Pseudogap Research Articles

Longitudinal fluctuations and decorrelation of anisotropic flow

We investigate the decorrelation of 2nd and 3rd order anisotropic flow for charged particles in two different pseudo rapidity (η) windows by varying the pseudo rapidity gap, in an event-by-event (3+1)D ideal hydrodynamic model, with fluctuating initial conditions from A Multi-Phase Transport (AMPT) model. We visualize the parton distribution at initial state for Pb+Pb collisions at LHC and Au+Au collisions at RHIC, and demonstrate the longitudinal fluctuations originating from the asymmetry between forward and backward going participants, the fluctuations of the string length and the fluctuations due to finite number of partons at different beam energies. The decorrelation of anisotropic flow of final hadrons with large η gaps is found to originate from the spatial decorrelation along the longitudinal direction in the AMPT initial conditions through hydrodynamic evolution. The agreement between our results and recent CMS data in most centralities suggests that the string-like mechanism of initial parton production in AMPT model captures the initial longitudinal fluctuation that is responsible for the measured decorrelation of anisotropic flow in Pb+Pb collisions at LHC. Our predictions for Au+Au collisions at the highest RHIC energy show stronger longitudinal decorrelation than at LHC, indicating larger longitudinal fluctuations at lower beam energies.

Effect of multiple defects and substituted impurities on the band structure of graphene: a DFT study

In graphene, band gap opening and tuning are important technological challenges for device applications. Various techniques have been suggested to this technologically complicated problem. Here, we present an ab initio study on the band gap opening in graphene through vacancy, adding impurity atom in the vacancy and substitutional co-doping. In the case of graphene with single vacancy a direct band gap of ~1 eV is obtained. This is a spin polarized state. The graphene system with two monovacancies gives rise to an effective indirect band gap (pseudo gap) of ~1 eV. The graphene substitutionally doped with B and N is co-doped (tri-doped) with S. This tri-doped graphene has turned into a semiconductor (band gap ~1 eV). These graphene semiconductors are better than the other semiconductor because of the presence of massless Dirac fermions in addition to normal electrons. This will have lot of application in device industry compared to a pristine graphene because of the presence of a gap and Dirac fermions. This type of band gap opening, with this type of defects and impurities, we are reporting for the first time.

Fluctuation conductivity and possible pseudogap state in FeAs-based superconductor EuFeAsO0.85F0.15

The study of excess conductivity in the textured polycrystalline FeAs-based superconductor EuFeAsO0.85F0.15 () prepared by the solid state synthesis is reported for the first time. The analysis has been performed within the local pair (LP) model based on the assumption of the LPs formation in cuprate high-Tc superconductors (cuprates) below the pseudogap (PG) temperature . Similarly to the cuprates, near is adequately described by the 3D term of the Aslamasov–Larkin (AL) theory but the range of the 3D-AL fluctuations, , is relatively short. Above the crossover temperature is described by the 2D Maki–Thompson (MT) fluctuation term of the Hikami–Larkin theory. But enhanced 2D-MT fluctuation contribution being typical for the magnetic superconductors is observed. Within the LP model the PG parameter, , was determined for the first time. It is shown that demonstrates the narrow maximum at followed by the descending linear length down to . Observed small , enlarged 2D and linear are considered to be the evidence of the enhanced magnetic interaction in EuFeAsO0.85F0.15. Importantly, the slop of the linear and its length are found to be the same as it is revealed for SmFeAsO0.85. The results suggest both the similarity of the magnetic interaction processes in different Fe-pnictides and applicability of the LP model to the analysis even in magnetic superconductors.

Effect of the particle-hole channel on BCS-Bose-Einstein condensation crossover in atomic Fermi gases.

BCS–Bose-Einstein condensation (BEC) crossover is effected by increasing pairing strength between fermions from weak to strong in the particle-particle channel, and has attracted a lot of attention since the experimental realization of quantum degenerate atomic Fermi gases. Here we study the effect of the (often dropped) particle-hole channel on the zero T gap Δ(0), superfluid transition temperature Tc, the pseudogap at Tc, and the mean-field ratio 2Δ(0)/, from BCS through BEC regimes, using a pairing fluctuation theory which includes self-consistently the contributions of finite-momentum pairs and features a pseudogap in single particle excitation spectrum. Summing over the infinite particle-hole ladder diagrams, we find a complex dynamical structure for the particle-hole susceptibility χph, and conclude that neglecting the self-energy feedback causes a serious over-estimate of χph. While our result in the BCS limit agrees with Gor’kov et al., the particle-hole channel effect becomes more complex and pronounced in the crossover regime, where χph is reduced by both a smaller Fermi surface and a big (pseudo)gap. Deep in the BEC regime, the particle-hole channel contributions drop to zero. We predict a density dependence of the magnetic field at the Feshbach resonance, which can be used to quantify χph and test different theories.

