Pseudogap Regime Research Articles

Hidden magnetism at the pseudogap critical point of a cuprate superconductor

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 electronic properties across p*. Furthermore, the continuous presence of quasi-static moments from the insulator up to p* suggests that the physics of the doped Mott insulator is relevant through the entire pseudogap regime and might be more fundamentally driving the transition at p* than just spin or charge ordering.

Pauli limited d-wave superconductors: quantum breached pair phase and thermal transitions

We report a quantum phase transition in Pauli limited d-wave superconductors and give the mean field estimates of the associated quantum critical point. For a population imbalanced d-wave superconductor a stable ground state phase viz quantum breached pair phase has been identified which comprises of spatial coexistence of gapless superconductivity and nonzero magnetization. Based on the thermodynamic and quasiparticle indicators we for the first time analyze this phase, discuss the thermal behavior of Pauli limited d-wave superconductor, give accurate estimates of the thermal scales associated with such systems and map out the pseudogap regime. Our work shows that while the Pauli limited superconductors are known to exhibit exotic modulated superconducting phase at large imbalance of fermion populations; in the regime of weak imbalance an intriguing phase of competing orders is realized. We have established that rather than the superconducting pairing field, it is the average magnetization of the system that quantifies this quantum phase transition. Given that the existing Pauli limited superconductors possess unconventional pairing state symmetry of the superconducting order, our work promises to open up new avenues in the experimental research of these materials. We have also demonstrated an alternate scenario wherein the quantum breached pair phase is a natural outcome for a d-wave superconductor with unequal effective masses of the fermion species.

Criticality across the energy spectrum from random artificial gravitational lensing in two-dimensional Dirac superconductors

We numerically study weak, random, spatial velocity modulation ["quenched gravitational disorder" (QGD)] in two-dimensional massless Dirac materials. QGD couples to the spatial components of the stress tensor; the gauge-invariant disorder strength is encoded in the quenched curvature. Although expected to produce negligible effects, wave interference due to QGD transforms all but the lowest-energy states into a quantum-critical "stack" with universal, energy-independent spatial fluctuations. We study five variants of velocity disorder, incorporating three different local deformations of the Dirac cone: flattening or steepening of the cone, pseudospin rotations, and nematic deformation (squishing) of the cone. QGD should arise for nodal excitations in the $d$-wave cuprate superconductors (SCs), due to gap inhomogeneity. Our results may explain the division between low-energy "coherent" (plane-wave-like) and finite-energy "incoherent" (spatially inhomogeneous) excitations in the SC and pseudogap regimes. The model variant that best matches the cuprate phenomenology possesses quenched random pseudospin rotations and nematic fluctuations. This model variant and another with pure nematic randomness exhibit a robust energy swath of stacked critical states, the width of which increases with increasing disorder strength. By contrast, quenched fluctuations that isotropically flatten or steepen the Dirac cone tend to produce strong disorder effects, with more rarified wave functions at low- and high-energies. Our models also describe the surface states of class DIII topological SCs.

Hard antinodal gap revealed by quantum oscillations in the pseudogap regime of underdoped high-Tc superconductors

An understanding of the missing antinodal electronic excitations in the pseudogap state is essential for uncovering the physics of the underdoped cuprate high temperature superconductors. The majority of high temperature experiments performed thus far, however, have been unable to discern whether the antinodal states are rendered unobservable due to their damping, or whether they vanish due to their gapping. Here we distinguish between these two scenarios by using quantum oscillations to examine whether the small Fermi surface pocket, found to occupy only 2% of the Brillouin zone in the underdoped cuprates, exists in isolation against a majority of completely gapped density of states spanning the antinodes, or whether it is thermodynamically coupled to a background of ungapped antinodal states. We find that quantum oscillations associated with the small Fermi surface pocket exhibit a signature sawtooth waveform characteristic of an isolated two-dimensional Fermi surface pocket. This finding reveals that the antinodal states are destroyed by a hard gap that extends over the majority of the Brillouin zone, placing strong constraints on a drastic underlying origin of quasiparticle disappearance over almost the entire Brillouin zone in the pseudogap regime.

