We present an extended zero-field muon spin relaxation (ZF-$μ$SR) study of overdoped Bi$_{2+x}$Sr$_{2-x}$CaCu$_2$O$_{8+δ}$ (Bi2212) single crystals, intended to elucidate the origin of weak quasistatic magnetism previously detected by $μ$SR in the superconducting and normal states of optimally-doped and overdoped samples. New results on heavily-overdoped single crystals show a similar monotonically decreasing ZF-$μ$SR relaxation rate with increasing temperature that persists above the pseudogap (PG) temperature $T^*$ and does not evolve with hole doping ($p$). Additional measurements using an ultra-low background apparatus confirm that this behavior is an intrinsic property of Bi2212, which cannot be due to magnetic order associated with the PG phase. Instead we show that the temperature-dependent relaxation rate is most likely caused by structural changes that modify the contribution of the nuclear dipole fields to the ZF-$μ$SR signal. Our results for Bi2212 emphasize the importance of not assuming the nuclear-dipole field contribution is independent of temperature in ZF-$μ$SR studies of high-temperature (high-$T_c$) cuprate superconductors, and do not support a recent $μ$SR study of YBa$_2$Cu$_3$O$_{6+x}$ that claims to detect magnetic order in the PG phase.
We study the behavior of the pseudogap in overdoped Bi$_{2}$Sr$_2$CaCu$_2$O$_{8+d}$ by electronic Raman scattering (ERS) and angle-resolved photoemission spectroscopy (ARPES) on the same single crystals. Using both techniques we find that, unlike the superconducting gap, the pseudogap related to the anti-bonding band vanishes above the critical doping p$_c$ = 0.22. Concomitantly, we show from ARPES measurements that the Fermi surface of the anti-bonding band is hole-like below pc and becomes electron-like above p$_c$. This reveals that the appearance of the pseudogap depends on the Fermi surfa…
The heating-compensated interlayer tunneling spectroscopy is performed on stacks of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ intrinsic junctions. The high-accuracy spectra without the local heating, for varying temperatures and magnetic fields, reveal that the spectral weight forming the superconducting coherence peak is mainly contributed from the dip position of the hump structure of the pseudogap state. The observed U-shaped subgap structure is consistent with the weighted antinodal tunneling between Cu-O double layers in a junction as suggested in Ref. [17].
We report a fine tuned doping study of strongly overdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ single crystals using electronic Raman scattering. Combined with theoretical calculations, we show that the doping, at which the normal state pseudogap closes, coincides with a Lifshitz quantum phase transition where the active hole-like Fermi surface becomes electron-like. This conclusion suggests that the microscopic cause of the pseudogap is sensitive to the Fermi surface topology. Furthermore, we find that the superconducting transition temperature is unaffected by this transition, demonstrating that th…
We report muon spin relaxation ($μ$SR) measurements of optimally-doped and overdoped Bi$_{2+x}$Sr$_{2-x}$CaCu$_2$O$_{8+δ}$ (Bi2212) single crystals that reveal the presence of a weak temperature-dependent quasi-static internal magnetic field of electronic origin in the superconducting (SC) and pseudogap (PG) phases. In both samples the internal magnetic field persists up to 160~K, but muon diffusion prevents following the evolution of the field to higher temperatures. We consider the evidence from our measurments in support of PG order parameter candidates, namely, electronic loop currents and…
We report heating-compensated interlayer tunneling spectroscopy (ITS) performed on stacks of overdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ intrinsic junctions, where most of bias-induced heating in the ITS was eliminated. The onset temperature of the pseudogap (PG), revealed in the hump structure of the electronic excitation spectra, reached nearly room temperature for our overdoped intrinsic junctions, which represented the genuine PG onset. At a temperature below but close to $T_c$, both the superconducting coherence peak and the pseudogap hump coexisted, implying that the two gaps are of separate…
We report on magnetization experiments from which we obtain the field-induced kinetic energy density, $E_k$, in the superconducting phase of several Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ single crystal samples. The kinetic energy magnitude changes according to the characteristic reduction of the single-electron density of states produced by the pseudogap in the underdoped limit. Moreover, a remarkable peak of $E_k$ occurring at the specific holes density $p\sim0.18$ is related to a van Hove singularity due to the pseudogap closure. We also extracted the superfluid density, $ρ_s$. We conclude that $E_k…
Photoexcited quasiparticle relaxation dynamics in overdoped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ ($T_{c}$=65~K, hole doping $p$=0.22) single crystal is investigated as a function of temperature. We provide evidence of a $\sim$22~meV pseudogap ($T^{\ast}$$\approx$100~K) at this doping level. Our data support the scenario where both the superconducting gap and pseudogap coexist in the superconducting state. Our results also suggest an increased scattering rate between electrons and spin fluctuations as the sample enters the pseudogap phase.
