Pseudogap Phase Research Articles

Evidence for a vestigial nematic state in the cuprate pseudogap phase

The CuO2 antiferromagnetic insulator is transformed by hole-doping into an exotic quantum fluid usually referred to as the pseudogap (PG) phase. Its defining characteristic is a strong suppression of the electronic density-of-states D(E) for energies |E| < [Formula: see text], where [Formula: see text] is the PG energy. Unanticipated broken-symmetry phases have been detected by a wide variety of techniques in the PG regime, most significantly a finite-Q density-wave (DW) state and a Q = 0 nematic (NE) state. Sublattice-phase-resolved imaging of electronic structure allows the doping and energy dependence of these distinct broken-symmetry states to be visualized simultaneously. Using this approach, we show that even though their reported ordering temperatures T DW and T NE are unrelated to each other, both the DW and NE states always exhibit their maximum spectral intensity at the same energy, and using independent measurements that this is the PG energy [Formula: see text] Moreover, no new energy-gap opening coincides with the appearance of the DW state (which should theoretically open an energy gap on the Fermi surface), while the observed PG opening coincides with the appearance of the NE state (which should theoretically be incapable of opening a Fermi-surface gap). We demonstrate how this perplexing phenomenology of thermal transitions and energy-gap opening at the breaking of two highly distinct symmetries may be understood as the natural consequence of a vestigial nematic state within the pseudogap phase of Bi2Sr2CaCu2O8.

Metal-insulator transition in the two-dimensional Hubbard model: Dual fermion approach with Lanczos exact diagonalization

In this study the metal-insulator transition in the square-lattice Hubbard model at half-filling is revisited in relation to the DOS and spectral functions by means of the ladder dual fermion approximation (LDFA). For this purpose, a new expression of the two-body Green's function in the form of resolvents is proposed, which provides tractable and efficient means to calculate the local vertex function with the Lanczos exact diagonalization (ED) method. This makes it possible to use the Lanczos ED method as a solver of the effective impurity Anderson model for LDFA, opening up the way to access low temperatures for these perturbative extensions of the dynamical mean field theory and to obtain accurate DOS and spectral functions on the real frequency axis by a new variant of the maximum entropy method. It is found that for $U\le 3.5t$, as temperature decreases, the pseudogap formation due to antiferromagnetic correlations in the quasiparticle peak of the spectral function occurs at the X point $[k=(\pi,0)]$, spreads through the Fermi surface and ends at the M$_2$ point $[k=(\pi/2,\pi/2)]$. The almost simultaneous creation of the pseudogap and the loss of the Fermi liquid feature is consistent with that expected in the Slater regime. Although the pseudogap still appears in the quasi-particle-like single peak for $U\ge 4.0t$, the Fermi-liquid feature is partially lost on the Fermi surface already at higher temperatures as expected in the Mott-Heisenberg regime, in which local spins are preformed at high temperatures. A sharp crossover from a pseudogap phase to a Mott insulator at finite $U^{*} \approx 4.7t$ is found to occur below the temperature of the pseudogap formation similar to a previous study with the non-linear $\sigma$ model approach.

Cavity-Mediated Electron-Photon Superconductivity.

We investigate electron paring in a two-dimensional electron system mediated by vacuum fluctuations inside a nanoplasmonic terahertz cavity. We show that the structured cavity vacuum can induce long-range attractive interactions between current fluctuations which lead to pairing in generic materials with critical temperatures in the low-kelvin regime for realistic parameters. The induced state is a pair-density wave superconductor which can show a transition from a fully gapped to a partially gapped phase-akin to the pseudogap phase in high-T_{c} superconductors. Our findings provide a promising tool for engineering intrinsic electron interactions in two-dimensional materials.

