Pseudogap Region Research Articles

Observations of Charge-Density-Wave States in W6Te6 Wires.

Determining the electronic ground state of a one-dimensional system is crucial to understanding the underlying physics of electronic behavior. Here, we demonstrate the discovery of charge-density wave states in few-wire W6Te6 arrays using scanning tunneling microscopy/spectroscopy. We directly visualize incommensurate charge orders, energy gaps with prominent coherence peaks, and the picometer-scale lattice distortion in nearly disorder-free double-wire systems, thereby demonstrating the existence of Peierls-type charge density waves. In the presence of disorder-induced charge order fluctuations, the coherence peaks resulting from phase correlation disappear and gradually transform the system into the pseudogap states. The power-law zero-bias anomaly and quasi-particle interference analysis further suggest the Tomonaga-Luttinger liquid behavior in such pseudogap region. In addition, we explicitly determined the evolution of the CDW energy gap as a function of stacking-wire numbers. The present study demonstrates the existence of electron-phonon interactions in few-wire W6Te6 that can be tuned by disorders and van der Waals stacking.

Temperature dependence of quasiparticle interference in $d$-wave superconductors

We investigate the temperature dependence of quasiparticle interference in the high T_cTc-cuprates using an exact-diagonalization + Monte-Carlo based scheme to simulate the dd-wave superconducting order parameter. The quasiparticle interference patterns have features largely resulting from the scattering vectors of the octet model at lower temperature. Our findings suggest that the features of quasiparticle interference in the pseudogap region of the phase diagram are also dominated by the set of scattering vectors belonging to the octet model because of the persisting antinodal gap beyond the superconducting transition T_cTc. However, beyond a temperature when the antinodal gap becomes very small, a set of scattering vectors different from those belonging to the octet model are responsible for the quasiparticle interference patterns. With a rise in temperature, the patterns are increasingly broadened.

Insulating vortex cores in disordered superconductors

In the standard paradigm, magnetic fields destroy superconductivity by creating Abrikosov vortices with metallic cores. Increasing field proliferates vortices, cores overlap, turning the system into a metal. In the disordered superconductors studied here, a starkly different scenario unfolds: Josephson vortices with insulating cores nucleate, long-range phase coherence of the superconductor and its energy-gap vanish at different critical fields, opening up a pseudogap region of Cooper-paired insulator. The resulting phase diagram uncovers an array of intriguing phenomena, including gigantic magnetoresistance peaks of disordered superconducting films.

Towards an effective mass model for the quasi-1D magnesium diboride superconducting nanostructures

We developed a parabolic effective mass model with the aim to describe the in-plane constricted superconductivity in few-monolayer MgB$_2$. The model was employed to study a constricted quasi-$1$D superlattice with the simplest version of the Anderson approximation. Resonant Fano-Feshbach-like effect was found, between a miniband of a continuous normal state dispersion cutting across $E_F$ and a miniband of quasi-discrete dispersion, even though the latter is significantly energetically distanced from the Fermi level. The origin of the phenomenon was identified to be the presence of characteristic strongly localised eigenstates, due to the specific material parameters. Moreover, the mechanism leading to a "precursor" pseudogap region in a system with a non-zero phase difference is described, when the strength of the coupling is still not sufficient to open a superconducting gap, but enough to introduce electron-hole mixing into the system.

Superconductinglike response in a driven gapped bosonic system

We propose a novel mechanism for the photo-induced superconducting-like response recently reported in cuprates and other strongly correlated materials. This mechanism relies on quantum-fluctuating bosons consisting of electron pairs. With periodic drive, the electron pairs and vacancies of pairs form a coherent non-equilibrium condensate, different from conventional superconductors, yet showing superconducting-like response in some regimes even with dissipation. Unlike the case of driven fermionic bands which results in the familiar Floquet bands with hybridization gaps, for driven bosons the "gap" opens up in the momentum direction, resulting in a resonant region in momentum space where the eigenvalues are complex. We give a simple physical argument why this picture leads to a "perfect conductor" which exhibits superconducting-like frequency-dependent conductivity but no Meissner response. While our model is quite general, in the case of cuprates, quantum-fluctuating pair density wave in the pseudogap region may serve as the origin of the quantum-fluctuating electron pairs.

