and $p_z$-wave pairing fluctuations around the node of the $p_x$-wave superfluid order parameter. Since pairing fluctuations are always suppressed in the isotropic $s$-wave superfluid state, this phenomenon is peculiar to an unconventional Fermi superfluid with a nodal superfluid order parameter. Since the $p$-wave Fermi superfluid is the most promising non $s$-wave pairing state in an ultracold Fermi gas, our results would contribute to understanding how the anisotropic pairing fluctuations, as well as the existence of plural superfluid phases, affect many-body properties of this unconventional Fermi superfluid.

Intra-unit-cell magnetic correlations near optimal doping in YBa2Cu3O6.85.

The pseudo-gap phenomenon in copper oxide superconductors is central to any description of these materials as it prefigures the superconducting state itself. A magnetic intra-unit-cell order was found to occur just at the pseudo-gap temperature in four cuprate high-Tc superconducting families. Here we present polarized neutron-scattering measurements of nearly optimally doped YBa2Cu3O6.85, carried out on two different spectrometers, that reveal several features. The intra-unit-cell order consists of finite-sized planar domains that are very weakly correlated along the c axis. At high temperature, only the out-of-plane magnetic components correlate, indicating a strong Ising anisotropy. An aditional in-plane response develops at low temperature, giving rise to an apparent tilt of the magnetic moment. The discovery of these two regimes puts stringent constraints, which are tightly bound to the pseudo-gap physics, on the intrinsic nature of intra-unit-cell order.

Pseudogap from ARPES experiment: Three gaps in cuprates and topological superconductivity (Review Article)

A term first coined by Mott back in 1968 a “pseudogap” is the depletion of the electronic density of states at the Fermi level, and pseudogaps have been observed in many systems. However, since the discovery of the high-temperature superconductors (HTSC) in 1986, the central role attributed to the pseudogap in these systems has meant that by many researchers now associate the term pseudogap exclusively with the HTSC phenomenon. Recently, the problem has got a lot of new attention with the rediscovery of two distinct energy scales (“two-gap scenario”) and charge density waves patterns in the cuprates. Despite many excellent reviews on the pseudogap phenomenon in HTSC, published from its very discovery up to now, the mechanism of the pseudogap and its relation to superconductivity are still open questions. The present review represents a contribution dealing with the pseudogap, focusing on results from angle resolved photoemission spectroscopy (ARPES) and ends up with the conclusion that the pseudogap in cuprates is a complex phenomenon which includes at least three different “intertwined” orders: spin and charge density waves and preformed pairs, which appears in different parts of the phase diagram. The density waves in cuprates are competing to superconductivity for the electronic states but, on the other hand, should drive the electronic structure to vicinity of Lifshitz transition, that could be a key similarity between the superconducting cuprates and iron-based superconductors. One may also note that since the pseudogap in cuprates has multiple origins there is no need to recoin the term suggested by Mott.

Phase diagram of the one-dimensional t-J model with long-range dipolar interactions

We study systematically the effect of long-range dipolar interactions on the ground-state phase diagram of the one-dimensional model by means of the density matrix renormalization group. While the basic phases described by the Luttinger parameter , namely, the repulsive Luttinger liquid (metallic phase, ), attractive Luttinger liquid (superconducting phase, ), and the phase separation , are similar to those of the conventional model, the presence of the long-range dipolar interactions leads to significant differences. i) At high-density regime, the phase boundaries of these three phases are even pushed to the large-J region; ii) at low-density regime, these phase boundaries shift toward the small-J region and, most importantly, iii) the spin-gap region spreads across the boundary of , suggesting an exotic metallic phase with spin-gap, which is absent in the conventional model. The result indicates that the long-range dipolar interactions have a significant influence on the ground-state properties of the one-dimensional model. Its implication on the pseudogap phenomenon of the hole-doped cuprates is briefly discussed.