Locating the pseudogap closing point in cuprate superconductors: Absence of entrant or reentrant behavior

Current descriptions of the pseudogap in underdoped cuprates envision a doping-dependent transition line $T^*(p)$ which descends monotonically towards zero just beyond optimal doping. There is much debate as to the location of the terminal point $p^*$ where $T^*(p)$ vanishes, whether or not there is a phase transition at $T^*$ and exactly how $T^*(p)$ behaves below $T_c$ within the superconducting dome. One perspective sees $T^*(p)$ cutting the dome and continuing to descend monotonically to zero at $p_{crit} \approx 0.19$ holes/Cu $-$ referred to here as `entrant behavior'. Another perspective derived from photoemission studies is that $T^*(p)$ intersects the dome near $p_{crit} \approx 0.23$ holes/Cu then turns back below $T_c$, falling to zero again around $p_{crit} \approx 0.19$ $-$ referred to here as `reentrant behavior'. By examining thermodynamic data for Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ we show that neither entrant nor reentrant behavior is experimentally supported. Rather, $p_{crit} \approx 0.19$ sharply delimits the pseudogap regime and for $p < 0.19$ the pseudogap is always present, independent of temperature. Similar results are found for Y$_{0.8}$Ca$_{0.2}$Ba$_2$Cu$_3$O$_{7-\delta}$. For both materials $T^*(p)$ is not a temperature but a crossover scale, $\approx E^*(p)/2k_B$, reflecting instead the underlying pseudogap energy $E^*(p)$ which vanishes as $p \rightarrow 0.19$.

Charge carrier drop at the onset of pseudogap behavior in the two-dimensional Hubbard model

We show that antiferromagnetic spin-density wave order in the two-dimensional Hubbard model yields a drop of the charge carrier density as observed in recent transport measurements for cuprate superconductors in high magnetic fields upon entering the pseudogap regime. The amplitude and the (generally incommensurate) wave vector of the spin-density wave is obtained from dynamical mean-field theory (DMFT). An extrapolation of the finite temperature results to zero temperature yields an approximately linear doping dependence of the magnetic gap $\Delta(p) \propto p^*-p$ in a broad doping range below the critical doping $p^*$. The magnetic order leads to a Fermi surface reconstruction with electron and hole pockets, where electron pockets exist only in a restricted doping range below $p^*$. DC charge transport properties are computed by combining the renormalized band structure as obtained from the DMFT with a doping-independent phenomenological scattering rate. A pronounced drop of the longitudinal conductivity and the Hall number in a narrow doping range below $p^*$ is obtained.

Pairing Correlations across the Superfluid Phase Transition in the Unitary Fermi Gas.

In the two-component Fermi gas with a contact interaction, a pseudogap regime can exist at temperatures between the superfluid critical temperature T_{c} and a temperature T^{*}>T_{c}. This regime is characterized by pairing correlations without superfluidity. However, in the unitary limit of infinite scattering length, the existence of this regime is still debated. To help address this, we have applied finite-temperature auxiliary-field quantum MonteCarlo (AFMC) methods to study the thermodynamics of the superfluid phase transition and signatures of the pseudogap in the spin-balanced homogeneous unitary Fermi gas. We present results at finite filling factor ν≃0.06 for the condensate fraction, an energy-staggering pairing gap, the spin susceptibility, and the heat capacity, and compare them to experimental data when available. In contrast to previous AFMC simulations, our model space consists of the complete first Brillouin zone of the lattice, and our calculations are performed in the canonical ensemble of fixed particle number. The canonical ensemble AFMC framework enables the calculation of a model-independent gap, providing direct information on pairing correlations without the need for numerical analytic continuation. We use finite-size scaling to estimate T_{c} at the corresponding filling factor. We find that the energy-staggering pairing gap vanishes above T_{c}, showing no pseudogap effects, and that the spin susceptibility shows a substantially reduced signature of a spin gap compared to previously reported AFMC simulations.

Identifying the Pseudogap in Cuprates with a Nematic Phase

A signature of rotational symmetry breaking was observed in the nematic susceptibility measured in the pseudogap regime of a Bi-based high-Tc cuprate. The observation suggests a phase transition at...

The analytical description of a doped Mott insulator

With the hierarchical Green’s function approach, we study a doped Mott insulator described with the Hubbard model by analytically solving the equations of motion of an one-particle Green’s function and related multiple-point correlation functions, and find that the separation of the spin and charge degrees of freedom of the electrons is an intrinsic character of the doped Mott insulator. For enough of large on-site repulsive Coulomb interaction, we show that the spectral weight of the one-particle Green’s function is proportional to the hole doping concentration that is mainly produced by the charge fluctuation of electrons, while the excitation spectrum of the electrons is composed of two parts: One is contributed by the spin fluctuation of the electrons, which is proportional to the hole doping concentration, and another one is coming from the coupling between the charge and spin fluctuations of the electrons that takes the maximum at undoping. All of these low energy/temperature physical properties originate from the strong on-site Coulomb interaction. The present results are consistent with the spectroscopy observations of the cuprate superconductors and the numerical calculations in normal state above the pseudogap regime.

