We present large-scale Monte Carlo results for the dynamical critical exponent z and the spatio-temporal two-point correlation function of a (2+1)-dimensional quantum XY model with bond dissipation, proposed to describe a quantum critical point in high-Tc cuprates near optimal doping. The phase variables of the model, originating with a parametrization of circulating currents within the CuO_2 unit cells in cuprates, are compact, {θ_{r,τ}} \in [-π,π>. The dynamical critical exponent is found to be z \approx 1, and the spatio-temporal correlation functions are explicitly demonstrated to be isotropic in space-imaginary time. The model thus has a fluctuation spectrum where momentum and frequency enter on equal footing, rather than having the essentially momentum-independent marginal Fermi liquid-like fluctuation spectrum previously reported for the same model.
We study a model of the quantum critical point of cuprates associated with the "circulating current" order parameter proposed by Varma. An effective action of the order parameter in the quantum disordered phase is derived using functional integral method, and the physical properties of the normal state are studied based on the action. The results derived within the ladder approximation indicate that the system is like Fermi liquid near the quantum critical point and in disordered regime up to minor corrections. This implies that the suggested marginal Fermi liquid behavior induced by the circu…
We derive an effective dissipative quantum field theory for fluctuating orbital currents in clean $CuO_2$ sheets of high-$T_c$ cuprates, based on a three-band model. The Coulomb repulsion term between $Cu$- and $O$-sites is decoupled in terms of current operators representing horizontal and vertical parts of circulating currents within each $CuO_2$ unit cell of the lattice. The model has ordering of currents at finite temperatures. The dissipative kernel in the model is of the form $|ω|/|{\bf q}|$, indicating Landau damping. Applications of the effective theory to other models are also discuss…
We consider the consequences for circulating-current states of a cyclic, four-spin, ``ring-exchange'' interaction of the type shown recently to be significant in cuprate systems. The real-space Hartree-Fock approach is used to establish the existence of charge-current and spin-current phases in a generalized Hubbard model for the CuO_2 planes in cuprates. We compare the results of the Hartree-Fock approximation with the correlated states renormalized by Gutzwiller projection factors which allows us to gauge the qualitative effects of projection to no double site occupancy. We find that charge …
Circulating current (CC) loops within the cuprate unit cell are proposed to play a key role in the physics of the pseudogap phase. However, main experimental observations motivated by this sophisticated proposal and seemingly supporting the CC model can be explained in frames of a simple and physically clear microscopic model. We argue that instead of a well-isolated Zhang-Rice (ZR) singlet $^1A_{1g}$ the ground state of the hole center [CuO$_4$]$^{5-}$ (cluster analog of Cu$^{3+}$ ion) in cuprates should be described by a complex $^1A_{1g}$-$^{1,3}B_{2g}$-$^{1,3}E_u$ multiplet, formed by a co…
I discuss a proposed phase diagram of the cuprate superconductors as a function of temperature, carrier concentration, and a strong magnetic field perpendicular to the layers. I show how the phase diagram gives a unified interpretation of a number of recent experiments.
Assuming, as suggested by recent neutron scattering experiments, that a broken symmetry state with orbital current order occurs in the pseudo-gap phase of the cuprate superconductors, we show that there must be associated equilibrium magnetic fields at various atomic sites in the unit cell, which should be detectable by NMR experiments.
We discuss how the quantum-critical-point scenario for high-T_c superconductors with density-driven charge order or stripe formation finds support from recent EXAFS experiments. Our phase diagram has the interesting feature, which is also suggested by the EXAFS experiments, that some cuprates may not show well-formed stripe phase. We also consider the extensions of the scenario to include the interesting possibility of first-order transitions which call for further experimental and theoretical investigation.