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.

Out-of-Plane Disorder Effects on the Energy Gaps and Electronic Charge Order in Bi2Sr1.7R0.3CuO6+δ (R = La and Eu)

We performed STM/STS experiments at 8 K in Bi2Sr1.7R0.3CuO6+δ (R-Bi2201) systems that had optimal (OP) hole-doping levels (∼0.17) but different Tc values, 35 K for R = La and 20 K for R = Eu, and examined out-of-plane disorder effects on the superconducting (SC) gap (SCG) and the pseudogap (PG) which is associated with the so-called “checkerboard charge order” (CCO). As out-of-plane disorders are strengthened by replacing La with Eu in OP R-Bi2201, the antinodal PG size ΔPG increases from ∼30 to ∼60 meV, the nodal SCG size ΔSC seems to decrease from ∼7 to ∼4 meV, and the pairing gap amplitude Δ0 or d-wave gap size at the antinodes is almost unchanged (Δ0 ∼ 15 meV). These gap sizes for OP doping in Eu-Bi2201 are comparable to those for an underdoping level of ∼0.1 in La-Bi2201. Although out-of-plane disorders strongly affect the electronic system of the Cu–O plane, they have no effect on the period of the CCO, which is five times the lattice constant (5a) along the Cu–O bond directions for OP doping and 4a...

Electronic structure of the ingredient planes of the cuprate superconductorBi2Sr2CuO6+δ: A comparison study withBi2Sr2CaCu2O8+δ

By means of low-temperature scanning tunneling microscopy, we report on the electronic structures of BiO and SrO planes of Bi2Sr2CuO6+{\delta} (Bi-2201) superconductor prepared by argon-ion bombardment and annealing. Depending on post annealing conditions, the BiO planes exhibit either pseudogap (PG) with sharp coherence peaks and an anomalously large gap of 49 meV or van Hove singularity (VHS) near the Fermi level, while the SrO is always characteristic of a PG-like feature. This contrasts with Bi2Sr2CaCu2O8+{\delta} (Bi-2212) superconductor where VHS occurs solely on the SrO plane. We disclose the interstitial oxygen dopants ({\delta} in the formulas) as a primary cause for the occurrence of VHS, which are located dominantly around the BiO and SrO planes, respectively, in Bi-2201 and Bi-2212. This is supported by the contrasting structural buckling amplitude of BiO and SrO planes in the two superconductors. Our findings provide solid evidence for the irrelevance of PG to the superconductivity in the two superconductors, as well as insights into why Bi-2212 can achieve a higher superconducting transition temperature than Bi-2201, and by implication, the mechanism of cuprate superconductivity.

A wave packet approach to interacting Fermions

In this thesis, we study the breakdown of the Fermi liquid state in cuprate superconductors using the renormalization group (RG). We seek to extend earlier work on the crossover from the Fermi liquid state to the pseudo gap phase based on RG flows in the so-called saddle point regime. Progress in the derivation of effective models for the conjectured spin liquid state has been hindered, by the difficulties involved in solving the strong coupling low energy Hamiltonian. We tackle the problem by introducing an orthogonal wave packet basis, the so-called Wilson-Wannier (WW) basis, that can be used to interpolate between the momentum space and the real space descriptions. We show how to combine the WW basis with the RG, such that the RG is used to eliminate high-energy degrees of freedom, and the remaining strongly correlated system is solved approximately in the WW basis. We exemplify the approach for different one-dimensional model systems, and find good qualitative agreement with exact solutions even for very simple approximations. Finally, we reinvestigate the saddle point regime of the two-dimensional Hubbard model. We show that the anti-nodal states are driven to an insulating spin-liquid state with strong singlet pairing correlations, thus corroborating earlier conjectures.