Emergent charge order near the doping-induced Mott-insulating quantum phase transition in Sr3Ru2O7

Search for novel electronically ordered states of matter emerging near quantum phase transitions is an intriguing frontier of condensed matter physics. In ruthenates, the interplay between Coulomb correlations among the 4d electronic states and their spin-orbit interactions, lead to complex forms of electronic phenomena. Here we investigate the double layered Sr3(Ru1−xMnx)2O7 and its doping-induced quantum phase transition from a metal to an antiferromagnetic Mott insulator. Using spectroscopic imaging with the scanning tunneling microscope, we visualize the evolution of the electronic states in real- and momentum-space. We find a partial-gap at the Fermi energy that develops with doping to form a weak Mott insulating state. Near the quantum phase transition, we discover a spatial electronic reorganization into a commensurate checkerboard charge order. These findings bear a resemblance to the universal charge order in the pseudogap phase of cuprates and demonstrate the ubiquity of charge order that emanates from doped Mott insulators.

The Remarkable Underlying Ground States of Cuprate Superconductors

Cuprates exhibit exceptionally strong superconductivity. To understand why, it is essential to elucidate the nature of the electronic interactions that cause pairing. Superconductivity occurs on the backdrop of several underlying electronic phases, including a doped Mott insulator at low doping, a strange metal at high doping, and an enigmatic pseudogap phase in between—inside which a phase of charge-density wave order appears. In this article, we shed light on the nature of these remarkable phases by focusing on the limit as [Formula: see text], where experimental signatures and theoretical statements become sharper. We therefore survey the ground-state properties of cuprates once superconductivity has been removed by the application of a magnetic field and distill their key universal features.

Thermodynamic signatures of quantum criticality in cuprate superconductors

The three central phenomena of cuprate (copper oxide) superconductors are linked by a common doping level p*-at which the enigmatic pseudogap phase ends and the resistivity exhibits an anomalous linear dependence on temperature, and around which the superconducting phase forms a dome-shaped area in the phase diagram1. However, the fundamental nature of p* remains unclear, in particular regarding whether it marks a true quantum phase transition. Here we measure 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 range2 that includes p*. As a function of doping, we find that Cel/T is strongly peaked at p*(where Cel is the electronic contribution to C) and exhibits a log(1/T) dependence as temperature T tends to zero. These are the classic thermodynamic signatures of a quantum critical point3-5, as observed in heavy-fermion6 and iron-based7 superconductors at the point where their antiferromagnetic phase comes to an end. We conclude that the pseudogap phase of cuprates ends at a quantum critical point, the associated fluctuations of which are probably involved in d-wave pairing and the anomalous scattering of charge carriers.

Evolution of Pairing Orders between Pseudogap and Superconducting Phases of Cuprate Superconductors

One of the most puzzling problems of high temperature cuprate superconductor is the pseudogap phase (PG) at temperatures above the superconducting transition temperature in the underdoped regime. The PG phase is found by the angle-resolved photoemission spectra (ARPES) to have a gap at some regions in momentum space and a fraction of Fermi surface remained, known as Fermi arcs. The arc turns into a d-wave SC gap with a node below the SC transition temperature. Here, by studying a strongly correlated model at low temperatures, we obtained a phase characterized by two kinds of pairing order parameters with the total momentum of the Cooper pair to be zero and finite. The finite momentum pairing is accompanied with a spatial modulation of pairing order, i.e. a pair density wave (PDW). These PDW phases are intertwined with modulations of charge density and intra-unit cell form factors. The coexistence of the two different pairing orders provides the unique two-gaps like spectra observed by ARPES for superconducting cuprates. As temperature raises, the zero-momentum pairing order vanishes while the finite momentum pairing orders are kept, thus Fermi arcs are realized. The calculated quasiparticle spectra have the similar doping and temperature dependence as reported by ARPES and scanning tunneling spectroscopy (STS). The consequence of breaking symmetry between x and y due to the unidirectional PDW and the possibility to probe such a PDW state in the PG phase is discussed.