Superconductivity research is like running a marathon. Three decades after the discovery of high-Tc cuprates, there have been mass data generated from transport measurements, which bring fruitful information. In this review, we give a brief summary of the intriguing phenomena reported in electron-doped cuprates from the aspect of electrical transport as well as the complementary thermal transport. We attempt to sort out common features of the electron-doped family, e.g. the strange metal, negative magnetoresistance, multiple sign reversals of Hall in mixed state, abnormal Nernst signal, comple…
For strongly correlated electrons the relation between total number of charge carriers $n_e$ and the chemical potential $μ$ reveals for large Coulomb energy the apparently paradoxical pinning of $μ$ within the Mott gap, as observed in high-$T_c$ cuprates. By unravelling consequences of the non-trivial topology of the charge gauge U(1) group and the associated ground state degeneracy we found a close kinship between the pinning of $μ$ and the zero-temperature divergence of the charge compressibility $κ\sim\partial n_e/\partialμ$, which marks a novel quantum criticality governed by topological c…
We argue that in strongly correlated electron system collective instanton excitations of the phase field (dual to the charge) arise with a great degree of stability, governed by gauge flux changes by an integer multiple of $2π$. By unraveling consequences of the non-trivial topology of the charge gauge U(1) group, we found that the pinning of $μ$ and the zero-temperature divergence of charge compressibility $κ\sim\partial n_e/\partialμ$ defines novel "hidden" quantum criticality on verge of the Mott transition governed by the protectorate of stable topological numbers rather than Landau paradi…
With particular reference to the role of the renormalization group approach and Ward identities, we start by recalling some old features of the one-dimensional Luttinger liquid as the prototype of non-Fermi-liquid behavior. Its dimensional crossover to the Landau normal Fermi liquid implies that a non-Fermi liquid, as, e.g., the normal phase of the cuprate high temperature superconductors, can be maintained in d>1, only in the presence of a sufficiently singular effective interaction among the charge carriers. This is the case when, nearby an instability, the interaction is mediated by fluctua…
A description of the electronic correlations contained in the Hubbard model on the square-lattice perturbed by very weak three-dimensional uniaxial anisotropy in terms of the residual interactions of charge $c$ fermions and spin-neutral composite two-spinon $s1$ fermions is used to access further information on the origin of quantum critical behavior in the hole-doped cuprate superconductors. Excellent quantitative agreement with their anisotropic linear-$ω$ one-electron scattering rate and normal-state linear-$T$ resistivity is achieved. Our results provide strong evidence that the normal-sta…
Motivated by the recent report of broken time-reversal symmetry and zero momentum magnetic scattering in underdoped cuprates, we investigate under which circumstances orbital currents circulating inside a unit cell might be stabilized in extended Hubbard models that explicitly include oxygen orbitals. Using Gutzwiller projected variational wave functions that treat on an equal footing all instabilities, we show that orbital currents indeed develop on finite clusters, and that they are stabilized in the thermodynamic limit if additional interactions, e.g. strong hybridization with apical oxygen…
The three central phenomena of cuprate superconductors are linked by a common doping $p^{\star}$, where the enigmatic pseudogap phase ends, around which the superconducting phase forms a dome, and at which the resistivity exhibits an anomalous linear dependence on temperature as $T \to 0$. However, the fundamental nature of $p^{\star}$ remains unclear, in particular whether it marks a true quantum phase transition. We have measured the specific heat $C$ of the cuprates Eu-LSCO and Nd-LSCO at low temperature in magnetic fields large enough to suppress superconductivity, over a wide doping range…
Antiferromagnetic Quantum Criticality in Infinite-Layer Cuprates Sr1-xNdxCuO2
Tsinghua University（清华大学）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Frontier Science Center for Quantum Information（量子信息前沿科学中心）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Southern University of Science and Technology（南方科技大学）
At the nematic quantum critical point that exists in the $d_{x^2-y^2}$-wave superconducting dome of cuprates, the massless nodal fermions interact strongly with the quantum critical fluctuation of nematic order. We study this problem by means of renormalization group approach and show that, the fermion damping rate $\left|\mathrm{Im}Σ^R(ω)\right|$ vanishes more rapidly than the energy $ω$ and the quasiparticle residue $Z_f\rightarrow 0$ in the limit $ω\rightarrow 0$. The nodal fermions thus constitute an unconventional non-Fermi liquid that represents an even weaker violation of Fermi liquid t…
Theoretical attempts to explain the origin of high temperature superconductivity are challenged by the complexity of the normal state, which exhibits three regimes with increasing hole doping: a pseudo-gap regime when underdoped, strange power laws near optimal doping and more conventional metallic behavior when heavily overdoped. We suggest that the origin of this behavior is linked to a zero temperature quantum phase transition separating the overdoped Fermi liquid from a spin-charge separated underdoped phase. Central to our analysis is a new $Z_2$ gauge theory formulation, which supports t…