Mapping the Electronic Structure of Each Ingredient Oxide Layer of High-T\{c} Cuprate Superconductor Bi{2}Sr{2}CaCu{2}O{8+δ}.

Understanding the mechanism of high transition temperature (T{c}) superconductivity in cuprates has been hindered by the apparent complexity of their multilayered crystal structure. Using a cryogenic scanning tunneling microscopy (STM), we report on layer-by-layer probing of the electronic structures of all ingredient planes (BiO, SrO, CuO{2}) of Bi{2}Sr{2}CaCu_2}O{8+δ} superconductor prepared by argon-ion bombardment and annealing technique. We show that the well-known pseudogap (PG) feature observed by STM is inherently a property of the BiO planes and thus irrelevant directly to Cooper pairing. The SrO planes exhibit an unexpected van Hove singularity near the Fermi level, while the CuO{2} planes are exclusively characterized by a smaller gap inside the PG. The small gap becomes invisible near T{c}, which we identify as the superconducting gap. The above results constitute severe constraints on any microscopic model for high T{c} superconductivity in cuprates.

STM/STS studies for interplane disorder effects on the electronic states of the Cu–O plane in Bi2201

STM/STS experiments have been performed in [Formula: see text] (R-Bi2201) systems with [Formula: see text] and Eu, which are of a nearly optimal doping level [Formula: see text] but have different [Formula: see text] values, 35 K and 20 K, respectively, to examine interplane disorder effects on the superconducting (SC) gap and the pseudogap (PG) that is accompanied by a checkerboard-type charge order (CCO). We report that as interplane disorders are strengthened by replacing La with Eu in optimal Bi2201, the antinodal PG size [Formula: see text] increases from [Formula: see text] to [Formula: see text], which is comparable to the value for an underdoping level [Formula: see text] in La-Bi2201. On the other hand, the period of CCO in optimal Eu-Bi2201 is the same as in optimal La-Bi2201, about five times lattice constant [Formula: see text] along the Cu–O bond directions; it remains unchanged even if the PG develops markedly to the same degree as for [Formula: see text] in La-Bi2201, whose period is [Formula: see text].

Time-resolved polarimetry for photoexcited QP dynamics in Bi2212

The dynamics of quasi-particle (QP) excitations with different symmetry is investigated in the superconducting (SC) and pseudogap (PG) states of the high-temperature superconductor [Formula: see text] (Bi2212) using a polarization-sensitive optical pump-probe measurement. The observation of distinct anisotropies for SC excitations and for PG excitations by the probe beam polarization and absence of any dependence on the pump beam polarization evidence the existence of a spontaneous spatial symmetry breaking in the PG state.

Pair–pair interactions as a mechanism for high-Tc superconductivity

The mutual interaction between Cooper pairs is proposed as a mechanism for the superconducting state. Above Tc, pre-existing but fluctuating Cooper pairs give rise to the unconventional pseudogap (PG) state, well-characterized by experiment. At the critical temperature, the pair–pair interaction induces a Bose-like condensation of these preformed pairs leading to the superconducting (SC) state. Below Tc, both the condensation energy and the pair–pair interaction β are proportional to the condensate density Noc(T), while the usual Fermi-level spectral gap is independent of temperature. The new order parameter , can be followed as a function of temperature, carrier concentration and disorder—i.e. the phase diagrams. The complexity of the cuprates, revealed by the large number of parameters, is a consequence of the coupling of quasiparticles to Cooper-pair excitations. The latter interpretation is strongly supported by the observed quasiparticle spectral function.

SU(2) symmetry in a realistic spin-fermion model for cuprate superconductors

We consider the Pseudo-Gap (PG) state of high-$T_c$ superconductors in form of a composite order parameter fluctuating between 2$p_F$-charge ordering and superconducting (SC) pairing. In the limit of linear dispersion and at the hotspots, both order parameters are related by a SU(2) symmetry and the eight hotspot model of Efetov $\textit{et al.}$ [Nat. Phys. $\bf{9}$, 442 (2013)] is recovered. In the general case however, curvature terms of the dispersion will break this symmetry and the degeneracy between both states is lifted. Taking the full momentum dependence of the order parameter into account, we measure the strength of this SU(2) symmetry breaking over the full Brillouin zone. For realistic dispersion relations including curvature we find generically that the SU(2) symmetry breaking is small and robust to the fermiology and that the symmetric situation is restored in the large paramagnon mass and coupling limit. Comparing the level splitting for different materials we propose a scenario that could account for the competition between the PG and the SC states in the phase diagram of high-$T_c$ superconductors.