Unconventional quantum vortex matter state hosts quantum oscillations in the underdoped high-temperature cuprate superconductors

A central question in the underdoped cuprates pertains to the nature of the pseudogap ground state. A conventional metallic ground state of the pseudogap region has been argued to host quantum oscillations upon destruction of the superconducting order parameter by modest magnetic fields. Here, we use low applied measurement currents and millikelvin temperatures on ultrapure single crystals of underdoped [Formula: see text] to unearth an unconventional quantum vortex matter ground state characterized by vanishing electrical resistivity, magnetic hysteresis, and nonohmic electrical transport characteristics beyond the highest laboratory-accessible static fields. A model of the pseudogap ground state is now required to explain quantum oscillations that are hosted by the bulk quantum vortex matter state without experiencing sizable additional damping in the presence of a large maximum superconducting gap; possibilities include a pair density wave.

Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal. IV. The γ model and its phase diagram at 1<γ<2

In this paper we continue our analysis of the interplay between the pairing and the non-Fermi liquid behavior in a metal for a set of quantum-critical (QC) systems with an effective dynamical electron-electron interaction $V(\Omega_m) \propto 1/|\Omega_m|^\gamma$ (the $\gamma$-model). In previous papers we studied the cases $0<\gamma <1$ and $\gamma \approx 1$. We argued that the pairing by a gapless boson is fundamentally different from BCS/Eliashberg pairing by a massive boson as for the former there exists an infinite number of topologically distinct solutions for the gap function $\Delta_n (\omega_m)$ at $T=0$ ($n=0,1,2...$), each with its own condensation energy $E_{c,n}$. Here we extend the analysis to larger $1< \gamma <2$. We argue that the discrete set of solutions survives, and the spectrum of $E_{c,n}$ gets progressively denser as $\gamma$ approaches $2$ and eventually becomes continuous at $\gamma \to 2$. This increases the strength of "longitudinal" gap fluctuations, which tend to reduce the actual superconducting $T_c$ and give rise to a pseudogap region of preformed pairs. We also detect two features on the real axis for $\gamma >1$ which become critical at $\gamma\to 2$. First, the density of states evolves towards a set of discrete $\delta-$functions. Second, an array of dynamical vortices emerges in the upper frequency half-plane. These two features come about because on a real axis, the real part of the interaction, $V' (\Omega) \propto \cos(\pi \gamma/2)/|\Omega|^\gamma$, becomes repulsive for $\gamma >1$, and the imaginary $V^{''} (\Omega) \propto \sin(\pi \gamma/2)/|\Omega|^\gamma$, gets progressively smaller at $\gamma \to 2$. The features on the real axis are consistent with the development of a continuum spectrum of $E_{c,n}$ obtained using $\Delta_n (\omega_m)$ on the Matsubara axis. We consider the case $\gamma =2$ separately in the next paper.

The effect of the chaotic pinning potential on intrinsic pinning in YBa2Cu3O7−δ single crystals

We study the temperature dependence of the in-plane magneto-resistance ρab(T) in the untwined YBa2Cu3O7−δ single crystals after irradiation by fast electrons (energy 0.5–2.5 MeV, dose 1018 cm−2), also with a small oxygen hypostoichiometry at different angles between the external magnetic field 15 kOe and the ab-planes α. We found that at high temperatures in the pseudogap region external magnetic field does not affect the ρab(T), but it broadens transitional region Tc – Tc0 from 0.3 K at zero field and α = 0 to approximately 6 K at α = 90° in the field. In the case of an unirradiated sample, ρab(T) display a 3D to 2D dimensional crossover when temperature decreases from Tc to Tc0 and scaling near the Tc0 which we relate to the flux-flow and vortex-lattice melting. The reasons for the appearance of low-temperature “tails” (paracoherent transitions) on resistive transitions corresponding to different phase regimes of the vortex matter are discussed.

Residual stress distributions in amorphous solids from atomistic simulations.

The distribution of local residual stresses (threshold to instability) that controls the statistical properties of plastic flow in athermal amorphous solids is examined with an atomistic simulation technique. For quiescent configurations, the distribution has a pseudogap (power-law) form with an exponent that agrees well with global yielding statistics. As soon as deformation sets in, the pseudogap region gives way to a system size dependent plateau at small residual stresses that can be understood from the statistics of local residual stress differences between plastic events. Results further suggest that the local yield stress in amorphous solids changes even if the given region does not participate in plastic activity.

