I present a formalism for dealing directly with the effects of the Gutzwiller projection, which is implicit in the t-J model widely believed to underly the phenomenology of the high-Tc cuprates. I suggest that a true BCS condensation from a Fermi liquid state takes place, but in the unphysical space prior to projection. The theory which results upon projection does not follow conventional rules of diagram theory and in fact in the normal state is a Z=0 non-Fermi liquid. Anomalous properties of this strange metal normal state are predicted and compared to experiments.
Electrical and magnetic properties of underdoped cuprates in the spin gap phase, a precursor to high Tc superconducting state, is riddled with puzzles. We propose a novel reference state to study this phase, where each hole dopant adds one real holon and one real spinon, with Haldane exclusion statistics $g_{\rm h} =1$ and $g_{\rm s} = {1/2}$, to a fairly inert (pseudo gaped) spin liquid vacuum, resulting in a low density spin-charge liquid. Spins and charges interact and form a novel collective state, a \textit{3/2-Fermi liquid}. A holon pairs with a spinon; this hole like fermion composite c…
In superconductors, electrons bound into Cooper pairs conduct a dissipationless current. The strength of the Cooper pairs scales with the value of the critical transition temperature (Tc). In cuprate high-Tc superconductors, however, the pairing mechanism is still unexplained. Here we unveil why in the cuprates the Cooper pairs are so strongly bound to work out the extraordinary high Tc. From one-to-one correspondence between numerical simulation on a microscopic cuprate model and a simple two-component fermion model, we show that hidden fermions emerge from the strong electron correlation and…
The quantum interference effects due to the Aharonov-Bohm-type phase factors are studied in the layered $t-t'-t_\perp-U-J$ strongly correlated system relevant for cuprates. Casting Coulomb interaction in terms of composite-fermions via the flux attachment facility, we argue that U(1) compact group instanton events labeled by a topological winding number are essential configurations of the phase field dual to the charge. The impact of these topological excitations is calculated for the phase diagram, which displays the "hidden" quantum critical point.
Systematic analysis of the planar resistivity, Hall effect and cotangent of the Hall angle for the electron-doped cuprates reveals underlying Fermi-liquid behavior even deep in the antiferromagnetic part of the phase diagram. The transport scattering rate exhibits a quadratic temperature dependence, and is nearly independent of doping, compound and carrier type (electrons vs. holes), and hence universal. Our analysis moreover indicates that the material-specific resistivity upturn at low temperatures and low doping has the same origin in both electron- and hole-doped cuprates.
We present the first demonstration of vortices in an electron-type cuprate superconductor, the highest $T_c$ (= 43 K) electron-type cuprate $Sr_{0.9}La_{0.1}CuO_2$. Our spatially resolved quasiparticle tunneling spectra reveal a hidden low-energy pseudogap inside the vortex core and unconventional spectral evolution with temperature and magnetic field. These results cannot be easily explained by the scenario of pure superconductivity in the ground state of high-$T_c$ superconductivity.
We study a model for low doped cuprates where holes aggregate into oriented stripe segments which have a vortex and an antivortex fixed to the extremes. We argue that due to the interaction between segments a state with macroscopic polarization is stabilized, which we call a ferronematic. This state can be characterized as a charge nematic which, due to the net polarization, breaks inversion symmetry and also exhibits an incommensurate spin modulation. Our calculation can reproduce the doping dependent spin structure factor of lanthanum cuprates in excellent agreement with experiment and allow…
We report extensive muon spin rotation measurements on the lightly doped Y1-xCaxBa2Cu3O6+y compound, which allows us to disentangle the effect of disorder, controlled by random Ca2+ substitution, from that of mere doping. A 3D phase diagram of lightly doped cuprates is accurately drawn, showing that a thermally activated antiferromagnetic phase competes with superconductivity around a quantum critical point, hidden underneath a frozen insulating magnetic state. Disorder suppresses both competing order parameters and unveils the underlying frozen state. Doping and disorder destroy the activated…
We follow the line of reasoning that hidden broken symmetries are the root of quantum oscillations observed in underdoped superconductors and examine the role of bilayer splitting and incommensuration. This is a view that eschews the notion of a featureless Mott liquid as the source of complexity. Instead, our view is grounded in a conventional Fermi surface and quasiparticles. We show that bilayer splitting and/or incommensurate $d$-density wave order can lead to many interesting results, in particular a splitting of the main frequency of the quantum oscillations.