Collective mode in the SU(2) theory of cuprates

Recent advances in momentum-resolved electron energy-loss spectroscopy (MEELS) and resonant inelastic X-ray scattering (RIXS) now allow one to access the charge response function with unprecedented versatility and accuracy. This allows for the study of excitations which were inaccessible recently, such as low-energy and finite momentum collective modes. The SU(2) theory of the cuprates is based on a composite order parameter with SU(2) symmetry fluctuating between superconductivity and charge order. The phase where it fluctuates is a candidate for the pseudogap phase of the cuprates. This theory has a signature, enabling its strict experimental test, which is the fluctuation between these two orders, corresponding to a charge 2 spin 0 mode at the charge ordering wave-vector. Here we derive the influence of this SU(2) collective mode on the charge susceptibility in both strong and weak coupling limits, and discuss its relation to MEELS, RIXS and Raman experiments. We find two peaks in the charge susceptibility at finite energy, whose middle is the charge ordering wave-vector, and discuss their evolution in the phase diagram.

Fermi surface reconstruction in underdoped cuprates: Origin of electron pockets

A new phenomenological model is proposed to describe the evolution of the Fermi surface (FS) in a wide range of dopings. It reproduces the key features of the cuprates in the underdoped phase above the superconducting temperature $T_c$. It is shown that the explicit accounting of strong electron correlation in the framework of the $t-J$ model taken in complementary to the translational symmetry breaking induced by the charge density wave (CDW) gives rise to the Fermi surface reconstruction (FSR) into small electron pockets. While the strong Coulomb repulsion leads to an emergence of the arc-like Fermi surface in the pseudogap (PG) phase, the Bragg reflection on the boundaries of the reduced Brillouin zone (BZ) opens up a possibility to close the quasiparticle orbits. Direct calculation of the FS properties allows us to unveil the scenario of the experimentally observed transition to the CDW phase that sets in at the doping level $\delta\approx0.08$ and is accompanied by a divergence of the carriers effective mass and the sign reversals of the Hall and Seebeck coefficients.

Valence transition model of the pseudogap, charge order, and superconductivity in electron-doped and hole-doped copper oxides

We present a valence transition model for electron- and hole-doped cuprates, within which there occurs a discrete jump in ionicity ${\mathrm{Cu}}^{2+}\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}{\mathrm{Cu}}^{1+}$ in both families upon doping, at or near optimal doping in the conventionally prepared electron-doped compounds and at the pseudogap phase transition in the hole-doped materials. In thin films of the ${\mathrm{T}}^{\ensuremath{'}}$ compounds, the valence transition has occurred already in the undoped state. The phenomenology of the valence transition is closely related to that of the neutral-to-ionic transition in mixed-stack organic charge-transfer solids. Doped cuprates have negative charge-transfer gaps, just as rare-earth nickelates and ${\mathrm{BaBiO}}_{3}$. The unusually high ionization energy of the closed shell ${\mathrm{Cu}}^{1+}$ ion, taken together with the doping-driven reduction in three-dimensional Madelung energy and gain in two-dimensional delocalization energy in the negative charge transfer gap state drives the transition in the cuprates. The combined effects of strong correlations and small $d\ensuremath{-}p$ electron hoppings ensure that the systems behave as effective 1/2-filled Cu band with the closed shell electronically inactive ${\mathrm{O}}^{2\ensuremath{-}}$ ions in the undoped state, and as correlated two-dimensional geometrically frustrated 1/4-filled oxygen hole band, now with electronically inactive closed-shell ${\mathrm{Cu}}^{1+}$ ions, in the doped state. The model thus gives microscopic justification for the two-fluid models suggested by many authors. The theory gives the simplest yet most comprehensive understanding of experiments in the normal states. The robust commensurate antiferromagnetism in the conventional ${T}^{\ensuremath{'}}$ crystals, the strong role of oxygen deficiency in driving superconductivity and charge carrier sign corresponding to holes at optimal doping are all manifestations of the same quantum state. In the hole-doped pseudogapped state, there occurs a biaxial commensurate period 4 charge density wave state consisting of ${\mathrm{O}}^{1\ensuremath{-}}\ensuremath{-}{\mathrm{Cu}}^{1+}\ensuremath{-}{\mathrm{O}}^{1\ensuremath{-}}$ spin singlets that coexists with broken rotational ${\mathrm{C}}_{4}$ symmetry due to intraunit cell oxygen inequivalence. Finite domains of this broken symmetry state will exhibit two-dimensional chirality and the polar Kerr effect. Superconductivity within the model results from a destabilization of the 1/4-filled band paired Wigner crystal [Phys. Rev. B 93, 165110 (2016) and Phys. Rev. B 93, 205111 (2016)]. We posit that a similar valence transition, ${\mathrm{Ir}}^{4+}\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}{\mathrm{Ir}}^{3+}$, occurs upon electron doping ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$. We make testable experimental predictions in cuprates including superoxygenated ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4+\ensuremath{\delta}}$ and iridates. Finally, as indirect evidence for the valence bond theory of superconductivity proposed here, we note that there exist an unusually large number of unconventional superconductors that exhibit superconductivity proximate to exotic charge ordered states, whose band fillings are universally 1/4 or 3/4, exactly where the paired Wigner crystal is most stable.

