Gap Inhomogeneity Research Articles

Gap distribution in overdoped La 2− xSr xCuO 4 observed by scanning tunneling spectroscopy

Low-temperature scanning tunneling spectroscopy on the highly overdoped La 1.78Sr 0.22CuO 4 ( T c = 27 K) single crystal reveals gap inhomogeneity at 4.2 K. The energy gap Δ observed in the tunneling spectra distributes around 7 meV: it ranges from 4 to 20 meV. The spectra with smaller Δ (4–10 meV) exhibit gap edge peaks and flat background density-of-states, which is general characteristics of the overdoped cuprate high-temperature superconductors. On the other hand, the spectra with Δ exceeding 10 meV shows broad feature without clear gap edge peaks.

Fluctuating Cu–O–Cu bond model of high-temperature superconductivity

Twenty years of research have yet to produce a consensus on the origin of high-temperature superconductivity (HTS). However, several generic characteristics of the copper oxide superconductors have emerged as the essential ingredients of and/or constraints on any viable microscopic model of HTS. Besides a critical temperature Tc of the order of 100 K, they include a d-wave superconducting gap with Fermi liquid nodal excitations, a pseudogap with d-symmetry and the characteristic temperature scale T*, an anomalous doping-dependent oxygen isotope shift, nanometre-scale gap inhomogeneity and so on. The isotope shift implies a key role for oxygen vibrations, but conventional Bardeen–Cooper–Schrieffer single-phonon coupling is essentially forbidden by symmetry and by the on-site Coulomb interaction U. Here we invoke the nonlinear modulation of the Cu–Cu bond by planar oxygen vibrations. The Fermi liquid nature of the d-wave superconducting ground state supports a weak-coupling treatment of this modulation. The dominant fluctuations are manifested in a pattern of oxygen vibrational square amplitudes with quadrupolar symmetry around a given Cu site. On the basis of such bond fluctuations, both dynamic and static, we can understand the salient features of HTS.

Effects of Pairing Potential Scattering on Fourier-Transformed Inelastic Tunneling Spectra of High-TcCuprate Superconductors with Bosonic Modes

Recent scanning tunneling microscopy (STM) experimentally observed strong gap inhomogeneity in Bi2Sr2CaCu2O(8+delta) (BSCCO). We argue that disorder in the pair potential underlies the gap inhomogeneity, and investigate its role in the Fourier-transformed inelastic tunneling spectra as revealed in the STM. We find that the random pair potential induces unique q-space patterns in the local density of states (LDOS) of a d-wave superconductor. We consider the effects of electron coupling to various bosonic modes and find the pattern of LDOS modulation due to coupling to the B(1g) phonon mode to be consistent with the one observed in the inelastic electron tunnneling STM experiment in BSCCO. These results suggest strong electron-lattice coupling as an essential part of the superconducting state in high-Tc materials.

Observations of electronic inhomogeneity in heavily Pb-dopedBi2Sr2CaCu2Oysingle crystals by scanning tunneling microscopy

Cleaved $\mathrm{ab}$ surfaces of heavily Pb-doped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{y}$ single crystals, including phase separation into Pb-poor $\ensuremath{\alpha}$ and Pb-rich $\ensuremath{\beta}$ phases, were probed by cryogenic scanning tunneling microscopy/spectroscopy at 4.3 K. We could resolve individual Pb atoms substituted into Bi sites, which tend to be concentrated on the crest of modulation in the $\ensuremath{\alpha}$ phase, but are almost randomly dispersed throughout the $\ensuremath{\beta}$ phase. The scanning tunneling spectroscopy results revealed a considerably wide range of gap values $\ensuremath{\Delta},$ originating from the presence of both superconducting and pseudogap regions on a nanometer scale. Furthermore, we found that oxygen annealing substantially increases gap inhomogeneity. This strongly suggests that disorder of excess oxygen, possibly coupled with structural deformation of ${\mathrm{CuO}}_{2}$ sheets, destroys superconducting coherence, resulting in the appearance of a pseudogap.

Single-gap timing RPCs with bidimensional position-sensitive readout for very accurate TOF systems

In this work, we report the development and performance of single-gap timing RPCs equipped with a 3mm FWHM resolution bidimensional position-sensitive readout and reaching a timing resolution of 55ps σ at an efficiency of 75% for MIPs. These chambers are aimed to be applied in a multilayer geometry, forming small and very accurate TOF systems. The avalanche localization capability would provide information for accurate flight-path determination and allow the offline correction of any position dependent effects in the chamber, like gap inhomogeneities or edge effects. The multilayer geometry would provide redundant timing information, which, besides improving the timing resolution, can be used for reducing the timing tails and for the self-calibration of the device. From the experimental single-chamber data it can be calculated that a four-layer configuration of such chambers would yield a time resolution of 33ps σ at a 95% efficiency, essentially free of timing tails.

Gap inhomogeneity, phase separation and a pseudogap in Bi2Sr2CaCu2O8+δ

Gap inhomogeneity in Bi2Sr2CaCu2O8 has been studied by low-temperature STM. We found a systematic relation between the local gap energy and local background density of states. A model analysis of the dip–hump structure gave evidence of in-plane charge inhomogeneity. The temperature/doping dependences of the pattern shape of inhomogeneity as well as the gap distribution function were measured. We could identify the signature of phase separation into the superconducting and pseudogapped phases as the appearance of a double-peak structure in the distribution function.