Motivated by recent studies of odd-parity multipole order in condensed matter physics, we theoretically study magnetoelectric responses in an electric octupole state. Investigating the Edelstein effect and spin Hall effect in a locally noncentrosymmetric bilayer Rashba model, we clarify characteristic properties due to parity violation in the electric octupole state. Furthermore, a possible realization of electric octupole order in bilayer high-Tc cuprate superconductors is proposed. Our calculation of magnetic torque is consistent with recent experimental observation of a kink above the super…
In this paper, we show that the theory of high $T_c$ superconductivity based on a microscopic model with $d$-density wave (DDW) scenario in the pseudogap phase is able to reproduce some of the most important features of the recent experimentally discovered hidden charge order in several families of Cuprates. In particular, by computing and comparing energies of charge orders of different modulation directions derived from a full microscopic theory with $d$-density wave scenario, the axial charge order $ϕ_{X(Y)}$ with wavevector $\mathbf{Q}=(Q_0,0)((0,Q_0))$ is shown to be unambiguously energet…
In the present paper II, we will gain an understanding of the nematicity, insulating ground state (IGS), nematicity to stripe phase transition, Fermi pockets evolution, and resistivity temperature upturn, as to be metal - insulator (fermion-boson)- crossover (MIC) phenomena for the pseudogap (PG) region of cuprates. While in the paper I [1], we obtained an understanding of the observed heat conductivity downturn, anomalous Lorentz ratio, insulator resistivity boundary, nonlinear entropy as manifestations of the same MIC. The recently observed nematicity and hidden magnetic order are related to…
The elucidation of the pseudogap phenomenon of the cuprates, a set of anomalous physical properties below the characteristic temperature T* and above the superconducting transition temperature Tc, has been a major challenge in condensed matter physics for the past two decades. Following initial indications of broken time-reversal symmetry in photoemission experiments, recent polarized neutron diffraction work demonstrated the universal existence of an unusual magnetic order below T*. These findings have the profound implication that the pseudogap regime constitutes a genuine new phase of matte…
Experimental data are the source of understanding matter. However, measurable quantities are limited and theoretically important quantities are sometimes hidden. Nonetheless, recent progress of machine-learning techniques opens possibilities of exposing them only from available experimental data. In this paper, after establishing the reliability of the method in various careful benchmark tests, the Boltzmann-machine method is applied to the angle-resolved photoemission spectroscopy spectra of cuprate high temperature superconductors, Bi$_2$Sr$_2$CuO$_{6+δ}$ (Bi2201) and Bi$_2$Sr$_2$CaCuO$_{8+δ…
An emergence of magnetic boson of instantonic nature, that provides a Cooper-'pairing glue', is considered in the repulsive 'nested' Hubbard model of superconducting cuprates. It is demonstrated, that antiferromagnetic instantons of a spin density wave type may have negative energy due to coupling with Cooper pair condensate. A set of Eliashberg-like equations is derived and solved self-consistently, proving the above suggestion. An instantonic propagator plays the role of Green function of pairing 'glue' boson. Simultaneously, the instantons defy condensation of the mean-field SDW order. We h…
The strange metal phase of optimally and overdoped cuprates exhibits a number of anomalous transport properties: unsaturating linear T resistivity, distinct relaxation times for Hall angle and resistivity, temperature dependent anisotropic relaxation times, and a characteristic crossover from supposed Fermi Liquid to linear T behavior. All receive natural explanations and quantitative fits in terms of the Hidden Fermi Liquid theory.
The interplay of charge orders with superconductivity in underdoped cuprates at high magnetic fields ($H$) is an open question, and even the value of the upper critical field ($H_{c2}$), a measure of the strength of superconductivity, has been the subject of a long-term debate. We combined three complementary transport techniques on underdoped La$_{1.8-x}$Eu$_{0.2}$Sr$_{x}$CuO$_{4}$ with a "striped" charge order and a low $H=0$ transition temperature $T_{c}^{0}$, to establish the $T-H$ phase diagram and reveal the ground states in CuO$_2$ planes: a superconductor, a wide regime of superconduct…
The renormalization factor, dubbed ``quasiparticle charge'' Z_e, of the coupling between the supercurrent and quasiparticles was analyzed in the context of high temperature cuprates in a recent paper by Ioffe and Millis. They observed that Z_e in cuprates deviates from the BCS value (Z_e=1), which was interpreted as the proximity effect near a Mott insulator. Here we show that the deviation from Z_e=1 can occur, in general, even in the absence of quasiparticle interactions, when the superconducting order coexists with another order parameter with the same internal symmetry. As an example, we c…
The pseudogap phase of the cuprate superconductors is argued to be characterized by a hidden broken symmetry of d-wave character in the particle-hole channel that leads to staggered orbital magnetism. This proposal has many striking phenomenological consequences, but the most direct signature of this order should be visible in the neutron scattering experiments. The theoretical underpinning of these experiments is discussed.