We report atomic scale characterization of the pseudogap state in a high-T$_c$ superconductor, Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. The electronic states at low energies within the pseudogap exhibit spatial modulations having an energy-independent incommensurate periodicity. These patterns, which are oriented along the copper-oxygen bond directions, appear to be a consequence of an electronic ordering phenomenon--the observation of which correlates with the pseudogap in the density of electronic states. Our results provide a stringent test for various ordering scenarios in the cuprates, which have b…
We report the transverse relaxation rates 1/$T_2$'s of the $^{63}$Cu nuclear spin-echo envelope for double-layer high-$T_c$ cuprate superconductors HgBa$_{2}$CaCu$_{2}$O$_{6+d}$ from underdoped to overdoped. The relaxation rate 1/$T_{2L}$ of the exponential function (Lorentzian component) shows a peak at 220$-$240 K in the underdoped ($T_c$ = 103 K) and the optimally doped ($T_c$ = 127 K) samples but no peak in the overdoped ($T_c$ = 93 K) sample. The enhancement in 1/$T_{2L}$ suggests development of the zero frequency components of local field fluctuations. Ultraslow fluctuations are hidden i…
The tunneling spectra obtained within the ab-plane of Bi$_2$Sr$_2$CaCu$_2$O$_y$ (Bi2212) for temperatures below and above the critical temperature (T$_c$) are analyzed. We find that the tunneling conductance spectra for the underdoped compound in the superconducting state do not follow the conservation of states rule. There is a consistent loss of states for the underdoped BI2212 implying an underlying depression in the density of states (DOS) and hence the pseudogap near the Fermi energy (E$_F$). Such an underlying depression can also explain the peak-dip-hump structure observed in the spectr…
Tunneling spectra of near optimally doped, submicron Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ intrinsic Josephson junctions are presented, and examined in the region where the superconducting gap evolves into pseudogap. The spectra are analyzed using a self-energy model, proposed by Norman {\it et al.}, in which both quasiparticle scattering rate $Γ$ and pair decay rate $Γ_Δ$ are considered. The density of states derived from the model has the familiar Dynes' form with a simple replacement of $Γ$ by $γ_+$ = ($Γ$ + $Γ_Δ$)/2. The $γ_+$ parameter obtained from fitting the experimental spectra shows a roughl…
We investigate the electron-boson spectral density function, $I^2χ(ω,T)$, of CuO$_2$ plane in underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi-2212) and underdoped YBa$_2$Cu$_3$O$_{6.50}$ (Y-123) using the Eliashberg formalism. We apply a new (in-plane) pseudogap model to extract the electron-boson spectral function. For extracting the spectral function we assume that the spectral density function consists of two components: a sharp mode and the broad Millis-Monien-Pines (MMP) mode. We observe that both the resulting spectral density function and the intensity of the pseudogap show strong temperat…
To elucidate the pseudogap phase diagram including the overdoped state of high transition temperature (high-$T_c$) cuprates, we must understand the origin of the positive out-of-plane magnetoconductivity (MC) observed in these compounds. For this purpose, the out-of-plane resistivity $ρ_c(T,H)$ of an overdoped Bi$_{1.6}$Pb$_{0.4}$Sr$_{2}$CaCu$_{1.96}$Fe$_{0.04}$O$_{8+δ}$ (Bi-2212) single crystal is measured under pulsed magnetic fields up to 60 T. We show that the superconductive density-of-states (DOS) depletion effect, in addition to the pseudogap effect, clearly appears below the supercondu…
In the high-temperature ($T_{c}$) cuprate superconductors, increasing evidence suggests that the pseudogap, existing below the pseudogap temperature $T$*, has a distinct broken electronic symmetry from that of superconductivity. Particularly, recent scattering experiments on the underdoped cuprates have suggested that a charge ordering competes with superconductivity. However, no direct link of this physics and the important low-energy excitations has been identified. Here we report an antagonistic singularity at $T_{c}$ in the spectral weight of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ as a compel…