Evidence for a universal Fermi-liquid scattering rate throughout the phase diagram of the copper-oxide superconductors

The phase diagram of the cuprate superconductors continues to pose formidable scientific challenges. While these materials are typically viewed as doped Mott insulators, it is well known that they are Fermi liquids at high hole-dopant concentrations. It was recently demonstrated that at moderate doping, in the pseudogap (PG) region of the phase diagram, the charge carriers are also best described as a Fermi liquid. Nevertheless, the relationship between the two Fermi-liquid (FL) regions and the nature of the strange-metal (SM) state at intermediate doping have remained unsolved. Here we show for the case of the model cuprate superconductor HgBa2CuO4+δ that the normal-state transport scattering rate determined from the cotangent of the Hall angle remains quadratic in temperature across the PG temperature, upon entering the SM state, and that it is doping-independent below optimal doping. Analysis of prior transport results for other cuprates reveals that this behavior is universal throughout the entire phase diagram and points to a pervasive FL transport scattering rate. These observations can be reconciled with a variety of other experimental results for the cuprates upon considering the possibility that the PG phenomenon is associated with the gradual, non-uniform localization of one hole per planar CuO2 unit.

Atomic-scale fragmentation and collapse of antiferromagnetic order in a doped Mott insulator

Disentangling the relationship between the insulating state with a charge gap and the magnetic order in an antiferromagnetic (AF) Mott insulator remains difficult due to inherent phase separation as the Mott state is perturbed. Measuring magnetic and electronic properties at the atomic length scales would provide crucial insight, but this is yet to be experimentally achieved. Here we use spectroscopic-imaging spin-polarized scanning tunneling microscopy (SP-STM) to visualize periodic spin-resolved modulations originating from the AF order in a relativistic Mott insulator Sr2IrO4, and study these as a function of doping. We find that near insulator-to-metal transition (IMT), the long-range AF order melts into a fragmented state with short-range AF correlations. Crucially, we discover that the short-range AF order is locally uncorrelated with the observed spectral gap magnitude. This strongly suggests that short range AF correlations are unlikely to be the culprit behind inhomogeneous gap closing and the emergence of pseudogap regions near IMT. Our work establishes SP-STM as a powerful tool for revealing atomic-scale magnetic information in complex oxides.

Electron pairing in the pseudogap state revealed by shot noise in copper oxide junctions.

In the quest to understand high-temperature superconductivity in copper oxides, debate has been focused on the pseudogap-a partial energy gap that opens over portions of the Fermi surface in the 'normal' state above the bulk critical temperature1. The pseudogap has been attributed to precursor superconductivity, to the existence of preformed pairs and to competing orders such as charge-density waves1-4. A direct determination of the charge of carriers as a function of temperature and bias could help resolve among these alternatives. Here we report measurements of the shot noise of tunnelling current in high-quality La2-xSrxCuO4/La2CuO4/La2-xSrxCuO4 (LSCO/LCO/LSCO) heterostructures fabricated using atomic layer-by-layer molecular beam epitaxy at several doping levels. The data delineate three distinct regions in the bias voltage-temperature space. Well outside the superconducting gap region, the shot noise agrees quantitatively with independent tunnelling of individual charge carriers. Deep within the superconducting gap, shot noise is greatly enhanced, reminiscent of multiple Andreev reflections5-7. Above the critical temperature and extending to biases much larger than the superconducting gap, there is a broad region in which the noise substantially exceeds theoretical expectations for single-charge tunnelling, indicating pairing of charge carriers. These pairs are detectable deep into the pseudogap region of temperature and bias. The presence of these pairs constrains current models of the pseudogap and broken symmetry states, whilephase fluctuations limit the domain of superconductivity.