Thermal transport to the rescue

Superconductivity The pseudogap phase in cuprate superconductors remains one of the most puzzling aspects of these materials. To shed light on the nature of the pseudogap, Michon et al. studied thermal transport in the cuprate La1.6-xNd0.4SrxCuO4. By applying magnetic fields high enough to destroy superconductivity and approaching absolute zero temperature, the researchers found that the thermal and charge transport in the pseudogap phase were locked in step. This indicates that the ground state of the nonsuperconducting pseudogap phase has the character of a conventional metal. Comparison to the data at zero field further suggests that applying magnetic fields does not affect some of the signatures of the pseudogap phase. Phys. Rev. X 8 , 041010 (2018).

Effect of Short-Range Correlations on Spectral Properties of Doped Mott Insulators

In the framework of cluster perturbation theory for the 2D Hubbard and Hubbard-Holstein models at low hole doping we have studied the effect of local and short-range correlations in strongly correlated systems on the anomalous features in the electronic spectrum by investigating the fine structure of quasiparticle bands. Different anomalous features of spectrum are obtained as the result of intrinsic properties of strongly correlated electron and polaron bands in the presence of short-range correlations. Particularly, features similar to the electron-like Fermi-pockets of cuprates at hole doping $p\sim0.1$ are obtained without ad hoc introducing a charge density wave order parameter within the Hubbard model in a unified manner with other known peculiarities of the pseudogap phase like Fermi-arcs, pockets, waterfalls, and kink-like features. The Fermi surface is mainly formed by dispersive quasiparticle bands with large spectral weight, formed by coherent low-energy exications. Within the Hubbard-Holstein model at moderate phonon frequencies we show that modest values of local electron-phonon interaction are capable of introducing low-energy kink-like features and affecting the Fermi surface by hybridization of the fermionic quasiparticle bands with the Franck-Condon resonances.

Wiedemann-Franz Law and Abrupt Change in Conductivity across the Pseudogap Critical Point of a Cuprate Superconductor

The thermal conductivity $\kappa$ of the cuprate superconductor La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ was measured down to 50 mK in seven crystals with doping from $p=0.12$ to $p=0.24$, both in the superconducting state and in the magnetic field-induced normal state. We obtain the electronic residual linear term $\kappa_0/T$ as $T \to 0$ across the pseudogap critical point $p^{\star}= 0.23$. In the normal state, we observe an abrupt drop in $\kappa_0/T$ upon crossing below $p^{\star}$, consistent with a drop in carrier density $n$ from $1 + p$ to $p$, the signature of the pseudogap phase inferred from the Hall coefficient. A similar drop in $\kappa_0/T$ is observed at $H=0$, showing that the pseudogap critical point and its signatures are unaffected by the magnetic field. In the normal state, the Wiedemann-Franz law, $\kappa_0/T=L_0/\rho(0)$, is obeyed at all dopings, including at the critical point where the electrical resistivity $\rho(T)$ is $T$-linear down to $T \to 0$. We conclude that the non-superconducting ground state of the pseudogap phase at $T=0$ is a metal whose fermionic excitations carry heat and charge as conventional electrons do.