The origins of macroscopic quantum coherence in high temperature superconductivity

A new, theoretical approach to macroscopic quantum coherence and superconductivity in the p-type (hole doped) cuprates is proposed. The theory includes mechanisms to account for e-pair coupling in the superconducting and pseudogap phases and their inter relations observed in these materials.Electron pair coupling in the superconducting phase is facilitated by local quantum potentials created by static dopants in a mechanism which explains experimentally observed optimal doping levels and the associated peak in critical temperature. By contrast, evidence suggests that electrons contributing to the pseudogap are predominantly coupled by fractal spin waves (fractons) induced by the fractal arrangement of dopants.On another level, the theory offers new insights into the emergence of a macroscopic quantum potential generated by a fractal distribution of dopants. This, in turn, leads to the emergence of coherent, macroscopic spin waves and a second associated macroscopic quantum potential, possibly supported by charge order. These quantum potentials play two key roles. The first involves the transition of an expected diffusive process (normally associated with Anderson localization) in fractal networks, into e-pair coherence. The second involves the facilitation of tunnelling between localized e-pairs. These combined effects lead to the merger of the super conducting and pseudo gap phases into a single coherent condensate at optimal doping. The underlying theory relating to the diffusion to quantum transition is supported by Coherent Random Lasing, which can be explained using an analogous approach. As a final step, an experimental program is outlined to validate the theory and suggests a new approach to increase the stability of electron pair condensates at higher temperatures.

In-plane paraconductivity of optimally doped and slightly overdoped cuprates: implication and origin of the pseudogap

In conventional superconductors the magnitude of the pairing fluctuation is primarily determined by Tc and the superconducting coherence length ξ. In low-dimensional systems with strong structural and electronic anisotropies, the interlayer separation s plays a significant role. In cuprates, the pseudogap (PG) correlation induces a downturn in the temperature-dependent resistivity. As Tc is approached from above, this downturn in the resistivity is supposed to either (i) add independently to, or (ii) join smoothly to that due to paraconductivity caused by short-lived Cooper pairs. It is important to differentiate between these two possibilities, since they are closely linked to the nature of the PG. It would be reasonable to assume that if the first scenario is correct, then the PG has a non-superconducting origin, while the second scenario, if found to hold, would relate precursor pairing to the PG correlations. In this paper we have studied the in-plane fluctuation conductivity of two c-axis-oriented thin films of Y0.95Ca0.05Ba2Cu3O7−δ with similar hole contents (p), p = 0.165 (optimally doped (OPD)) and p = 0.184 (slightly overdoped (SOD)). The hole contents are fixed at these values so that the PG affects the slope of the resistivity data only at temperatures close to Tc. Analysis of paraconductivity Δσab(T) within the mean-field Gaussian Ginzburg–Landau (MFGGL) framework reveals different qualitative and quantitative features for the OPD and the SOD compounds. The excess conductivity due to Cooper pair fluctuations of the SOD sample can be described reasonably well by the MFGGL formalism. The excess conductivity of the OPD compound, on the other hand, cannot be accounted for by the MFGGL formalism with a reasonable set of parameters. There is a significant added contribution to Δσab(T) for the OPD sample that appears to come from the presence of a PG in the quasiparticle (QP) spectral density. These findings point towards a non-pairing origin of the PG.

Unusual isotope effects on the pseudogap in high-[formula omitted] cuprate superconductors as support for the BCS-like pairing theory of large polarons above [formula omitted