Hubbard model on a triangular lattice: Pseudogap due to spin density wave fluctuations

We calculate the fermionic spectral function $A_k (\omega)$ in the spiral spin-density-wave (SDW) state of the Hubbard model on a quasi-2D triangular lattice at small but finite temperature $T$. The spiral SDW order $\Delta (T)$ develops below $T = T_N$ and has momentum ${ \bf K} = (4\pi/3,0)$. We pay special attention to fermions with momenta ${\bf k}$, for which ${\bf k}$ and ${\bf k} + {\bf K}$ are close to Fermi surface in the absence of SDW. At the mean field level, $A_k (\omega)$ for such fermions has peaks at $\omega = \pm \Delta (T)$ at $T < T_N$ and displays a conventional Fermi liquid behavior at $T > T_N$. We show that this behavior changes qualitatively beyond mean-field due to singular self-energy contributions from thermal fluctuations in a quasi-2D system. We use a non-perturbative eikonal approach and sum up infinite series of thermal self-energy terms. We show that $A_k (\omega)$ shows peak/dip/hump features at $T < T_N$, with the peak position at $\Delta (T)$ and hump position at $\Delta (T=0)$. Above $T_N$, the hump survives up to $T = T_p > T_N$, and in between $T_N$ and $T_p$ the spectral function displays the pseudogap behavior. We show that the difference between $T_p$ and $T_N$ is controlled by the ratio of in-plane and out-of-plane static spin susceptibilities, which determines the combinatoric factors in the diagrammatic series for the self-energy. For certain values of this ratio, $T_p = T_N$, i.e., the pseudogap region collapses. In this last case, thermal fluctuations are logarithmically singular, yet they do not give rise to pseudogap behavior. Our computational method can be used to study pseudogap physics due to thermal fluctuations in other systems.

Josephson Scanning Tunneling Spectroscopy in dx2−y2 -Wave Superconductors: A Probe for the Nature of the Pseudogap in the Cuprate Superconductors

Recent advances in the development of Josephson scanning tunneling spectroscopy (JSTS) have opened a new path for the exploration of unconventional superconductors. We demonstrate that the critical current I_{c}, measured via JSTS, images the spatial form of the superconducting order parameter in d_{x^{2}-y^{2}}-wave superconductors around defects and in the Fulde-Ferrell-Larkin-Ovchinnikov state. Moreover, we show that I_{c} probes the existence of phase-incoherent superconducting correlations in the pseudogap region of the cuprate superconductors, thus providing unprecedented insight into its elusive nature. These results provide the missing theoretical link between the experimentally measured I_{c} and the spatial structure of the superconducting order parameter.

Pf-hybridization and magnetic phase transitions in ferromagnetic superconductors

Abstract In the framework of the Anderson pf-model, magnetic phase transitions in 5f-ferromagnetic superconductors with hybridization of localized (f-) and delocalized (p-) electrons are discussed. We consider a free-energy functional containing a contribution due to the mode-mode coupling spin fluctuations. The calculated p-T-diagram of magnetic states describes transitions of the first and second order and the region of the ferromagnetic short-range order too. It is shown that when the temperature and pressure change, a shift of the chemical potential to the pseudogap region is possible, with a jump-like increase in the occupation of the spin-symmetrized electronic states and an increase in the screening of the local magnetic moments.

Multistage electronic nematic transitions in cuprate superconductors: A functional-renormalization-group analysis

Recently, complex phase transitions accompanied by the rotational symmetry breaking have been discovered experimentally in cuprate superconductors. To find the realized order parameters, we study various charge susceptibilities in an unbiased way, by applying the functional-renormalization-group method to the realistic $d$-$p$ Hubbard model. Without assuming the wavevector of the order parameter, we reveal that the most dominant instability is the uniform ($q = 0$) charge modulation on the $p_x$ and $p_y$ orbitals, which possesses the d-symmetry. This uniform nematic order triggers another nematic p-orbital density wave along the axial (Cu-Cu) direction at $Q_a = (\pi/2,0)$. It is predicted that uniform nematic order is driven by the spin fluctuations in the pseudogap region, and another nematic density-wave order at $q = Q_a$ is triggered by the uniform order. The predicted multistage nematic transitions are caused by the Aslamazov-Larkin-type fluctuation-exchange processes.