Effects of Ca and Sr chemical doping on the average superconducting kinetic energy of YBa2Cu3O7-δ

In this brief communication we applied the MZFC(T) and MFCC(T) reversible dc magnetizations to get the average superconducting kinetic energy density, kS(T,B) of YBa2Cu3O7-δ, Y0.95Ca0.05Ba2Cu3O7-δ and YBa1.75Sr0.25Cu3O7-δ ceramic samples with the aim of study the effects of Ca and Sr doping on the kS(T,B). The MZFC(T) and MFCC(T) measurements were performed with a SQUID magnetometer from quantum design to dc magnetic fields up to 50kOe. The determination of the kS(T,B) from reversible dc magnetization is supported by virial theorem of superconductivity [kS(T,B) = – MB]. The kS(T,B) results show an common temperature profile for all the samples which is smoothly affected by the magnetic field. On the other hand the kS(T,B) results to T > Tc could not be associated to the pseudogap phenomenon. The Ca doping affects more effectively the kS(T,B) behaviour then Sr doping. A possible explanation to this feature could be associated to the fact that the hole doping promoted by Ca doping depress more considerably the superconducting state and enhances the granular character of the YBa2Cu3O7-δ superconductor than the chemical pressure effect promoted by Sr doping.

Pairing effects in the normal phase of a two-dimensional Fermi gas

In a recent experiment [M. Feld et al., Nature (London) 480, 75 (2011); B. Fr\"ohlich et al., Phys. Rev. Lett. 109, 130403 (2012)], a pairing gap was detected in a two-dimensional (2D) Fermi gas with attractive interaction at temperatures where superfluidity does not occur. The question remains open as to whether this gap is a pseudogap phenomenon or is due to a molecular state. In this paper, by using a $t\ensuremath{-}\text{matrix}$ approach, we reproduce quite well the experimental data for a 2D Fermi gas, and set the boundary between the pseudogap and molecular regimes. We also show that pseudogap phenomena occurring in 2D and 3D can be related through a variable spanning the BCS-BEC crossover in a universal way.

Hetero-pairing and pseudogap phenomena in an ultracold Fermi gas with mass imbalance

We investigate strong-coupling properties of a unitary Fermi gas consisting of two different species with different masses. Including pairing fluctuations within the self-consistent T-matrix approximation, we calculate the single-particle density of states in the normal state. We show that the pseudogap phenomenon, which is characterized by a dip structure in the density of states around ω = 0, appears more remarkably in the light mass component than in the heavy mass component. As a result, the pseudogap temperature, which is determined as the temperature at which the pseudogap disappears in the density of states, is higher in the former than in the latter. We also find that this different pseudogap temperatures lead to the existence of two kinds of pseudogap regions. That is, one is the ordinary pseudogap regime where the pseudogap appears in both the component, and the other case is that the light mass component only exhibits the pseudogap phenomenon. As the origin of these component- dependent pseudogap phenomena, we point out the importance of different Fermi temperatures between the two components. Since the formation of hetero-Cooper pairs and their condensation are expected in various systems, such as a 6Li-40K Fermi gas mixture, an exciton (polariton) gas, as well as color superconductivity, our results would be useful for the understanding of strong-coupling properties of these novel Fermi condensates.

Heteropairing and component-dependent pseudogap phenomena in an ultracold Fermi gas with different species with different masses

We investigate the superfluid phase transition and single-particle excitations in the BCS (Bareen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas with mass imbalance. In our recent paper [R. Hanai, et. al., Phys. Rev. A 88, 053621 (2013)], we showed that an extended $T$-matrix approximation (ETMA) can overcome the serious problem known in the ordinary (non-self-consistent) $T$-matrix approximation that it unphysically gives double-valued superfluid phase transition temperature $T_{\rm c}$ in the presence of mass imbalance. However, at the same time, the ETMA was also found to give the vanishing $T_{\rm c}$ in the weak-coupling and highly mass-imbalanced case. In this paper, we inspect the correctness of this ETMA result, using the self-consistent $T$-matrix approximation (SCTMA). We show that the vanishing $T_{\rm c}$ is an artifact of the ETMA, coming from an internal inconsistency of this theory. The superfluid phase transition actually always occurs, irrespective of the ratio of mass imbalance. We also apply the SCTMA to the pseudogap problem in a mass-imbalanced Fermi gas. We show that pairing fluctuations induce different pseudogap phenomena between the the light component and heavy component. We also point out that a $^6$Li-$^{40}$K mixture is a useful system for the realization of a hetero pairing state, as well as for the study of component-dependent pseudogap phenomena.