We have found a quantitative connection between the evolution of the inhomogeneous nanoscale electronic gaps (INSEG) state detected in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ by scanning tunneling microscopy/spectroscopy (STM/S) and the two universal, the upper and the lower, pseudogaps in high-temperature cuprate superconductors (HTCS). When the doping and temperature dependent INSEG map were analyzed by using our proposed hole-scale, we find that the two pseudogaps are connected to two specific coverages of the CuO$_2$ plane by INSEG: the 50\% and 100\% coverages of the CuO$_2$ planes by INSEG corresp…
To investigate the relationship between the pseudogap and superconductivity, we measured both the in-plane ($ρ_{ab}$) and out-of-plane ($ρ_c$) resistivity for oxygen-controlled Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ single crystals subject to magnetic fields (parallel to the $c$ axis) of up to 17.5 T. The onset temperature for the superconductive fluctuation, $T_{scf}$, is determined by the large positive in-plane magnetoresistance (MR) and negative out-of-plane MR observed near $T_c$, whereas the pseudogap opening temperature $T^*$ is determined by the semiconductive upturn of the zero-field $ρ_…
Although phase diagrams can be leveraged to investigate high transition temperature (high-$T_c$) superconductivity, the issue has not been discussed thoroughly. In this study, we elucidate the phase diagram of the overdoped side of high-$T_c$ cuprates via systematic anisotropic transport measurements for Pb-doped Bi-2212 single crystals. We demonstrate that the characteristic temperatures of the "weak" pseudogap opening and electronic coherence cross each other at a critical doping level, while those of the "strong" pseudogap merges into that of superconducting fluctuations above the critical …
We consider the problem of c-axis transport in double-layered cuprates, in particular with reference to Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ compounds. We exploit the effect of the two barriers on the thermal and tunnel transport. The resulting model is able to describe accurately the normal state c-axis resistivity in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$, from the underdoped side up to the strongly overdoped. We extend the model, without introducing additional parameters, in order to allow for the decrease of the barrier when an external voltage bias is applied. The extended model is found to d…
We report tunneling spectra of near optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ intrinsic Josephson junctions with area of 0.09 $μ$m$^2$, which avoid some fundamental difficulties in the previous tunneling experiments and allow a stable temperature-dependent measurement. A d-wave Eliashberg analysis shows that the spectrum at 4.2 K can be well fitted by considering electron couplings to a bosonic magnetic resonance mode and a broad high-energy continuum. Above $T_c$, the spectra show a clear pseudogap that persists up to 230 K, and a crossover can be seen indicating two different pseudogap p…
We study the reconfiguration of the angular resolved photoemission spectrum near $M$ point which occurs in Bi$_2$Sr$_2$CaCu$_2$O$_8$ upon cooling below the superconducting transition temperature. Restricting our attention to the case of underdoped samples we offer a phenomenological mechanism-independent argument which explains the emergence of a peak in the spectrum in terms of the normal state pseudogap. All of the basic experimental observations, including the peak dispersion, `dip-and-hump' shape of the superconducting state spectrum and appearance of the peak at the temperatures somewhat …
We present realistic multiband calculations of scanning tunneling spectra in Bi_{2}Sr_{2}CaCu_{2} O_{8+δ} over a wide doping range. Our modeling incorporates effects of a competing pseudogap and pairing gap as well as effects of strong electronic correlations, which are included by introducing self-energy corrections in the one-particle propagators. The calculations provide a good description of the two-gap features seen in experiments at low energies and the evolution of the Van Hove singularity (VHS) with doping, and suggest a possible quantum critical point near the point where the VHS cros…
We express the superconducting gap, $Δ(T)$, in terms of thermodynamic functions in both $s$- and d-wave symmetries. Applying to Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ and Y$_{0.8}$Ca$_{0.2}$Ba$_2$Cu$_3$O$_{7-δ}$ we find that for all dopings $Δ(T)$ persists, as a partial gap, high above $T_c$ due to strong superconducting fluctuations. Therefore in general two gaps are present above $T_c$, the superconducting gap and the pseudogap, effectively reconciling two highly polarized views concerning pseudogap physics.
