Pseudogap Phase Research Articles

Lattice study of SU(2) gauge theory coupled to four adjoint Higgs fields

Gauge theories with matter fields in various representations play an important role in different branches of physics. Recently, it was proposed that several aspects of the pseudogap phase of cuprate superconductors near optimal doping may be explained by an emergent SU(2) gauge symmetry. Around the transition with positive hole doping, one can construct a (2+1)−dimensional SU(2) gauge theory coupled to four adjoint scalar fields which gives rise to a rich phase diagram with a myriad of phases having different broken symmetries. We study the phase diagram of this model on the Euclidean lattice using the hybrid Monte Carlo algorithm. We find the existence of multiple broken phases as predicted by previous mean-field studies. Depending on the quartic couplings, the SU(2) gauge symmetry is broken down either to U(1) or Z2 in the perturbative description of the model. We further study the confinement-deconfinement transition in this theory, and find that both the broken phases are deconfining in the range of volumes that we studied. However, there exists a marked difference in the behavior of the Polyakov loop between the two phases. Published by the American Physical Society 2024

Pseudogap phases, chiral anomaly, and topological order with quantum loop entanglement

Pseudogap phases, chiral anomaly, and topological order with quantum loop entanglement

Magnetic field expulsion in optically driven YBa2Cu3O6.48.

Coherent optical driving in quantum solids is emerging as a research frontier, with many reports of interesting non-equilibrium quantum phases1-4 and transient photo-induced functional phenomena such as ferroelectricity5,6, magnetism7-10 and superconductivity11-14. In high-temperature cupratesuperconductors, coherent driving of certain phonon modes has resulted in a transient state with superconducting-like optical properties, observed far above their transition temperatureTc and throughout the pseudogap phase15-18. However, questions remain on the microscopic nature of this transient state and how to distinguish it from a non-superconducting state with enhanced carrier mobility. For example, it is not known whether cuprates driven in this fashion exhibit Meissner diamagnetism. Here we examine the time-dependent magnetic field surrounding an optically driven YBa2Cu3O6.48 crystal by measuring Faraday rotation in a magneto-optic material placed in the vicinity of the sample. For a constant applied magnetic field and under the same driving conditions that result in superconducting-like optical properties15-18, a transient diamagnetic response was observed. This response is comparable in size with that expected in an equilibrium type II superconductor of similar shape and size with a volume susceptibility χv of order -0.3. This value is incompatible with a photo-induced increase in mobility without superconductivity. Rather, it underscores the notion of a pseudogap phase in which incipient superconducting correlations are enhanced or synchronized by the drive.

Dynamical analysis of the low-temperature phase diagram of a cuprate superconductor

For a cuprate superconductor, specifically the yttrium barium copper oxide system, we analyze the low-temperature phase diagram consisting of the superconducting, pseudogap, and normal phases by using a phonon-mediated attraction and Coulomb repulsion mechanism. Through this analysis, we show this mechanism in the cuprate is quite important for its key dynamics. For the pairing mechanism, a variational method is developed and applied, and a generalized mean field theory is used to calculate the condensate energy and the energy gap of the quasiparticle. We obtain a self-consistent system of equations for these quantities. The superconducting and pseudogap phases, which involve pair-condensates, are assumed to be equilibrium systems of the condensate and normal subphases. The condition for the phase transition point is given by the equal total electronic energy gains. Assuming that the difference in the pairing range of the pair condensate is small between just above and below the transition temperature, computations are performed to solve the self-consistent system of equations. We find solutions compatible with experimental data. Plausible values of the energy gap in the superconducting phase and in the pseudogap phase are obtained. The present analysis shows that the phonon-mediated attraction and Coulomb repulsion mechanism itself is compatible with the experimental data. The importance of the screening effect through one-phonon exchange in the pairing mechanism and of the structure of the valence band is discussed.