Pairing near the Mott insulating limit

The nanometer-scale gap inhomogeneity revealed by recent scanning tunnel microscope images of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+x}$ (BSCCO) surface suggests that the ``gap coherence length'' is of that order. Thus a robust pairing gap can develop despite the poorly screened Coulomb interaction. This can be taken as an evidence that the pairing in high-${T}_{c}$ materials hardly affects the charge correlation and hence occurs primarily among the spin degrees of freedom. We provide theoretical support for this point of view.

Current-Voltage Characteristics of p-n Structures with Band Gap Inhomogeneity in Base Region

The paper theoretically investigates the peculiarities of the reverse branch of current–voltage characteristics (CVC) of p–n structures whose base region contains a wide band gap layer. The analysis carried out is based on the derived analytical formula for the reverse current connected with the thermal generation of carriers both in the base region and at the Ohmic contact. It is shown that in the case when the wide-gap-layer is remote from the metallurgical edge of p–n junction at a distance comparable with the thickness of the space charge region (SCR) a portion of negative differential resistance (NDR) may appear on the reverse branch of CVC.

Current–Voltage Characteristics of p–n Structures with Band Gap Inhomogeneity in Base Region

Current–Voltage Characteristics of p–n Structures with Band Gap Inhomogeneity in Base Region

Effective band gap inhomogeneity and piezoelectric field in InGaN/GaN multiquantum well structures

The emission mechanisms of strained InxGa1−xN quantum wells (QWs) were shown to vary depending on the well thickness, L, and x. The absorption edge was modulated by the quantum confined Stark effect and quantum confined Franz-Keldysh effect (QCFK) for the wells, in which, for the first approximation, the product of the piezoelectric field, FPZ, and L exceed the valence band discontinuity, ΔEV. In this case, holes are confined in the triangular potential well formed at one side of the well producing the apparent Stokes-like shift. Under the condition that FPZ×L exceeds the conduction band discontinuity ΔEC, the electron-hole pair is confined at opposite sides of the well. The QCFK further modulated the emission energy for the wells with L greater than the three dimensional free exciton Bohr radius aB. On the other hand, effective in-plane localization of carriers in quantum disk size potential minima, which are produced by nonrandom alloy compositional fluctuation enhanced by the large bowing parameter and FPZ, produces a confined electron-hole pair whose wave functions are still overlapped (quantized excitons) provided that L<aB.

Exciton localization in InGaN quantum well devices

Emission mechanisms of a device-quality quantum well (QW) structure and bulk three dimensional (3D) InGaN materials grown on sapphire substrates without any epitaxial lateral overgrown GaN base layers were investigated. The InxGa1−xN layers showed various degrees of in-plane spatial potential (band gap) inhomogeneity, which is due to a compositional fluctuation or a few monolayers thickness fluctuation. The degree of fluctuation changed remarkably around a nominal InN molar fraction x=0.2, which changes to nearly 0.08–0.1 for the strained InxGa1−xN. This potential fluctuation induces localized energy states both in the QW and 3D InGaN, showing a large Stokes-like shift. The spontaneous emission from undoped InGaN single QW light-emitting diodes (LEDs), undoped 3D LEDs, and multiple QW (MQW) laser diode (LD) wafers was assigned as being due to the recombination of excitons localized at the potential minima, whose lateral size was determined by cathodoluminescence mapping to vary from less than 60 to 300 nm in QWs. Those structures are referred to as quantum disks (Q disks) or segmented QWs depending on the lateral size. Blueshift of the emission peak by an increase of the driving current was explained to be combined effects of band filling of the localized states by excitons and Coulomb screening of the quantum confined Stark effect induced by the piezoelectric field. The lasing mechanisms of the continuous wave In0.15Ga0.85N MQW LDs having small potential fluctuations can be described by the well-known electron-hole-plasma (EHP) picture. However, the inhomogeneous MQW LDs are considered to lase by EHP in segmented QWs or Q disks. It is desirable to use entire QW planes with small potential inhomogeneity as gain media for higher performance LD operation.

TUNNELING MEASUREMENTS OF THE ENERGY GAP IN HIGH-Tc SUPERCONDUCTORS

The current status of tunneling measurements of the superconducting density of states near the Fermi level of high-T c superconductors is reviewed. A number of the characteristics of the tunneling data that had previously been considered to be "non-ideal" follow quite naturally from conventional tunneling theory, if the effects of the unusually large energy gap, often unusually small tunneling barriers, and gap anisotropy and/or inhomogeneity are correctly accounted for. Despite formidable problems in making these measurements, due to both the very short coherence lengths and materials problems in these superconductors, a consistent body of data is emerging. A consistent picture can be drawn from this data with the aid of the new modelling presented here.

Probing the spatial distribution of the energy gap in Josephson tunnel junctions.

It is explicitly shown that the spatial distribution of the energy gap in a superconducting tunnel junction can be determined quantitatively. This is verified experimentally using superconducting-insulator-superconducting tunnel junctions where gap inhomogeneity is deliberately induced with patterned laser illumination.