Using a new variant of photoelectron spectroscopy, we measure the homogeneous near-nodal pairing ($Δ$) and pair-breaking self-energy ($Γ_S$) processes for a wide range of doping levels of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. For all samples we find that the pairing extends above the superconducting transition T$_c$ to a scale T$_{Pair}$ that is distinct from the antinodal pseudogap scale T$^*$ and near but slightly above T$_c$. We find that $Δ$ and T$_{Pair}$ are related with a strong coupling ratio 2$Δ$ /k$_B$T$_{Pair}\approx6$ across the entire doping phase diagram, i.e. independent of the effects…
A Fermi arc is a disconnected segment of a Fermi surface observed in the pseudogap phase of cuprate superconductors. This simple description belies the fundamental inconsistency in the physics of Fermi arcs, specifically that such segments violate the topological integrity of the band. Efforts to resolve this contradiction of experiment and theory have focused on connecting the ends of the Fermi arc back on itself to form a pocket, with limited and controversial success. Here we show the Fermi arc, while composed of real spectral weight, lacks the quasiparticles to be a true Fermi surface. To …
Recent scanning tunneling microscopy (STM) experiments of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ have shown evidence of real-space organization of electronic states at low energies in the pseudogap state. We argue based on symmetry considerations as well as model calculations that the experimentally observed modulations are due to a density wave of d-wave Cooper-pairs without global phase coherence. We show that STM measurements can distinguish a pair-density-wave from more typical electronic modulations such as those due to charge density wave ordering or scattering from an onsite periodic poten…
Establishing the presence and the nature of a quantum critical point in their phase diagram is a central enigma of the high-temperature superconducting cuprates. It could explain their pseudogap and strange metal phases, and ultimately their high superconducting temperatures. Yet, while solid evidences exist in several unconventional superconductors of ubiquitous critical fluctuations associated to a quantum critical point, in the cuprates they remain undetected until now. Here using symmetry-resolved electronic Raman scattering in the cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, we report the obser…
A magnetic field applied to type-II superconductors introduces quantized vortices that locally quench superconductivity, providing a unique opportunity to investigate electronic orders that may compete with superconductivity. This is especially true in cuprate superconductors in which mutual relationships among superconductivity, pseudogap, and broken-spatial-symmetry states have attracted much attention. Here we observe energy and momentum dependent bipartite electronic superstructures in the vortex core of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ using spectroscopic-imaging scanning tunneling microscop…
The real part of the in-plane optical self-energy data in underdoped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ (Bi-2212) and ortho II YBa$_{2}$Cu$_{3}$O$_{6.5}$ contains new and important information on the pseudogap. Using a theoretical model approach we find that the density of state lost below the pseudogap $Δ_{pg}$ is accompanied with a pileup just above this energy. The pileup along with a sharp mode in the bosonic spectral function leads to an unusually rapid increase in the optical scattering rate and a characteristically sloped peak in the real part of the optical self-energy. These features…
The in-plane optical properties of two crystals of the bilayer cuprate \LSxCCO, one with excess Ca and $x=0.10$ and the other with Sr and $x=0.15$, were investigated over the frequency range of 45--25000 cm$^{-1}$. The optical conductivity has been derived from Kramers-Kronig transformation. Each crystal exhibits a peak at around 15000 cm$^{-1}$ which corresponds to the charge-transfer gap of the parent insulator. With increasing carrier density, spectral weight shifts from the CT excitation to the low-$ω$ region. For the superconducting sample ($x=0.15$), the optical conductivity displays a p…
Evidence that the pseudogap (PG) in a near-optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ sample destroys the BCS logarithmic pairing instability [1] raises again the question of the role of the PG in the high-temperature superconducting cuprates [2]. The elimination of the BCS instability is consistent with the view that the PG competes with superconductivity. However, as noted in [1], the onset of superconductivity with a $T_c \sim 90$ K suggests an alternative scenario in which the PG reflects the formation of short range pairing correlations. Here, we report results obtained from a dynamic …
Interlayer tunneling resistivity is used to probe the low-energy density-of-states (DOS) depletion due to the pseudogap in the normal state of Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$. Measurements up to 60 T reveal that a field that restores DOS to its ungapped state shows strikingly different temperature and doping dependencies from the characteristic fields of the superconducting state. The pseudogap closing field and the pseudogap temperature $T^{\star}$ evaluated independently are related through a simple Zeeman energy scaling. These findings indicate a predominant role of spins over the orbital eff…
The ab-plane reflectance of Bi2Sr2CaCu2O(8+d) thin films was measured in the 30-25000 cm^(-1) range for one underdoped (Tc = 70 K), and one overdoped sample (Tc = 63 K) as a function of temperature (10-300 K). We find qualitatively similar behaviors in the temperature dependence of the normal-state infrared response of both samples. Above Tc, the effective spectral weight, obtained from the integrated conductivity, does not decrease when T decreases, so that no opening of an optical pseudogap is seen. We suggest that these are consequences of the pseudogap opening first in the k=(0, pi) direct…
The autocorrelation of angle resolved photoemission data from the high temperature superconductor Bi2Sr2CaCu2O8+d shows distinct peaks in momentum space which disperse with binding energy in the superconducting state, but not in the pseudogap phase. Although it is tempting to attribute a non-dispersive behavior in momentum space to some ordering phenomenon, a de-construction of the autocorrelation reveals that the non-dispersive peaks arise not from ordering, but rather from the tips of the Fermi arcs, which themselves do not change with binding energy.