Pseudogap, Fermi arc, and Peierls-insulating phase induced by 3D–2D crossover in monolayer VSe2

One of important challenges in condensed-matter physics is to realize new quantum states of matter by manipulating the dimensionality of materials, as represented by the discovery of high-temperature superconductivity in atomic-layer pnictides and room-temperature quantum Hall effect in graphene. Transition-metal dichalcogenides (TMDs) provide a fertile platform for exploring novel quantum phenomena accompanied by the dimensionality change, since they exhibit a variety of electronic/magnetic states owing to quantum confinement. Here we report an anomalous metal-insulator transition induced by three-dimensional (3D)–two-dimensional (2D) crossover in monolayer 1T-VSe2 grown on bilayer graphene. We observed a complete insulating state with a finite energy gap on the entire Fermi surface in monolayer 1T-VSe2 at low temperatures, in sharp contrast to metallic nature of bulk. More surprisingly, monolayer 1T-VSe2 exhibits a pseudogap with Fermi arc at temperatures above the charge-density-wave temperature, showing a close resemblance to high-temperature cuprates. This similarity suggests a common underlying physics between two apparently different systems, pointing to the importance of charge/spin fluctuations to create the novel electronic states, such as pseudogap and Fermi arc, in these materials.

Sensitivity of Tc to pressure and magnetic field in the cuprate superconductor YBa2Cu3Oy : Evidence of charge-order suppression by pressure

Cuprate superconductors have a universal tendency to form charge density-wave (CDW) order which competes with superconductivity and is strongest at a doping $p \simeq 0.12$. Here we show that in the archetypal cuprate YBa$_{2}$Cu$_{3}$O$_{y}$ (YBCO) pressure suppresses charge order, but does not affect the pseudogap phase. This is based on transport measurements under pressure, which reveal that the onset of the pseudogap at $T^*$ is independent of pressure, while the negative Hall effect, a clear signature of CDW order in YBCO, is suppressed by pressure. We also find that pressure and magnetic field shift the superconducting transition temperature $T_{\rm c}$ of YBCO in the same way as a function of doping - but in opposite directions - and most effectively at $p \simeq 0.12$. This shows that the competition between superconductivity and CDW order can be tuned in two ways, either by suppressing superconductivity with field or suppressing CDW order by pressure. Based on existing high-pressure data and our own work, we observe that when CDW order is fully suppressed at high pressure, the so-called "1/8 anomaly" in the superconducting dome vanishes, revealing a smooth $T_{\rm c}$ dome which now peaks at $p \simeq 0.13$. We propose that this $T_{\rm c}$ dome is shaped by the competing effects of the pseudogap phase below its critical point $p^{\star} \sim 0.19$ and spin order at low doping.

Three-Dimensional Fermi Surface of Overdoped La-Based Cuprates.

We present a soft x-ray angle-resolved photoemission spectroscopy study of overdoped high-temperature superconductors. In-plane and out-of-plane components of the Fermi surface are mapped by varying the photoemission angle and the incident photon energy. No k_{z} dispersion is observed along the nodal direction, whereas a significant antinodal k_{z} dispersion is identified for La-based cuprates. Based on a tight-binding parametrization, we discuss the implications for the density of states near the van Hove singularity. Our results suggest that the large electronic specific heat found in overdoped La_{2-x}Sr_{x}CuO_{4} cannot be assigned to the van Hove singularity alone. We therefore propose quantum criticality induced by a collapsing pseudogap phase as a plausible explanation for observed enhancement of electronic specific heat.

Analysis of the diverging effective mass in YaBa2Cu3O6+x for high-Tc mechanism and pairing symmetry

