Screened superexchange mechanism for superconductivity applied to cuprates

The low-temperature linear-in-T resistivity of ``strange metals,'' such as the metallic state of the cuprate high-temperature superconductors, has long been thought to be associated with a quantum critical point. However, recent transport studies of the cuprates have found this behavior persists over a finite range of overdoping. In this work, we report magnetoresistance and Hall effect results for electron-doped films of the cuprate superconductor ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Ce}}_{x}{\mathrm{CuO}}_{4}$ (LCCO) for temperatures from 0.7 to 45 K and magnetic fields up to 65 T. For $x=0.12$ and 0.13, just below the Fermi surface reconstruction (FSR) at $x=0.14$, the normal state in-plane resistivity exhibits a well-known upturn at low temperature. Our new results show that this resistivity upturn is eliminated at high magnetic field and the resistivity becomes linear-in-temperature from \ensuremath{\sim}40 K down to 0.7 K. The magnitude of the linear coefficient scales with Tc and doping, as found previously [K. Jin, Nature(London) 476, 73 (2011), T. Sarkar, Sci. Adv. 5, eaav6753 (2019)] for dopings above the FSR. This striking observation suggests that the strange metal is not confined to a single ``critical point'' in the phase diagram, but rather is a robust universal feature of the metallic ground state of the cuprates.

The high-temperature superconducting state in cuprates appears if charge carriers are doped into a Mott insulating parent compound. An unresolved puzzle is the unconventional nature of the normal state above the superconducting dome, and its connection to the superconducting instability. At weak hole-doping, a "pseudo-gap" metal state with signatures of time-reversal symmetry breaking is observed, which near optimal doping changes into a "strange metal" with non-Fermi liquid properties. Qualitatively similar phase diagrams are found in multi-orbital systems, such as pnictides, where the unconventional metal states arise from a Hund coupling induced spin-freezing. Here, we show that the relevant model for cuprates, the single-orbital Hubbard model on the square lattice, can be mapped onto an effective multi-orbital problem with strong ferromagnetic Hund coupling. The spin-freezing physics of this multi-orbital system explains the phenomenology of cuprates, including the pseudo-gap, the strange metal, and the d-wave superconducting instability. Our analysis suggests that spin-freezing is the universal mechanism which controls the properties of unconventional superconductors.

In spite of much interest in various unconventional properties of superconducting cuprates such as the anisotropic superconductivity, the pseudogap state, the competing state in the underdoped region, strange metal in normal state, and anomalies in the optical sum rules etc, its microscopic mechanism still remains unsolved issues. Here these properties are considered using our recently proposed theory emphasizing that the electronic state of superconductors can be described by doping-dependent composite fermions. It is found that the anisotropy of the superconductive gap and the pseudogap are evaluated, the competing states is derived by mixed states model, and that T-linearity of resistivity and the anomaly of optical sum rules in the nearly optimal doping can be derived from considering the interplay between the composite fermion bands. It is also suggested that a crossover separating the strange metal and the normal metal in the overdoped region can be explained by the coupling effect of composite fermions

Many unconventional superconductors exhibit a common set of anomalous charge transport properties that characterize them as `strange metals', which provides hope that there is single theory that describes them. However, model-independent connections between the strange metal and superconductivity have remained elusive. In this letter, we show that the Hall effect of the unconventional superconductor BaFe$_2$(As$_{1-x}$P$_x$)$_2$ contains an anomalous contribution arising from the correlations within the strange metal. This term has a distinctive dependence on magnetic field, which allows us to track its behavior across the doping-temperature phase diagram, even under the superconducting dome. These measurements demonstrate that the strange metal Hall component emanates from a quantum critical point and, in the zero temperature limit, decays in proportion to the superconducting critical temperature. This creates a clear and novel connection between quantum criticality and superconductivity, and suggests that similar connections exist in other strange metal superconductors.

I present a formalism for dealing directly with the effects of the Gutzwiller projection implicit in the $t\text{\ensuremath{-}}J$ model which is widely believed to underlie the phenomenology of the high-${T}_{c}$ 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 the ``strange metal'' normal state are predicted and compared to experiments.

Strongly correlated electron systems host a variety of poorly understood correlations in their high-temperature normal state. Unlike ordered phases defined by order parameters, regions of the normal state are often defined through unconventional properties such as strange metallic transport or spectroscopic pseudogaps. Characterizing the microscopic correlations in the normal state is necessary to elucidate mechanisms that lead to these properties and their connection to ground-state orders. Here we establish the presence of intertwined charge and spin stripes in the strange metal normal state of the Hubbard model using determinant quantum Monte Carlo calculations. The charge and spin density waves constituting the stripes are fluctuating and short ranged; yet they obey a mutual commensurability relation and remain microscopically interlocked, as evidenced through measurements of three-point spin-spin-hole correlation functions. Our findings demonstrate the ability of many-body numerical simulations to unravel the microscopic correlations that define quantum states of matter.

We present a formalism for dealing directly with the effects of the Gutzwiller projection implicit in thet–J model which is widely believed to underlie the phenomenology of the high-Tc cuprates. We suggest that a true Bardeen–Cooper–Schrieffer condensationfrom a Fermi liquid state takes place, but in the unphysical space prior toprojection. At low doping, however, instead of a hidden Fermi liquid one getsa ‘hidden’ non-superconducting resonating valence bond state which developshole pockets upon doping. The theory which results upon projection does notfollow conventional rules of diagram theory and in fact in the normal state is aZ = 0 non-Fermi liquid. Anomalous properties of the ‘strange metal’ normal state are predictedand compared against experimental findings.