Scanning tunneling microscopy/spectroscopy is used to examine the $4a$$\times$$4a$ electronic charge order (CO) in the pseudogap (PG) state above {\it T}$_{\rm c}$ on Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$. It is demonstrated that the static CO develops markedly in the inhomogeneous PG state, while it is very weak in the homogeneous PG state. We suggest that this static CO, which is considered to be stabilized by the pinning of the dynamically fluctuating CO, will remain below {\it T}$_{\rm c}$, together with the inhomogeneous gap structure, and coexist with the superconductivity.
Discriminating superconducting fluctuations from the pseudogap in Bi$_2$Sr$_2$Ca$_{n-1}$Cu$_n$O$_{2n+4+δ} (n = 2,3)$: A magnetotransport study
Hirosaki University（弘前大学）；Kyoto University of Advanced Science (KUAS)（京都先端科学大学）；University of Tokyo（东京大学）；Tohoku University（东北大学）；Kyoto University（京都大学）；Iwate University（岩手大学）
A detailed phenomenology of low energy excitations is a crucial starting point for microscopic understanding of complex materials such as the cuprate high temperature superconductors. Because of its unique momentum-space discrimination, angle-resolved photoemission spectroscopy (ARPES) is ideally suited for this task in the cuprates where emergent phases, particularly superconductivity and the pseudogap, have anisotropic gap structure in momentum space. We present a comprehensive doping-and-temperature dependence ARPES study of spectral gaps in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi-2212), covering…
From measurements of the ^{63}Cu Knight shift (K) and the nuclear spin-lattice relaxation rate (1/T_{1}) under magnetic fields from zero up to 28 T in the slightly overdoped superconductor TlSr_{2}CaCu_{2}O_{6.8} (T_{c}=68 K), we find that the pseudogap behavior, {\em i.e.}, the reductions of 1/T_{1}T and K above T_{c} from the values expected from the normal state at high T, is strongly field dependent and follows a scaling relation. We show that this scaling is consistent with the effects of the Cooper pair density fluctuations. The present finding contrasts sharply with the pseudogap proper…
We report the ultra-fast optical response of quasi-particles (QPs) in both the pseudogap (PG) and superconducting (SC) states of underdoped (UD) Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ (Bi2212) single crystal measured with the time-resolved pump-probe technique. At a probe energy $\hbarω_{pr}$=1.55 eV, it is found that the reflectivity change $Δ$R/R changes its sign at exactly $T_{c}$, which allows the direct separation of the charge dynamics of PG and SC QPs. Further systematic investigations indicate that the transient signals associated with PG and SC QPs depend on the probe beam energy and pol…
We reanalyze the data on the in-plane far infrared conductivity of underdoped orthoII YBa$_{2}$Cu$_{3}$O$_{6.50}$ (YBCO$_{6.50}$) in terms of a model in which a pseudogap opens on part of the Fermi surface with the remaining ungaped piece proportional to the temperature. The motivation for our model comes from recent angle-resolved photoemission spectroscopy data in underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi-2212), which have revealed the existence of arcs on the Fermi surface. We find the optical data to be consistent with arc formation. In addition we find some evidence that the electronic…
Mixing of topological states with superconductivity could result in topological superconductivity with the elusive Majorana fermions potentially applicable in fault-tolerant quantum computing. One possible candidate considered for realization of topological superconductivity is thin bismuth films on Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212). Here, we present angle-resolved and core-level photoemission spectroscopy studies of thin Bi films grown {\it in-situ} on as-grown Bi2212 that show the absence of proximity effect. We find that the electron transfer from the film to the substrate and the resu…
The physical properties of hole-doped cuprate high-temperature superconductors are heavily influenced by an energy gap known as the pseudogap whose origin remains a mystery second only to that of superconductivity itself. A key question is whether the pseudogap closes at a temperature T*. The absence of a specific heat anomaly, together with persistent entropy losses up to 300K, have long suggested that the pseudogap does not vanish at T*. However, amid a growing body of evidence from other techniques pointing to the contrary we revisit this question. Here we investigate if, by adding a temper…
Low magnetic field scanning tunneling spectroscopy of individual Abrikosov vortices in heavily overdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ unveils a clear d-wave electronic structure of the vortex core, with a zero-bias conductance peak at the vortex center that splits with increasing distance from the core. We show that previously reported unconventional electronic structures, including the low energy checkerboard charge order in the vortex halo and the absence of a zero-bias conductance peak at the vortex center, are direct consequences of short inter-vortex distance and consequent vortex-vortex…