A rare combination of strong spin-orbit coupling and electron-electron correlations makes the iridate Mott insulator Sr$_2$IrO$_4$ a promising host for novel electronic phases of matter. The resemblance of its crystallographic, magnetic and electronic structures to La$_2$CuO$_4$, as well as the emergence upon doping of a pseudogap region and a low temperature $d$-wave gap, has particularly strengthened analogies to cuprate high-$T_c$ superconductors. However, unlike the cuprate phase diagram that features a plethora of broken symmetry phases in a pseudogap region that include charge density wa…
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…
In the present work we address a long standing problem of the magnetic ground state and magnetic excitations in underdoped cuprates. Modelling cuprates by the extended $t-J$ model we show that there is a hidden dimensionless parameter $λ$ which drives magnetic criticality at low doping $x$. Hence we derive the zero temperature $λ-x$ phase diagram of the model. It is argued that all underdoped cuprates are close to the quantum tricritical point $x=0$, $λ=1$. The three phases "meet" at the tricritical point: (i) Néel antiferromagnet, (ii) spin spiral with antinodal direction of the spiral wave v…
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…
The intrinsic metastable crystal structure of the cuprates results in local dynamical lattice instabilities, strongly coupled to the density fluctuations of the charge carriers. They acquire in this way simultaneously both, delocalized and localized features. It is responsible for a partial fractioning of the Fermi surface, i.e., the Fermi surface gets hidden in a region around the anti-nodal points, because of the opening of a pseudogap in the normal state, arising from a partial charge localization. The high energy localized single-particle features are a result of a segregation of the homog…
Hidden Fermi liquid theory explicitly accounts for the effects of Gutzwiller projection in the t-J Hamiltonian, widely believed to contain the essential physics of the high-Tc superconductors. We derive expressions for the entire "strange metal", normal state relating angle-resolved photoemission, resistivity, Hall angle, and by generalizing the formalism to include the Fermi surface topology - angle-dependent magnetoresistance. We show this theory to be the first self-consistent description for the normal state of the cuprates based on transparent, fundamental assumptions. Our well-defined fo…
Analogs of the high-T$_c$ cuprates have been long sought after in transition metal oxides. Due to the strong spin-orbit coupling (SOC), the $5d$ perovskite iridates Sr$_2$IrO$_4$ exhibit a low-energy electronic structure remarkably similar to the cuprates. Whether a superconducting state exists as in the cuprates requires understanding the correlated spin-orbit entangled electronic states. Recent experiments discovered hidden order in the parent and electron doped iridates, some with striking analogies to the cuprates, including Fermi surface pockets, Fermi arcs, and pseudogap. Here, we study …
High-$T_c$ superconductors with CuO$_2$ layers, manganites La$_{1-x}$Sr$_x$MnO$_3$, and cobaltites LaCoO$_3$ present several mysteries in their physical properties. Most of them are believed to come from the strongly-correlated nature of these materials. From the theoretical viewpoint, there are many hidden rocks in making the consistent description of the band structure and low-energy physics starting from the Fermi-liquid approach. Here we discuss the alternative method -- multielectron approach to the electronic structure calculations for the Mott insulators -- called LDA+GTB (local density…
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…
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.
The most intriguing observation of cuprate experiments is most likely the metal-insulator-crossover (MIC), seen in the underdome region of the temperature-doping phase diagram of copper-oxides under a strong magnetic field, when the superconductivity is suppressed. This MIC, which results in such phenomena as heat conductivity downturn, anomalous Lorentz ratio, nonlinear entropy, insulating ground state, nematicity- and stripe-phases and Fermi pockets, reveals the nonconventional dielectric property of the pseudogap-normal phase. Since conventional superconductivity appears from a conducting n…
The concept of topological excitations and the related ground state degeneracy are employed to establish an effective theory of the superconducting state evolving from the Mott insulator for high-Tc cuprates. Casting the Coulomb interaction in terms of composite-fermions via the gauge flux attachment facility, we show that instanton events in the Matsubara "imaginary time," labeled by topological winding numbers, are essential configurations of the phase field dual to the charge. In analogy to the usual phase transition that is characterized by a sudden change of the symmetry, the topological …
The charge density fluctuations and the Shrinking Fermi Liquid scenario for strange metallicity in cuprates
CNR-INFM-SMC, and Dipartimento di Fisica, Sapienza Università di Roma（罗马大学物理系）；Institute for Theoretical Physics and Astrophysics, Computational Quantum Materials, Julius-Maximilians-Universität（维尔茨堡大学理论物理与天体物理研究所）；Institut für Physik, BTU Cottbus-Senftenberg（科特布斯-森夫滕贝格技术大学物理研究所）