Thermal Hall effect and neutral spinons in a doped Mott insulator

In the pseudogap phase of the cuprate, a thermal Hall response of neutral objects has been recently detected experimentally, which continuously persists into the antiferromagnetic insulating phase. In this paper, we study the transport properties of neutral spinons as the elementary excitation of a doped Mott insulator, which is governed by a mutual Chern-Simons topological gauge structure. We show that such a chiral spinon as a composite of an S=1/2 spin sitting at the core of a supercurrent vortex, can contribute to the thermal Hall effect, thermopower, and Hall effect due to its intrinsic transverse (cyclotron) motion under internal fictitious fluxes. In particular, the magnitudes of the transport coefficients are phenomenologically determined by two basic parameters: the doping concentration and Tc, quantitatively consistent with the experimental measurements including the signs and qualitative temperature and magnetic-field dependence. Combined with the predictions of the spinon longitudinal transport properties, including the Nernst and spin Hall effects, a phenomenological description of the pseudogap phase is established as characterized by the neutral spinon excitations, which eventually become “confined” with an intrinsic superconducting transition at Tc. Finally, within this theoretical framework, the “order to order” phase transition between the superconducting and antiferromagnetic insulating phases are briefly discussed, with the thermal Hall monotonically increasing into the latter. Published by the American Physical Society 2024

Strain-induced long-range charge-density wave order in the optimally doped Bi2Sr2−xLaxCuO6 superconductor

The mechanism of high-temperature superconductivity in copper oxides (cuprate) remains elusive, with the pseudogap phase considered a potential factor. Recent attention has focused on a long-range symmetry-broken charge-density wave (CDW) order in the underdoped regime, induced by strong magnetic fields. Here by 63,65Cu-nuclear magnetic resonance, we report the discovery of a long-range CDW order in the optimally doped Bi2Sr2−xLaxCuO6 superconductor, induced by in-plane strain exceeding ∣ε∣ = 0.15 %, which deliberately breaks the crystal symmetry of the CuO2 plane. We find that compressive/tensile strains reduce superconductivity but enhance CDW, leaving superconductivity to coexist with CDW. The findings show that a long-range CDW order is an underlying hidden order in the pseudogap state, not limited to the underdoped regime, becoming apparent under strain. Our result sheds light on the intertwining of various orders in the cuprates.

Doping dependence of scattering rate for linear-in-temperature resistivity in cuprate superconductors

The origin of the linear-in-temperature (T-linear) resistivity in cuprate superconductors remains a profound mystery in condensed matter physics. Here, we investigate the dependence of the T-linear resistivity coefficient on doping, i.e., A1(p), for three typical regions in the temperature versus doping phase diagram of hole-doped cuprates, from which the doping dependence of the scattering rate, i.e., α1(p), is further derived. It is found that for region I (p<p* and T>T*), α1(p) is almost a constant; for region II (p>p* and T>Tcoh), α1(p)∝p; for region III (p>p* and T<Tcoh), α1(p)∝p(pc−p), where T* is the onset temperature of the pseudogap phase, p* indicates the doping at which T* goes to zero, Tcoh marks the onset of antinodal quasiparticle coherence, and pc is the doping where the low-temperature linear behavior in the overdoped regime vanishes. Moreover, the deduced α1(p) relations are verified with the experimental data from previous reports. The discovered scattering rate versus doping relationship will shed light on the scattering mechanism underlying the T-linear resistivity in cuprate superconductors. Published by the American Physical Society 2024

Effect of next-nearest neighbor hopping on the single-particle excitations at finite temperature

In the half-filled one-orbital Hubbard model on a square lattice, we study the effect of next-nearest neighbor hopping on the single-particle spectral function at finite temperature using an exact-diagonalization + Monte-Carlo based approach to the simulation process. We find that the pseudogap-like dip, existing in the density of states in between the Néel temperature T_NTN and a relatively higher temperature scale T^*T*, is accompanied with a significant asymmetry in the hole- and particle-excitation energy along the high-symmetry directions as well as along the normal-state Fermi surface. On moving from (\pi/2, \pi/2π/2,π/2) toward (\pi, 0)(π,0) along the normal state Fermi surface, the hole-excitation energy increases, a behavior remarkably similar to what is observed in the dd-wave state and pseudogap phase of high-T_cTc cuprates, whereas the particle-excitation energy decreases. The quasiparticle peak height is the largest near (\pi/2, \pi/2π/2,π/2) whereas it is the smallest near (\pi, 0)(π,0). These spectral features survive beyond T_NTN. The temperature window T_N ≲ T ≲ T^*TN≲T≲T* shrinks with an increase in the next-nearest neighbor hopping, which indicates that the next-nearest neighbor hopping may not be supportive to the pseudogap-like features.