We study quantum oscillations for a system of fermionic and bosonic dimers and compare the results to those experimentally observed in the cuprate superconductors in their underdoped regime. Based on gauge invariance, we argue that the charge carriers obey the Onsager quantization condition and quantum oscillations take on a Lifshitz-Kosevich form. We obtain the effective mass and find good qualitative agreement with experiments if we tune the model to the point where the observed mass divergence at optimum doping is associated to a van Hove singularity at which four free-dimer Fermi pockets t…
In the high temperature cuprate superconductors, the pervasiveness of anomalous electronic transport properties suggests that violation of conventional Fermi liquid behavior is closely tied to superconductivity. In other classes of unconventional superconductors, atypical transport is well correlated with proximity to a quantum critical point, but the relative importance of quantum criticality in the cuprates remains uncertain. Here we identify quantum critical scaling in the electron-doped cuprate material La2-xCexCuO4 with a line of quantum critical points that surrounds the superconducting …
In a frame of the $t-J-G$ model we derive the microscopical expression for the circulating orbital currents in layered cuprates using the anomalous correlation functions. In agreement with $μ$-on spin relaxation ($μ$SR), nuclear quadrupolar resonance (NQR) and inelastic neutron scattering(INS) experiments in YBa$_2$Cu$_3$O$_{6+x}$ we successfully explain the order of magnitude and the monotonous increase of the {\it internal} magnetic fields resulting from these currents upon cooling. However, the jump in the intensity of the magnetic fields at T$_c$ reported recently seems to indicate a non-m…
We argue that nuclear magnetic resonance experiments are a site-sensitive probe for the electronic spectrum in the mixed state of the high-$T_c$ cuprates. Within a spin-fermion model, we show that the Doppler-shifted electronic spectrum arising from the circulating supercurrent changes the low-frequency behavior of the imaginary part of the spin-susceptibility. For a hexagonal vortex lattice, we predict that these changes lead to {\it (a)} a unique dependence of the $^{63}$Cu spin lattice relaxation rate, $1/T_1$, on resonance frequency, and {\it (b)} a temperature dependence of $T_1$ which va…
We study three proposals for broken symmetry in the cuprate pseudogap - oxygen antiferromagnetism, $Θ_{II}$ orbital loop currents, and circulating currents involving apex oxygens - through numerical exploration of multi-orbital Hubbard models. Our numerically exact results show no evidence for the existence of oxygen antiferromagnetic order or the $Θ_{II}$ phase in the three-orbital Hubbard model. The model also fails to sustain an ordered current pattern even with the presence of additional apex oxygen orbitals. We thereby conclude that it is difficult to stabilize the aforementioned phases i…
The effect of uniaxial pressure on superconductivity was examined for a high-Tc cuprate La1.64Eu0.2Sr0.16CuO4, which is located at the boundary between the superconducting and stripe phases. We found remarkably large anisotropy of the uniaxial pressure effect not only between the in-plane and out-of-plane pressures but also within the CuO2-plane. When the pressure is applied along the tetragonal [110] direction, we found the largest pressure effect ever observed in cuprates, dTc/dP - 2.5 K/kbar, while the change of Tc was not appreciable when applied along [100]. This substantial in-plane anis…
There exists increasing evidence that the phase diagram of the high-transition temperature (Tc) cuprate superconductors is controlled by a quantum critical point. One distinct theoretical proposal is that, with decreasing hole-carrier concentration, a transition occurs to an ordered state with two circulating orbital currents per CuO2 square. Below the 'pseudogap' temperature T* (T* > Tc), the theory predicts a discrete order parameter and two weakly-dispersive magnetic excitations in structurally simple compounds that should be measurable by neutron scattering. Indeed, novel magnetic order an…
We investigate the possibility of spin texture in the bilayer cuprate superconductor $\rm Bi_2Sr_2CaCu_2O_{8+δ}$ using cluster dynamical mean field theory (CDMFT). The one-band Hubbard model with a small interlayer hopping and a Rashba spin-orbit coupling is used to describe the material. The $d$-wave order parameter is not much affected by the presence of the Rashba coupling, but a small triplet component appears. We find a spin texture circulating in the same direction around $\mathbf{k}=(0,0)$ and $\mathbf{k}=(π,π)$ and stable against the superconducting phase. The amplitude of the spin str…
One of the leading issues in high-$T_C$ superconductors is the origin of the pseudogap phase in underdoped cuprates. Using polarized elastic neutron diffraction, we identify a novel magnetic order in the YBa$_2$Cu$_3$O$_{6+x}$ system. The observed magnetic order preserves translational symmetry as proposed for orbital moments in the circulating current theory of the pseudogap state. To date, it is the first direct evidence of an hidden order parameter characterizing the pseudogap phase in high-$T_C$ cuprates.