Numerical Study of Fermi Surface on Cuprate Using One-Band Hubbard Model: Role of Charge Density Wave in The Antiferromagnetic Mott-Insulator and Pseudogap Region

Numerical study of Fermi surface has been done using one-band Hubbard model with exact diagonalization method to study the effect of doping factor on Charge Density Wave (CDW) development in Anti ferromagnetic Mott Insulator (AFM) and pseudogap region in cuprate material. In this study the effect of CDW is characterized by Fermi Surface Nesting (FSN) vector in which it might be formed in pseudogap region. The wavelength of CDW increases when the value of disorder, which is representing the doping level in cuprate material, is increased. However, the CDW pattern will dissapear as the doping reaches the value which represented by Hubbard parameters: t = 1 eV, U = 4 eV, µ = 2 eV, and vi = -6 eV, marked by the decreasing of charge density wavelength.

Pseudogap Regime of a Two-dimensional Uniform Fermi Gas

We investigate pseudogap phenomena in a two-dimensional Fermi gas. Including pairing fluctuations within a self-consistent $T$-matrix approximation, we determine the pseudogap temperature $T^*$ below which a dip appears in the density of states $\rho(\omega)$ around the Fermi level. Evaluating $T^*$, we identify the pseudogap region in the phase diagram of this system. We find that, while the observed BKT (Berezinskii-Kosterlitz-Thouless) transition temperature $T^{\rm exp}_{\rm BKT}$ in a $^6$Li Fermi gas is in the pseudogap regime, the detailed pseudogap structure in $\rho(\omega)$ at $T^{\rm exp}_{\rm BKT}$ still differs from a fully-gapped one, indicating the importance of amplitude fluctuations in the Cooper channel there. Since the observed $T^{\rm exp}_{\rm BKT}$ in the weak-coupling regime cannot be explained by the recent BKT theory which only includes phase fluctuations, our results may provide a hint about how to improve this BKT theory. Although $\rho(\omega)$ has not been measured in this system, we show that the assessment of our results is still possible by using the observable Tan's contact.

Metal-insulator (fermion-boson)-crossover origin of pseudogap phase of cuprates I: anomalous heat conductivity, insulator resistivity boundary, nonlinear entropy

Among all experimental observations of cuprate physics, the metal-insulator-crossover (MIC), seen in the pseudogap (PG) region of the temperature-doping phase diagram of copper-oxides under a strong magnetic field, when the superconductivity is suppressed, is most likely the most intriguing one. Since it was expected that the PG-normal state for these materials, as for conventional superconductors, is conducting. This MIC, revealed in such phenomena as heat conductivity downturn, anomalous Lorentz ratio, insulator resistivity boundary, nonlinear entropy, resistivity temperature upturn, insulating ground state, nematicity- and stripe-phases and Fermi pockets, unambiguously indicates on the insulating normal state, from which the high-temperature superconductivity (HTS) appears. In the present work (article I), we discuss the MIC phenomena mentioned in the title of article. The second work (article II) will be devoted to discussion of other listed above MIC phenomena and also to interpretation of the recent observations in the hidden magnetic order and scanning tunneling microscopy (STM) experiments spin and charge fluctuations as the intra PG and HTS pair ones. We find that all these MIC (called in the literature as non-Fermi liquid) phenomena can be obtained within the Coulomb single boson and single fermion two liquid model, which we recently developed, and the MIC is a crossover of single fermions into those of single bosons. We show that this MIC originates from bosons of Coulomb two liquid model and fermions, whose origin is these bosons. At an increase of doping up to critical value or temperature up to PG boundary temperature, the boson system undegoes bosonic insulator - bosonic metal - fermionic metal transitions.

Normal state pair nematicity and hidden magnetic order and metal-insulator (fermionboson) crossover origin of pseudogap phase of cuprates II

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 the PG pair intra charge and spin fluctuations. We will try to obtain an answer on the question: why ground state of YBCO is Fermi liquid oscillating and of Bi-2212 is insulating? We will also clarify the physics of the recently observed MIC results of Lalibert\'e et al. [2] and explain the long-discussed transition of the electric charge density from doping to doping+1 dependence at the critical doping. We predict that at the upturns this density should have the temperature dependence $n\sim T^3n_2$ for $T\rightarrow 0$, where $n_2$ is density for dopings close to the critical value. We understood that the upturns before and after the first critical doping have the same nature. We will find understanding of all above mentioned phenomena within the PG pair physics.