Nuclear Magnetic Resonance (NMR) is a powerful local quantum probe of the electronic structure of materials, but in the absence of reliable theory the interpretation of the NMR data can be challenging. This is true in particular for the cuprate high-temperature superconductors. Over the years, a large base of NMR data became available, which makes a review of the early interpretation possible. Recently, it was shown that all planar $^{17}$O NMR shift and relaxation data available in the literature point to a temperature independent but doping dependent pseudogap, very similar to what was propo…
Current descriptions of the pseudogap in underdoped cuprates envision a doping-dependent transition line $T^*(p)$ which descends monotonically towards zero just beyond optimal doping. There is much debate as to the location of the terminal point $p^*$ where $T^*(p)$ vanishes, whether or not there is a phase transition at $T^*$ and exactly how $T^*(p)$ behaves below $T_c$ within the superconducting dome. One perspective sees $T^*(p)$ cutting the dome and continuing to descend monotonically to zero at $p_{crit} \approx 0.19$ holes/Cu $-$ referred to here as `entrant behavior'. Another perspectiv…
We used 2D coupled sine-Gordon equations combined with 3D heat diffusion equations to numerically investigate the thermal and electromagnetic properties of a $250 \times 70\,μ\mathrm{m}^2$ intrinsic Josephson junction stack. The 700 junctions are grouped to 20 segments; we assume that in a segment all junctions behave identically. At large input power a hot spot forms in the stack. Resonant electromagnetic modes, oscillating either along the length ((0, $n$) modes) or the width (($m$, 0) modes) of the stack or having a more complex structure, can be excited both with and without a hot spot. At…
We investigate the low-energy quasiparticle excitation spectra of cuprate superconductors by incorporating both superconductivity (SC) and competing orders (CO) in the bare Green's function and quantum phase fluctuations in the proper self-energy. Our approach provides consistent explanations for various empirical observations, including the excess subgap quasiparticle density of states, ``dichotomy'' in the momentum-dependent quasiparticle coherence and the temperature-dependent gap evolution, and the presence (absence) of the low-energy pseudogap in hole- (electron-) type cuprates depending …
Planar oxygen nuclear magnetic resonance (NMR) relaxation and shift data from all cuprate superconductors available in the literature are analyzed. They reveal a temperature independent pseudogap at the Fermi surface, which increases with decreasing doping in family specific ways, i.e., for some materials the pseudogap is substantial at optimal doping while for others it is nearly closed at optimal doping. The states above the pseudogap, or in its absence are similar for all cuprates and doping levels, and Fermi liquid-like. If the pseudogap is assumed exponential it can be as large as about 1…
Two contradictory phase diagrams have dominated the literature of high-$T_c$ cuprate superconductors. Does the pseudogap line cross the superconducting $T_c$-dome or not? To answer, we have revisited the experimental magnetic susceptibility and knight shift of four different compounds, La$_{1-x}$Sr$_x$CuO$_4$, Bi$_2$Sr$_2$Ca$_{1-x}$Y$_x$Cu$_2$O$_8$, Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$, and YBa$_2$Cu$_3$O$_{6+y}$, as a function of temperature and doping. The susceptibility can be described by the same function for all materials, having a magnetic and an electronic contributions. The former is the 2D …
Recent observations of broken symmetries have partly demystified the pseudogap phase. Here we review evidence for long-range intra-unit-cell(IUC) nematic order and its unexpectedly strong coupling to the phase of the fluctuating stripes in the pseudogap states of underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. In particular, we focus on the analysis techniques that reveal this evidence in scanning tunneling spectroscopy data, the definition of the extracted IUC nematic order parameter, and a phenomenological theory of the coupling between the IUC nematic order and the previously reported coexisting …
We propose and show that the c-axis transport in high-temperature superconductors is controlled by the pseudogap energy and the c-axis resistivity satisfies a universal scaling law in the pseudogap phase. We derived approximately a scaling function for the c-axis resistivity and found that it fits well with the experimental data of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+δ}$, and YBa$_2$Cu$_3$O$_{7-δ}$. Our works reveals the physical origin of the semiconductor-like behavior of the c-axis resistivity and suggests that the c-axis hopping is predominantly coherent.