Electrical resistivity measurements on a single crystal of the heavy-fermion superconductor CeCoIn_5 at pressures to 4.2 GPa reveal a strong crossover in transport properties near P^* \approx 1.6 GPa, where T_c is a maximum. The temperature-pressure phase diagram constructed from these data provides a natural connection to cuprate physics, including the possible existence of a pseudogap.
Universality of linear in temperature and linear in field Planckian scattering rate in high temperature cuprate superconductors
National Center for Theoretical Sciences（国家理论科学中心）；National Yang Ming Chiao Tung University（国立阳明交通大学）；Universidad de Los Andes（洛斯安第斯大学）；Universidad del Rosario（玫瑰大学）；National High Magnetic Field Laboratory（国家高磁场实验室）；Florida State University（佛罗里达州立大学）
We study the optical conductivity sigma(Omega) of an electron system near a quantum-critical point with finite-wavelength ordering. sigma(Omega) vanishes in clean Galilean-invariant systems, unless electrons are coupled to dynamical collective modes, which dissipate the current. This coupling introduces a nonuniversal energy scale. Depending on the parameters of each specific system, a variety of responses arise near criticality: scaling peaks at a temperature- and doping-dependent frequency, peaks at a fixed frequency, or no peaks to be associated with criticality. Therefore the lack of scali…
This paper is concerned with the possibility of a direct second order transition out of a collinear Neel phase to a paramagnetic spin liquid in two dimensional quantum antiferromagnets. Contrary to conventional wisdom, we show that such second order quantum transitions can potentially occur to certain spin liquid states popular in theories of the cuprates. We provide a theory of this transition and study its universal properties in an $ε$ expansion. The existence of such a transition has a number of interesting implications for spin liquid based approaches to the underdoped cuprates. In partic…
The occurrence of high-T_c superconductivity in systems including the cuprates and the iron-based superconductors, is known to coincide with the existence of anomalous normal-state properties which have been associated with quantum criticality. We argue here that this observation results from the fact that quantum criticality can allow the occurrence of very-strong-coupling superconductivity by preventing its suppression due to competing symmetry-breaking instabilities. Treating the electrons through a large-U ansatz yields their separation into boson quasiparticles which are directly involved…
IIn the pseudogap regime of the cuprates, charge order breaks a $\mathbb{Z}_{2}$ symmetry. Therefore, the interaction of charge order and quenched disorder due to potential scattering, can, in principle, be treated as a random field Ising model. A numerical analysis of the ground state of such a random field Ising model reveals local, glassy dynamics in both $2D$ and $3D$. The glassy dynamics are treated as a heat bath which couple to the itinerant electrons, leading to an unusual electronic non-Fermi liquid. If the dynamics are strong enough, the electron spectral function has no quasiparticl…
With understood exceptions, conventional superconductivity does not coexist with long-range magnetic order[1]. In contrast, unconventional superconductivity develops near a boundary separating magnetically ordered and magnetically disordered phases[2,3]. A maximum in the superconducting transition temperature Tc develops where this boundary extrapolates to T=0 K, suggesting that fluctuations associated with this magnetic quantum-critical point are essential for unconventional superconductivity[4,5]. Invariably though, unconventional superconductivity hides the magnetic boundary when T < Tc, pr…
We investigate the effect of anti-ferromagnetic (AF) quantum criticality on the magnetic penetration depth $λ(T)$ in line-nodal superconductors, including the cuprates, the iron pnictides, and the heavy-fermion superconductors. The critical magnetic fluctuation renormalizes the current vertex and drastically enhances zero-temperature penetration depth $λ(0)$, which is more remarkable in the iron-pnictide case due to the Fermi-surface topology. Additional temperature ($T$) dependence of the current renormalization makes the expected $T$-linear behavior at low temperatures approaching to $T^{1.5…
We analyze a candidate theory for the strange metal near optimal hole-doping in the cuprate superconductors. The theory contains a quantum phase transition between metals with large and small Fermi surfaces of spinless fermions carrying the electromagnetic charge of the electron, but the transition does not directly involve any broken global symmetries. The two metals have emergent SU(2) and U(1) gauge fields respectively, and the transition is driven by the condensation of a real Higgs field, carrying a finite lattice momentum and an adjoint SU(2) gauge charge. This Higgs field measures the l…