Angle-resolved photoemission spectroscopy of a Fermi–Hubbard system

Angle-resolved photoemission spectroscopy (ARPES) measures the single-particle excitations of a many-body quantum system with both energy and momentum resolution, providing detailed information about strongly interacting materials. ARPES is a direct probe of fermion pairing, and hence a natural technique to study the development of superconductivity in a variety of experimental systems ranging from high temperature superconductors to unitary Fermi gases. In these systems a remnant gap-like feature persists in the normal state, which is referred to as a pseudogap. A quantitative understanding of pseudogap regimes may elucidate details about the pairing mechanisms that lead to superconductivity, but developing this is difficult in real materials partly because the microscopic Hamiltonian is not known. Here we report on the development of ARPES to study strongly interacting fermions in an optical lattice using a quantum gas microscope. We benchmark the technique by measuring the occupied single-particle spectral function of an attractive Fermi-Hubbard system across the BCS-BEC crossover and comparing to quantum Monte Carlo calculations. We find evidence for a pseudogap in our system that opens well above the expected critical temperature for superfluidity. This technique may also be applied to the doped repulsive Hubbard model which is expected to exhibit a pseudogap at temperatures close to those achieved in recent experiments.

Transverse conductivity and the pseudogap in YBCO single crystals irradiated with fast electrons

Temperature dependences of the electrical resistance along the c-axis of [Formula: see text] single crystals are investigated before and after irradiation with electrons at 0.5–2.5 MeV energies. The irradiation was done at [Formula: see text] K and the irradiation dose was varied from [Formula: see text] to [Formula: see text]. An enhancement of the charge carriers localization with increase of the irradiation dose has been revealed. A crossover from the pseudogap (PG) regime to the variable-range hopping conductivity has been observed.

Finite-temperature charge dynamics and the melting of the Mott insulator

The Mott insulator is the quintessential strongly correlated electronic state. We obtain complete insight into the physics of the two-dimensional Mott insulator by extending the slave-fermion (holon-doublon) description to finite temperatures. We first benchmark its predictions against state-of-the-art quantum Monte Carlo simulations, demonstrating quantitative agreement. Qualitatively, the short-ranged spin fluctuations both induce holon-doublon bound states and renormalize the charge sector to form the Hubbard bands. The Mott gap is understood as the charge gap renormalized downwards by these spin fluctuations. As temperature increases, the Mott gap closes before the charge gap, causing a pseudogap regime to appear naturally during the melting of the Mott insulator.

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.

Pseudogap crossover in the electron-phonon system

Thermodynamic properties of the square-lattice Holstein model of the electron-phonon problem with phonon frequencies small compared to the bare Fermi energy are obtained using Monte Carlo methods, a strong-coupling (bipolaronic) expansion, and a weak coupling Migdal-Eliashberg approach. Already at elevated temperatures where the charge-density wave (CDW) and superconducting (SC) correlations are very short-range, a crossover occurs as a function of increasing electron-phonon coupling, $\lambda_0$, from a normal metallic regime to a pseudogap regime. At sufficiently low $T$, a SC phase is found for small $\lambda_0$ and a commensurate insulating CDW phase for large $\lambda_0$.

The pseudogap regime in the unitary Fermi gas

We discuss the pseudogap regime in the cold atomic unitary Fermi gas, with a particular emphasis on the auxiliary-field quantum Monte Carlo (AFMC) approach. We discuss possible signatures of the pseudogap, review experimental results, and survey analytic and quantum Monte Carlo techniques before focusing on AFMC calculations in the canonical ensemble. For the latter method, we discuss results for the heat capacity, energy-staggering pairing gap, spin susceptibility, and compare to experiment and other theoretical methods.

Spin stiffness and domain walls in Dirac-electron mediated magnets

Spin interactions of magnetic impurities mediated by conduction electrons is one of the most interesting and potentially useful routes to ferromagnetism in condensed matter. In recent years such systems have received renewed attention due to the advent of materials in which Dirac electrons are the mediating particles, with prominent examples being graphene and topological insulator surfaces. In this paper, we demonstrate that such systems can host a remarkable variety of behaviors, in many cases controlled only by the density of electrons in the system. Uniquely characteristic of these systems is an emergent long-range form of the spin stiffnes when the Fermi energy resides at a Dirac point, becoming truly long-range as the magnetization density becomes very small. It is demonstrated that this leads to screened Coulomb-like interactions among domain walls, via a subtle mechanism in which the topology of the Dirac electrons plays a key role: the combination of attraction due to bound in-gap states that the topology necessitates, and repulsion due to scattering phase shifts, yields logarithmic interactions over a range of length scales. We present detailed results for domain walls in a particularly rich system, the (111) surface of a model topological crystalline insulator. This hosts two-fold and six- fold degenerate groundstates, with either short-range or emergent long-range interactions among the spins. In the latter case we demonstrate in detail the presence of in-gap states associated with domain walls, and argue that this stabilizes a pseudogap regime at finite temperature. Thus the topological nature of these systems, through its impact on domain wall excitations, leads to unique behaviors distinguishing them markedly from their non-topological analogs.