In order to clarify the high-T[Formula: see text] mechanism in inhomogeneous cuprate layer superconductors, we deduce and find the correlation strength which has not revealed before, contributing to the formation of the Cooper pair and the two-dimensional density of state, and demonstrate the pairing symmetry in the superconductors which is still controversial. To the open questions, the fitting and analysis of the diverging effective mass with decreasing doping, extracted from the acquired quantum-oscillation data in underdoped YaBa2Cu3O[Formula: see text] superconductors, using the extended Brinkman–Rice (BR) picture, reveal the nodal constant Fermi energy with the maximum carrier density, a constant Coulomb correlation strength [Formula: see text]=U/U[Formula: see text]0.90, and a growing Fermi arc from the nodal Fermi point to the isotropic Fermi surface with an increasing x. The growing of the Fermi arc indicates that a superconducting gap develops with x from the node (underdoped) to the anti-node (optimally or over-doped). The large [Formula: see text] results from the [Formula: see text]-wave metal–insulator transition for the pseudogap phase in lightly doped superconductors, which can be direct evidence for high-T[Formula: see text] superconductivity. The quantum critical point is regarded as the nodal Fermi point satisfied with the BR picture. The experimentally measured mass diverging behavior is an average effect and the true effective mass is constant. As an application of the nodal constant carrier density, the superconducting node gap analyzed by an angle-resolved photoemission spectroscopy (ARPES) is a precursor of s-wave symmetry in underdoped cuprates. Furthermore, the half-flux quantum, induced by the circulation of d-wave supercurrent and observed by the phase sensitive Josephson-[Formula: see text] junction experiments, is not shown due to “anisotropic or asymmetric effect” appearing in superconductors with trapped flux.

Pseudo-spin skyrmions in the phase diagram of cuprate superconductors

Topological states of matter are at the root of some of the most fascinating phenomena in condensed matter physics. Here we argue that skyrmions in the pseudo-spin space related to an emerging SU(2) symmetry enlighten many mysterious properties of the pseudogap phase in under-doped cuprates. We detail the role of the SU(2) symmetry in controlling the phase diagram of the cuprates, in particular how a cascade of phase transitions explains the arising of the pseudogap, superconducting and charge modulation phases seen at low temperature. We specify the structure of the charge modulations inside the vortex core below Tc, as well as in a wide temperature region above Tc, which is a signature of the skyrmion topological structure. We argue that the underlying SU(2) symmetry is the main structure controlling the emergent complexity of excitations at the pseudogap scale T*. The theory yields a gapping of a large part of the anti-nodal region of the Brillouin zone, along with q = 0 phase transitions, of both nematic and loop currents characters.

Magnetotransport properties and pseudogap phase diagram of superconducting EuBa2Cu3Oy thin films: the influence of Eu substitution

This research explores and debates magnetotransport properties and the pseudogap phase diagram of high-temperature superconducting EuBa2Cu3Oy (EBCO) films through ρxx(T) and ρxy(T) measurements. The mixed state transport properties of samples with higher doped levels show a power-law field-dependence of activation energy U, U ∝ H−α with α = 0.52 ± 0.05, while the slightly doped samples reveal a logarithmic field-dependence of U. In addition, for the first time, all samples in the underdoped region display an unusual power-law behavior of U ∝ pγ with γ = −5.90 ± 0.28, which is qualitatively explained. A sign reversal of transverse resistivity in the mixed state is also present in the nearly optimum-doped samples, which have strong pinning energies. In the normal state, the cotangent of the Hall angle shows a wide range quadratic temperature dependence for all the samples, which can be described by Anderson’s theory. The values of spin excitation bandwidth W are coincident between two results obtained from the hidden Fermi-liquid theory and from the Hall angle for the slightly overdoped sample. Moreover, the phase diagram of EBCO, containing the superconducting transition temperatures, the T* and T** temperatures in the pseudogap (PG) phase, and the antiferromagnetic transition temperatures θN, in the whole underdoped region has been completed and compared with those for YBa2Cu3Oy (YBCO). The findings demonstrate that EBCO has lower T* and T** values, versus those of YBCO in the same doping region. The observed smaller magnitude of PG for EBCO is explained by considering the oxygen vibrational amplitudes in Cu−O−Cu bonds, which agrees with the inference based on the fluctuating bond model. The influence of Eu substitution is examined and discussed.

Raman and ARPES combined study on the connection between the existence of the pseudogap and the topology of the Fermi surface in Bi2Sr2CaCu2O8+δ

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 surface topology in Bi$_{2}$Sr$_2$CaCu$_2$O$_{8+d}$ , and more generally, puts strong constraint on theories of the pseudogap phase.