We use quantum Monte-Carlo simulations to calculate the phase diagram and the correlation functions for the quantum phase transitions in the two-dimensional dissipative XY model with and without four-fold anisotropy. Without anisotropy, the model describes the superconductor to insulator transition in two-dimensional dirty superconductors. With anisotropy, the model represents the loop-current order observed in the under-doped cuprates and its fluctuations, as well as the fluctuations near the ordering vector in simple models of itinerant antiferromagnets. These calculations test an analytic s…
The highly anisotropic and qualitatively different nature of in- and out-of-plane charge dynamics in high-Tc cuprates cannot be accommodated within the conventional Boltzmann transport theory. The variation of in- and out-of-plane resistivities with temperature and hole content are also anomalous and cannot be explained by Fermi-liquid theory. In this study we have proposed a simple phenomenological model for the dc resistivity of cuprates by incorporating two firmly established generic features of all hole doped cuprate superconductors- (1) the pseudogap in the quasiparticle energy spectrum a…
A grand challenge in many-body quantum physics is to explain the apparent connection between quantum criticality and high-temperature superconductivity in the cuprates and similar systems, such as the iron pnictides and chalcogenides. Here we argue that the quantum-critical regime plays an essential role in activating a strong-pairing mechanism: although pairing bosons create a symmetry-breaking instability which suppresses pairing, the combination of these broken-symmetry states within the critical regime can restore this symmetry for the paired quasiparticles. This condition is shown to be m…
A new phenomenology is proposed for the superfluid density of strongly underdoped cuprate superconductors based on recent data for ultra-clean single crystals of YBCO. The data feature a puzzling departure from Uemura scaling and a decline of the slope as the T_c = 0 quantum critical point is approached. We show that this behavior can be understood in terms of the renormalization of quasiparticle effective charge by quantum fluctuations of the superconducting phase as described by a (3+1)-dimensional XY model. We calculate the renormalization of the superfluid density and its slope, explain th…
One of the leading issues in high-$\rm T_c$ copper oxide superconductors is the origin of the pseudogap phase in the underdoped regime of their phase diagram. Using polarized neutron diffraction, a novel magnetic order has been identified as an hidden order parameter of the pseudogap as the transition temperature corresponds to what is expected for the pseudogap. The observed magnetic order preserves translational symmetry as predicted for orbital moments in the circulating current theory. Being now reported in three different cuprates familles, it appears as a universal phenomenon whatever th…
At quantum critical points (QCP) \cite{Pfeuty:1971,Young:1975,Hertz:1976,Chakravarty:1989,Millis:1993,Chubukov:1 994,Coleman:2005} there are quantum fluctuations on all length scales, from microscopic to macroscopic lengths, which, remarkably, can be observed at finite temperatures, the regime to which all experiments are necessarily confined. A fundamental question is how high in temperature can the effects of quantum criticality persist? That is, can physical observables be described in terms of universal scaling functions originating from the QCPs? Here we answer these questions by examinin…
Within the Hubbard-Holstein model, we evaluate the various crossover lines marking the opening of pseudogaps in the cuprates, which, in our scenario, are ruled by the proximity to a charge-ordering quantum criticality (stripe formation). We provide also an analysis of their isotopic dependencies, as produced by critical fluctuations. We find no isotopic shift of the temperature $T^0$ marked as a reduction of the quasiparticle density of states in various experiments, and a substantial positive shift of the pseudogap-formation temperature $T^*$. We infer that the superconducting critical temper…
We present finite temperature extension of the QED$_3$ theory of underdoped cuprates. The theory describes nodal quasiparticles whose interactions with quantum proliferated vortex-antivortex pairs are represented by an emergent U(1) gauge field. Finite temperature introduces a scale beyond which the long wavelength fluctuations in the spatial components of vorticity are suppressed. As a result, the spin susceptibility of the pseudogap state is bounded by $T^2$ at low T and crosses over to $\sim T$ at higher $T$, while the low-$T$ electronic specific heat scales as $T^2$, reflecting the thermod…