Pseudogap phenomena in ultracold atomic Fermi gases

The pairing and superfluid phenomena in a two-component ultracold atomic Fermi gas is an analogue of Cooper pairing and superconductivity in an electron system, in particular, the high $T_c$ superconductors. Owing to the various tunable parameters that have been made accessible experimentally in recent years, atomic Fermi gases can be explored as a prototype or quantum simulator of superconductors. It is hoped that, utilizing such an analogy, the study of atomic Fermi gases may shed light to the mysteries of high $T_c$ superconductivity. One obstacle to the ultimate understanding of high $T_c$ superconductivity, from day one of its discovery, is the anomalous yet widespread pseudogap phenomena, for which a consensus is yet to be reached within the physics community, after over 27 years of intensive research efforts. In this article, we shall review the progress in the study of pseudogap phenomena in atomic Fermi gases in terms of both theoretical understanding and experimental observations. We show that there is strong, unambiguous evidence for the existence of a pseudogap in strongly interacting Fermi gases. In this context, we shall present a pairing fluctuation theory of the pseudogap physics and show that it is indeed a strong candidate theory for high $T_c$ superconductivity.

Resonant x-ray scattering study of charge-density wave correlations inYBa2Cu3O6+x

We report the results a comprehensive study of charge density wave (CDW) correlations in untwinned YBCO6+x single crystals with 0.4<x<0.99 using Cu-L3 edge resonant x-ray scattering (RXS). Evidence of CDW formation is found for 0.45<x<0.93, but not for samples with x<0.44 that exhibit incommensurate spin-density-wave order, and in slightly overdoped samples with x=0.99. This suggests the presence of two proximate zero-temperature CDW critical points at doping pc1~0.08 and pc2~0.18. The CDW reflections are observed at incommensurate in-plane wave vectors (d_a, 0) and (0, d_b). Both decrease linearly with increasing doping, in agreement with recent reports on Bi-based high-Tc superconductors, but in sharp contrast to the behavior of the 214 family. The CDW intensity and correlation length exhibit maxima at p~0.12, coincident with a plateau in the superconducting transition temperature Tc. The onset temperature of the CDW reflections depends non-monotonically on p, with a maximum of~160 K for p~0.12. The RXS reflections exhibit a uniaxial intensity anisotropy. We further observe a depression of CDW correlations upon cooling below Tc, and (for samples with p> 0.09) an enhancement of the signal when an external magnetic field up to 6 T is applied in the superconducting state. For samples with p~0.08, where prior work has revealed a field-enhancement of incommensurate magnetic order, the RXS signal is field-independent. This supports a previously suggested scenario in which incommensurate charge and spin orders compete against each other, in addition to individually competing against. We discuss the relationship of these results to stripe order 214, the pseudogap phenomenon, superconducting fluctuations, and quantum oscillations.

Low-temperature pseudogap phenomenon: precursor of high-Tc superconductivity

In this paper, we try to understand the pseudogap phenomenon observed in the cuprate superconductor through a model study. Specifically, we explore the so-called low-temperature pseudogap state by turning off the superconducting (SC) off diagonal long range order in an ansatz state for the t–J model (Weng 2011 New J. Phys. 13 103039). Besides strong non-Gaussian SC fluctuations, the resulting state also exhibits a systematic pseudogap behavior in both spin and charge degrees of freedom, manifested in the uniform spin susceptibility, specific heat, non-Drude resistivity, Nernst effect, as well as the quantum oscillation associated with small Fermi pockets emerging in strong magnetic fields, etc. These anomalous ‘normal state’ properties are found in qualitative consistency with experimental measurements in the cuprates. Such a model study establishes an intrinsic connection between the peculiar pseudogap properties and the non-BCS nature of the SC ground state. A critical comparison with other approaches to the doped Mott insulator is also made.

Photo-enhanced antinodal conductivity in the pseudogap state of high-Tc cuprates

A major challenge in understanding the cuprate superconductors is to clarify the nature of the fundamental electronic correlations that lead to the pseudogap phenomenon. Here we use ultrashort light pulses to prepare a non-thermal distribution of excitations and capture novel properties that are hidden at equilibrium. Using a broadband (0.5–2 eV) probe, we are able to track the dynamics of the dielectric function and unveil an anomalous decrease in the scattering rate of the charge carriers in a pseudogap-like region of the temperature (T) and hole-doping (p) phase diagram. In this region, delimited by a well-defined T*neq(p) line, the photoexcitation process triggers the evolution of antinodal excitations from gapped (localized) to delocalized quasiparticles characterized by a longer lifetime. The novel concept of photo-enhanced antinodal conductivity is naturally explained within the single-band Hubbard model, in which the short-range Coulomb repulsion leads to a k-space differentiation between nodal quasiparticles and antinodal excitations.