The BCS-like pairing theory is extended to the intermediate coupling regime and to the cases of exotic cuprate superconductors with large and small Fermi surfaces, so as to describe the pairing correlations above Tc, the opening of a pseudogap (PG) at a mean-field temperature T∗>Tc and the unusual isotope effects on the PG in these materials within the large polaron model and two different BCS-like approaches. We argue that unconventional electron–phonon interactions are responsible for the polaron formation and the separation between temperatures T∗ (the onset of precursor Cooper pairing) and Tc (the onset of the superconducting transition) in exotic cuprate superconductors. Using the extended BCS-like approaches, we calculate the PG formation temperature T∗, isotope shifts ΔT∗, oxygen and copper isotope exponents and show that isotope effects on the PG basically depend on strengths of Coulomb and electron–phonon interactions, doping levels and dielectric constants of the cuprates. The new BCS-like pairing theory of polaronic carriers predicts the existence of small and sizable positive oxygen isotope effect and very large negative oxygen and copper isotope effects on the PG in the cuprates with large Fermi surfaces. The calculated results for T∗, isotope shifts and exponents are compared with experimental data on various cuprate superconductors. For all the considered cases, a good quantitative agreement was found between theory and experimental data. We also predict the existence of small and sizable negative isotope effects on T∗ in deeply underdoped cuprates with small Fermi surfaces. Further, we find that the isotope effects on T∗(=Tc) in heavily overdoped cuprates just like in some metals are relatively small positive or become even negative.

Photonic band-edge-induced enhancement in absorption and emission

An enhancement in photonic band-edge-induced absorption and emission from rhodamine-B dye doped polystyrene pseudo gap photonic crystals is studied. The band-edge-induced enhancement in absorption is achieved by selecting the incident angle of the excitation beam so that the absorption spectrum of the emitter overlaps the photonic band edge. The band-edge-induced enhancement in emission, on the other hand, is possible with and without an enhancement in band-edge-induced absorption, depending on the collection angle of emission. Through a simple set of measurements with suitably chosen angles for excitation and emission, we achieve a maximum enhancement of 70% in emission intensity with band-edge-induced effects over and above the intrinsic emission in the case of self-assembled opals. This is a comprehensive effort to interpret tunable lasing in opals as well as to predict the wavelength of lasing arising as a result of band-edge-induced distributed feedback effects.

Peculiar oxygen and copper isotope effects on the pseudogap formation temperature in underdoped to overdoped cuprates: Pseudogap induced by pairing correlations above Tc in cuprates with large and small Fermi surfaces

We investigate the pseudogap (PG) state and the peculiar oxygen and copper isotope effects on the PG onset temperature T⁎ in cuprate superconductors with large and small Fermi surfaces within the polaron model and two different BCS-based approaches extended to the intermediate coupling regime. We argue that the unconventional electron–phonon interactions are responsible for the polaron formation and BCS-like pairing correlations above Tc in underdoped to overdoped cuprates, which are exotic (non-BCS) superconductors. Using the generalized BCS-like theory, we calculate pseudogap formation temperatures T⁎, isotope shifts ΔT⁎, oxygen and copper isotope exponents (i.e. αT⁎O and αT⁎Cu) and show that isotope effects on T⁎ strongly depend on strengths of Coulomb and electron–phonon interactions, doping levels and dielectric constants of the cuprates. This theory explains the existence of small positive or sign reversed oxygen isotope effect, sizable and very large negative oxygen and copper isotope effects on T⁎ in cuprates with large Fermi surfaces. Further, we use another version of the extended BCS-like model to study the PG formation and the peculiar isotope effects on T⁎ in deeply underdoped cuprates with small Fermi surfaces and predict the existence of small and sizable negative oxygen and copper isotope effects on T⁎ in such underdoped cuprates. The results for T⁎, isotope shifts ΔT⁎ and exponents (αT⁎O and αT⁎Cu) in different classes of high-Tc cuprates are in good agreement with the existing well-established experimental data and explain the controversy between various experiments on isotope effects for T⁎ in the cuprates.

Pseudogap, superconductivity and magnetism

Pseudogap, superconductivity and magnetism

Concentration inequalities for Markov chains by Marton couplings and spectral methods

We prove a version of McDiarmid’s bounded differences inequality for Markov chains, with constants proportional to the mixing time of the chain. We also show variance bounds and Bernstein-type inequalities for empirical averages of Markov chains. In the case of non-reversible chains, we introduce a new quantity called the “pseudo spectral gap”, and show that it plays a similar role for non-reversible chains as the spectral gap plays for reversible chains. Our techniques for proving these results are based on a coupling construction of Katalin Marton, and on spectral techniques due to Pascal Lezaud. The pseudo spectral gap generalises the multiplicative reversiblication approach of Jim Fill.