The exotic nature of many strongly correlated materials at reasonably high temperatures, for instance cuprate superconductors in their normal state, has lead to the suggestion that such behavior occurs within a quantum critical region where the physics is controlled by the influence of a phase transition down at zero temperature. Such a scenario can be thought of as a bottom-up approach, with the zero temperature mechanisms finding a way to manifest critical behavior at high temperatures. Here we propose an alternative, top-down, mechanism by which strong kinematic constraints that can only be…
The anomalous transport and thermodynamic properties in the quantum-critical region, in the cuprates, and in the quasi-two dimensional Fe-based superconductors and heavy-fermion compounds, have the same temperature dependences. This can occur only if, despite their vast microscopic differences, a common statistical mechanical model describes their phase transitions. The antiferromagnetic (AFM)-ic models for the latter two, just as the loop-current model for the cuprates, map to the dissipative XY model. The solution of this model in 2+1 D reveals that the critical fluctuations are determined b…
We develop a concrete theory of continuous stripe melting quantum phase transitions in two dimensional metals and the associated Fermi surface reconstruction. Such phase transitions are strongly coupled but yet theoretically tractable in situations where the stripe ordering is destroyed by proliferating doubled dislocations of the charge stripe order. The resulting non-Landau quantum critical point (QCP) has strong stripe fluctuations which we show decouple dynamically from the Fermi surface even though static stripe ordering reconstructs the Fermi surface. We discuss connections to various st…
We derive the restricted optical-conductivity sum rule for a model with circulating orbital currents. It is shown that an unusual coupling of the vector potential to the interaction term of the model Hamiltonian results in a non-standard form of the sum rule. As a consequence, the temperature dependence of the restricted spectral weight could be compatible with existing experimental data for high-$T_c$ cuprates above the critical temperature $T_c$. We extend our results to the superconducting state, and comment on the differences and analogies between these two symmetry-breaking phenomena.
The in-plane resistivity $ρ$ and thermal conductivity $κ$ of FeAs-based superconductor KFe$_2$As$_2$ single crystal were measured down to 50 mK. We observe non-Fermi-liquid behavior $ρ(T) \sim T^{1.5}$ at $H_{c_2}$ = 5 T, and the development of a Fermi liquid state with $ρ(T) \sim T^2$ when further increasing field. This suggests a field-induced quantum critical point, occurring at the superconducting upper critical field $H_{c_2}$. In zero field there is a large residual linear term $κ_0/T$, and the field dependence of $κ_0/T$ mimics that in d-wave cuprate superconductors. This indicates that…
We describe two dimensional models with a metallic Fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension. The primary examples involve transitions with a topological order parameter associated with dislocations in collinear spin density wave ("stripe") correlations: the gapping of the order parameter fluctuations leads to a fractionalization of spin and charge collective modes, and this transition has been proposed as a candidate for the cuprates near optimal doping. The coupling between the order p…
We forward here the case that the anomalous electron states found in cuprate superconductors and related systems are rooted in a deeply non-classical fermion sign structure. The collapse of Mottness as advocated by Phillips and supported by recent DCA results on the Hubbard model is setting the necessary microscopic conditions. The crucial insight is due to Weng who demonstrated that in the presence of Mottness the fundamental workings of quantum statistics changes and we will elaborate on the effects of this Weng statistics with an emphasis on characterizing these further using numerical meth…
We investigate the effect of nonmagnetic disorder on the stability of the algebraic spin liquid ($ASL$) by deriving an effective field theory, nonlinear $σ$ model ($NLσM$). We find that the anomalous critical exponent characterizing the criticality of the $ASL$ causes an anomalous gradient in the $NLσM$. We show that the sign of the anomalous gradient exponent or the critical exponent of the $ASL$ determines the stability of the "dirty" $ASL$. A positive exponent results in an unstable fixed point separating delocalized and localized phases, which is consistent with our previous study [Phys. R…
In the high-Tc cuprates, the unusual dependence of Tc on external pressure results from the combination of the nonmonotonic dependence of Tc on hole doping or hole-doping distribution among inequivalent layers, and from an ``intrinsic'' contribution. After reviewing our work on the interplay among Tc, hole content, and pressure in the bilayered and multilayered cuprate superconductors, we will discuss how the proximity to an electronic topological transition (ETT) may give a microscopic justification of the ``intrinsic'' pressure dependence of Tc in the cuprates. As a function of the proximity…