In light of the new experimental and theoretical important developments in high-$T_c$ superconductivity, we revisit the fermionic hot-spot model relevant to the phenomenology of the cuprates. We extend previous results by means of a complete two-loop order renormalization group (RG) framework. Here, we explicitly study the effect of the charge-density-wave (CDW) order parameter with a $d$-wave form factor with the experimentally observed modulation $(\pm Q_0,0)$ and $(0,\pm Q_0)$ at the infrared-stable nontrivial fixed point obtained previously for this model. Additionally, we proceed to inves…
We report a state-of-the-art photoemission (ARPES) study of high quality single crystals of the NaxCoO2 series focusing on the fine details of the low-energy states. The Fermi velocity is found to be small (< 0.5 eV.A) and only weakly anisotropic over the Fermi surface at all dopings setting the size of the pair wavefunction to be on the order of 10-20 nanometers. In the low doping regime the exchange inter-layer splitting vanishes and two dimensional collective instabilities such as 120-type fluctuations become kinematically allowed. Our results suggest that the unusually small Fermi velocity…
An understanding of the normal state in the high-temperature superconducting cuprates is crucial to the ultimate understanding of the long-standing problem of the origin of the superconductivity itself. This so-called strange metal state is thought to be associated with a quantum critical point (QCP) hidden beneath the superconductivity(1,2). In electron-doped cuprates in contrast to hole-doped cuprates it is possible to access the normal state at very low temperatures and low magnetic fields to study this putative QCP and to probe the T~0 K state of these materials(3,4). We report measurement…
The mysterious pseudogap phase of cuprate superconductors ends at a critical hole doping level p* but the nature of the ground state below p* is still debated. Here, we show that the genuine nature of the magnetic ground state in La2-xSrxCuO4 is hidden by competing effects from superconductivity: applying intense magnetic fields to quench superconductivity, we uncover the presence of glassy antiferromagnetic order up to the pseudogap boundary p* ~ 0.19, and not above. There is thus a quantum phase transition at p*, which is likely to underlie highfield observations of a fundamental change in e…
We propose a new parton theory of the hole-doped cuprates, describing the evolution from the pseudogap metal with small Fermi surfaces to the conventional Fermi liquid with a large Fermi surface. We introduce 2 ancilla qubits per square lattice site, and employ them to obtain a variational wavefunction of a fractionalized Fermi liquid for the pseudogap metal state. We propose a multi-layer Hamiltonion for the cuprates, with the electrons residing in the 'physical' layer, and the ancilla qubits in two 'hidden' layers: the hidden layers can be decoupled from the physical layer by a canonical tra…
All previous cuprate superconductors display a set of common features: (i) vicinity to a Cu 3$d^{9}$ configuration; (ii) separated CuO$_2$ planes; (iii) superconductivity for doping $δ\sim$ 0.1$-$0.3. Recently [PNAS {\bf 24}, 12156 (2019)] challenged this picture by discovering "highly overdoped" superconducting Ba$_2$CuO$_{3+y}$. Using density-functional theory + dynamical mean-field theory, we reveal a bilayer structure of Ba$_2$CuO$_{3.2}$ of alternating quasi 2D and quasi 1D character. Correlations tune an inter-layer self-doping leading to an almost half-filled, strongly nested quasi 1D $…
A major challenge in understanding the cuprate superconductors is to clarify the nature of the fundamental electronic correlations that lead to the pseudogap phenomenon. Here we use ultrashort light pulses to prepare a non-thermal distribution of excitations and capture novel properties that are hidden at equilibrium. Using a broadband (0.5-2 eV) probe we are able to track the dynamics of the dielectric function, unveiling an anomalous decrease of the scattering rate of the charge carriers in a pseudogap-like region of the temperature ($T$) and hole-doping ($p$) phase diagram. In this region, …
We report Knight shift experiments on the superconducting heavy electron material CeCoIn$_5$ that allow one to track with some precision the behavior of the heavy electron Kondo liquid in the superconducting state with results in agreement with BCS theory. An analysis of the $^{115}$In nuclear quadrupole resonance (NQR) spin-lattice relaxation rate $T_1^{-1}$ measurements under pressure reveals the presence of 2d magnetic quantum critical fluctuations in the heavy electron component that are a promising candidate for the pairing mechanism in this material. Our results are consistent with an an…
Geometric orthogonal metals: Hidden antiferromagnetism and pseudogap from fluctuating stripes
Ludwig-Maximilians-Universität München（慕尼黑大学）；Arnold Sommerfeld Center for Theoretical Physics (ASC)（阿诺德·索末菲理论物理中心）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；University of Regensburg（雷根斯堡大学）
Effective theory of the hidden-order pseudogap phase in a doped antiferromagnet
Ludwig-Maximilians-Universität Munich（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Technical University of Munich（慕尼黑工业大学）；Harvard University（哈佛大学）