In scanning tunneling microscopy (STM) conductance curves, the superconducting gap of cuprates is sometimes accompanied by small sub-gap structures at very low energy. This was documented early on near vortex cores and later at zero magnetic field. Using mean-field toy models of coexisting d-wave superconductivity ($d$SC), \emph{d}-form factor density wave ($d$FF-DW), and extended s-wave pair density wave ($s'$PDW), we find agreement with this phenomenon, with $s'$PDW playing a critical role. We explore the high variability of the gap structure with changes in band structure and density wave (…
We analyze the anomalies of superconducting state within a simple exactly solvable model of the pseudogap state, induced by fluctuations of ``dielectric'' short range order, for the model of the Fermi surface with ``hot'' patches. The analysis is performed for the arbitrary values of the correlation length xi_{corr} of this short range order. It is shown that superconducting energy gap averaged over these fluctuations is non zero in a wide temperature range above T_c - the temperature of homogeneous superconducting transition. This follows from the absence of self averaging of the gap over the…
Diode Effect May Assist Finding Proper Superconductivity Mechanism in Copper Oxides
Institute for Physical Research, National Academy of Sciences（亚美尼亚国家科学院物理研究所）；Laboratory of Advanced Quantum Materials and Devices, Institute for Quantum Studies, Chapman University（查普曼大学量子研究所先进量子材料与器件实验室）
The pseudogap (PG) state and its related intra-unit-cell symmetry breaking remain the focus in the research of cuprate superconductors. Although the nematicity has been studied in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, especially underdoped samples, its behavior in other cuprates and different doping regions is still unclear. Here we apply a scanning tunneling microscope to explore an overdoped (Bi, Pb)$_2$Sr$_2$CuO$_{6+δ}$ with a large Fermi surface (FS). The establishment of a nematic order and its real-space distribution is visualized as the energy scale approaches the PG.
Recent scanning tunnelling microscopy (STM) studies on Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi-2212) revealed the presence of severe inhomogeneity with length scale $L_0 \approx ξ_0$, the coherence length. Other studies have been interpreted in terms of mesoscale or nanoscale phase segregation. Here we analyze heat capacity and NMR data on Bi-2212 and (Y,Ca)Ba$_2$Cu$_3$O$_{7-δ}$ and find no evidence for phase segregation or gross inhomogeneity. For Bi-2212 the coherence scale $L_0$ increases with doping from 5 to 17$ξ_0$ and the hole density inhomogeneity decreases from 0.028 to 0.005 holes/Cu. We c…
In magnetic measurements on Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi-2212) single crystals, a general peak with a dynamical feature on both $S-H$ and $S-T$ curves was found with S the magnetic relaxation rate. At higher fields, the characteristic exponent $μ$ becomes negative, together with the positive curvature of $logE$ vs. $ logj$ and the scaling based on the 2D vortex glass theory or plastic creep theory, we conclude that the vortex motion above the second peak is plastic when $j\to 0$ and there is no vortex glass phase at finite temperatures in Bi-2212. The peak of S is then explained as the cr…
We analyse fluctuations about $T_c$ in the specific heat of (Y,Ca)Ba$_2$Cu$_3$O$_{7-δ}$, YBa$_2$Cu$_4$O$_8$ and Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. The mean-field transition temperature, $T_c^{mf}$, in the absence of fluctuations lies well above $T_c$ especially at low doping where it reaches as high as 150K. We show that phase and amplitude fluctuations set in simultaneously and $T_c^{mf}$ scales with the gap, $Δ_0$, such that $2Δ_0/k_BT_c^{mf}$ is comparable to the BCS weak-coupling value, 4.3, for d-wave superconductivity. We also show that $T_c^{mf}$ is unrelated to the pseudogap temperature, $…