Isotropic Bipolaron–Fermion Exchange Theory and Unconventional Pairing in Cuprate Superconductors

AbstractThe appearance of unconventional pairing in superconducting cuprates is examined from a microscopic model, taking into account important properties of hole‐doped copper oxides. An exchange interaction between fermions and dominantly inter‐site bipolarons is considered to be the mechanism which leads to the pairing. Its momentum dependency is connected to the well‐established fermion–phonon anomalies in cuprate superconductors. Since charge carriers in these materials are strongly correlated, a screened Coulomb repulsion is added to this exchange term. Any ad hoc assumptions like anisotropy are avoided, but a microscopic explanation of unconventional pairing for coupling strengths that are in accordance with experimental facts is provided. One important outcome is a mathematically rigorous elucidation of the role of Coulomb repulsion in unconventional pairing, which is shown to be concomitant with a strong depletion of superconducting pairs. The theory, applied to the special case of LaSr 214, predicts at optimal doping i) a coherence length of , which is the same as that obtained from the Ginzburg–Landau critical magnetic field measured for this material, and ii) d‐wave pair formation in the pseudogap regime, that is, at temperatures much higher than the superconducting transition temperature.

Evolution of holographic Fermi arcs from a Mott insulator

We study fermions in asymptotically anti-de Sitter black hole spacetimes which interact via novel chiral symmetry-preserving interactions. Computing the dual fermion two-point correlator, we show that these bulk interactions anisotropically gap Fermi surfaces of the boundary spectrum. Consequently, the interactions we devise provide holographic models for Fermi arcs seen ubiquitously in the pseudogap regime of the cuprates. Our interactions are modifications of the chiral symmetry-breaking Pauli coupling, which has previously been proposed as the holographic realization of Mott physics. The onset of Mott insulation and pseudogap physics are respectively discussed in the context of bulk chiral and boundary parity symmetry breaking, and the Mott transition is interpreted as a deconfinement transition of non-Fermi liquid excitations.

Re-entrant charge order in overdoped (Bi,Pb)2.12Sr1.88CuO6+δ outside the pseudogap regime.

In the underdoped regime, the cuprate high-temperature superconductors exhibit a host of unusual collective phenomena, including unconventional spin and charge density modulations, Fermi surface reconstructions, and a pseudogap in various physical observables. Conversely, overdoped cuprates are generally regarded as conventional Fermi liquids possessing no collective electronic order. In partial contradiction to this widely held picture, we report resonant X-ray scattering measurements revealing incommensurate charge order reflections for overdoped (Bi,Pb)2.12Sr1.88CuO6+δ (Bi2201), with correlation lengths of 40-60 lattice units, that persist up to temperatures of at least 250 K. The value of the charge order wavevector decreases with doping, in line with the extrapolation of the trend previously observed in underdoped Bi2201. In overdoped materials, however, charge order coexists with a single, unreconstructed Fermi surface without nesting or pseudogap features. The discovery of re-entrant charge order in Bi2201 thus calls for investigations in other cuprate families and for a reconsideration of theories that posit an essential relationship between these phenomena.

Thermal transitions, pseudogap behavior, and BCS-BEC crossover in Fermi-Fermi mixtures

We study the mass imbalanced Fermi-Fermi mixture within the framework of a two-dimensional lattice fermion model. Based on the thermodynamic and species dependent quasiparticle behavior we map out the finite temperature phase diagram of this system and show that unlike the balanced Fermi superfluid there are now two different pseudogap regimes as PG-I and PG-II. While within the PG-I regime both the fermionic species are pseudogapped, PG-II corresponds to the regime where pseudogap feature survives only in the light species. We believe that the single particle spectral features that we discuss in this paper are observable through the species resolved radio frequency spectroscopy and momentum resolved photo emission spectroscopy measurements on systems such as, 6$_{Li}$-40$_{K}$ mixture. We further investigate the interplay between the population and mass imbalances and report that at a fixed population imbalance the BCS-BEC crossover in a Fermi-Fermi mixture would require a critical interaction (U$_{c}$), for the realization of the uniform superfluid state. The effect of imbalance in mass on the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase has been probed in detail in terms of the thermodynamic and quasiparticle behavior of this phase. It has been observed that in spite of the s-wave symmetry of the pairing field a nodal superfluid gap is realized in the LO regime. Our results on the various thermal scales and regimes are expected to serve as benchmarks for the experimental observations on 6$_{Li}$-40$_{K}$ mixture.