Spin and hole dynamics of high- Tc cuprates and their interconditional evolution with doping from antiferromagnetic to ‘strange metal’ state

The anomalous properties of High-$T_{{\rm c}}$ cuprates are investigated both in the normal state and in the superconducting state. In particular, we pay atte ntion to the pseudogap in the normal state and the phase transition from the pse udogap state to the superconducting state. The pseudogap phenomena observed in cuprates are naturally understood as a precursor of the strong coupling superconductivity. We have previously show n by using the self-consistent T-matrix calculation that the pseudogap is a resu lt of the strong superconducting fluctuations which are accompanied by the stron g coupling superconductivity in quasi-two dimensional systems [J. Phys. Soc. Jpn . {\bf68} (1999) 2999.]. We extend the scenario to the superconducting state. The close relation between the pseudogap state and the superconducting state is pointed out. Once t he superconducting phase transition occurs, the superconducting order parameter rapidly grows rather than the result of BCS theory. With the rapid growth of the order parameter, the gap structure becomes sharp, while it is remarkably broad in the pseudogap state. The characteristic energy scale of the gap does not chan ge. These results well explain the phase transition observed in the spectroscopi c measurements. Further, we calculate the magnetic and transport properties which show the pseu dogap phenomena. The comprehensive understanding of the NMR, the neutron scatter ing, the optical conductivity and the London penetration depth is obtained both in the pseudogap state and in the superconducting state.

Pseudogap state and superconducting state in high- Tc cuprates: anomalous properties in the observed quantities

Bednorz and Müller's discovery of superconductivity in the cuprate perovskite La2-xBaxCuO4 gave the modern condensed matter community arguably two of its greatest gifts – high-temperature superconductivity and strange metallicity; certainly two of its most profound and challenging problem. While it was the multi-fold increase in Tc that rightly catapulted cuprates to the summit of global media attention and scientific curiosity, it is the nature of their normal (non-superconducting) state that has sustained interest over the intervening years. This in turn has inspired condensed-matter experimentalists and theoreticians to revolutionise their respective fields. Yet despite such boundary-pushing endeavors, the origin of both phenomena remains elusive. In this brief note, I offer a personal reflection on the link between strange metallicity and high-Tc superconductivity, highlighting a number of simple observations that may hold profound implications for their ultimate resolution.

Tunneling differential conductivity (or resistivity) is a sensitive tool to experimentally test the non-Fermi liquid behavior of strongly correlated Fermi systems. In the case of common metals the Landau–Fermi liquid theory demonstrates that the differential conductivity is a symmetric function of bias voltage V. This is because the particle–hole symmetry is conserved in the Landau–Fermi liquid state. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition, its Landau–Fermi liquid properties disappear so that the particle–hole symmetry breaks making the differential tunneling conductivity to be asymmetric function of V. This asymmetry can be observed when a strongly correlated metal is in its normal, superconducting or pseudogap states. We show that the asymmetric part of the dynamic conductance does not depend on temperature provided that the metal is in its superconducting or pseudogap states. In normal state, the asymmetric part diminishes at rising temperatures. Under the application of magnetic field the metal transits to the Landau–Fermi liquid state and the differential tunneling conductivity becomes a symmetric function of V. These findings are in good agreement with recent experimental observations.

A one band Hubbard model with intermediate coupling is shown to describe the two most important unusual features of a normal state: linear resistivity strange metal and the pseudogap. Both the spectroscopic and transport properties of the cuprates are considered on the same footing by employing a relatively simple postgaussian approximation valid for the intermediate couplings $U/t=1.5-4$ in relevant temperatures $T>100{\rm K}.$ In the doping range $\ p=0.1-0.3$, the value of $U$ is smaller than that in the parent material. For a smaller doping, especially in the Mott insulator phase, the coupling is large compared to the effective tight binding scale and a different method is required. This scenario provides an alternative to the paradigm that the coupling should be strong, say $U/t>6$, in order to describe the strange metal. We argue that to obtain phenomenologically acceptable underdoped normal state characteristics like $T^{\ast }$, pseudogap values, and spectral weight distribution, a large value of $U$ is detrimental. Surprisingly the resistivity in the above temperature range is linear $\rho =\rho_{0}+\alpha \frac{m^{\ast }}{e^{2}n\hbar }T$ with the "Planckian" coefficient $\alpha $ of order one.

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-T(c) 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 formalism also serves as a guide for further experimental confirmation.

Ab initio pseudopotential calculations for H in Pd are used in order to construct an auxiliary short-ranged host-lattice-particle potential which well reproduces the large number of available ab initio data. This potential (instead of an empirical potential as employed in previous treatments) is used in a quantum mechanical calculation of hydrogen as well as of mu + and pi + states in Pd, which takes into account the dependence of the lattice relaxation on particle mass and particle state. These calculations allow us to determine Jahn-Teller coupling constants of excited states and the dependence of lattice displacements on the isotopic mass. It is found that coupling to lattice modes with E-symmetry is dominant. The effect of lattice relaxation on the total energy difference if hydrogen is localized at tetrahedral or octahedral sites and on the excitation energies as measured by inelastic neutron scattering experiments is also discussed.