Instanton confinement-deconfinement transitions: Stability of pseudogap phases and topological order

Instanton confinement-deconfinement transitions: Stability of pseudogap phases and topological order

Pseudogap in Sr2−xLaxIrO4: Gor'kov-Teitel'baum thermal activation model

Recently, Hall effect measurements are done on Lanthanum doped Strontium Iridate Sr2−xLaxIrO4 which is 5d analogue of cuprates [1]. Hall effect measurements show that the effective carrier density nH exhibits a crossover from nH∼x to nH∼1+x near x≃0.16. This is very similar to that found in cuprates around p≃0.19. It is proposed that a pseudogap (PG) state in Sr2−xLaxIrO4 exists and is ending at x≃0.16[1]. However, PG boundary (in doping-temperature phase diagram) remains unknown. In this work, we apply a very successfull the Gor'kov-Teitel'baum Thermal Activation (GTTA) model to Sr2−xLaxIrO4 and obtain its PG phase boundary and draw an updated phase diagram. Our results agree with previously known signatures of PG phase in this system [2–4]. Using results from GTTA model we also obtain the evolution of “Fermi arcs” in this system as a function temperature for doping concentration x≃0.08 which are in qualitative agreement with the reported results.

Dissipationless Counterflow Currents above T_{c} in Bilayer Superconductors.

We report the existence of dissipationless currents in bilayer superconductors above the critical temperature T_{c}, assuming that the superconducting phase transition is dominated by phase fluctuations. Using a semiclassical U(1) lattice gauge theory, we show that thermal fluctuations cause a transition from the superconducting state at low temperature to a resistive state above T_{c}, accompanied by the proliferation of unbound vortices. Remarkably, while the proliferation of vortex excitations causes dissipation of homogeneous in-plane currents, we find that counterflow currents, flowing in the opposite direction within a bilayer, remain dissipationless. The presence of a dissipationless current channel above T_{c} is attributed to the inhibition of vortex motion by local superconducting coherence within a single bilayer, in the presence of counterflow currents. Our theory presents a possible scenario for the pseudogap phase in bilayer cuprates.

Observation and quantification of the pseudogap in unitary Fermi gases.

The microscopic origin of high-temperature superconductivity in cuprates remains unknown. It is widely believed that substantial progress could be achieved by better understanding of the pseudogap phase, a normal non-superconducting state of cuprates1,2. In particular, a central issue is whether the pseudogap could originate from strong pairing fluctuations3. Unitary Fermi gases4,5, in which the pseudogap-if it exists-necessarily arises from many-body pairing, offer ideal quantum simulators to address this question. Here we report the observation of a pair-fluctuation-driven pseudogap in homogeneous unitary Fermi gases of lithium-6 atoms, by precisely measuring the fermion spectral function through momentum-resolved microwave spectroscopy and without spurious effects from final-state interactions. The temperature dependence of the pairing gap, inverse pair lifetime and single-particle scattering rate are quantitatively determined by analysing the spectra. We find a large pseudogap above the superfluid transition temperature. The inverse pair lifetime exhibits a thermally activated exponential behaviour, uncovering the microscopic virtual pair breaking and recombination mechanism. The obtained large, temperature-independent single-particle scattering rate is comparable with that set by the Planckian limit6. Our findings quantitatively characterize the pseudogap in strongly interacting Fermi gases and they lend support for the role of preformed pairing as a precursor to superfluidity.

On out-of-equilibrium phenomena in pseudogap phase of complex SYK+U model

In this Letter we consider the out-of-equilibrium phenomena in the complex Sachdev-Ye-Kitaev (SYK) model supplemented with the attractive Hubbard interaction (SYK+U). This model provides the clear-cut transition from non-Fermi liquid phase in pure SYK to the superconducting phase through the pseudogap phase with non-synchronized Cooper pairs. We investigate the quench of the phase soft mode in this model and the relaxation to the equilibrium state. Using the relation with Hamiltonian mean field (HMF) model we show that the SYK+U model enjoys the several interesting phenomena, like existence of quasi-stationary long living states, out-of-equilibrium finite time phase transitions, non-extensivity and tower of condensates. We comment on the holographic dual gravity counterparts of these phenomena.

Pseudogap in BaPb x Bi1‒x O3 (x = 0.7, 0.75 and 1.0)

In this work, we have investigated the crystal and electronic structure of the orthorhombic phase of BaPb x BiO3 (BPBO) for x = 0.7 (BPBO70), 0.75 (BPBO75) and 1.0 (BPO), using temperature dependent x-ray diffraction measurements, photoemission spectroscopy, and electronic structure calculations. Our results show the importance of particle size and strain in governing superconductivity. Interestingly, the temperature evolution of the structural parameters in the case of BPBO70 is similar to that of BPBO75 but the magnitude of the change is diminished. The BPBO75 and BPO compounds exhibit metallic nature, which is corroborated by the core level studies. The electronic structure calculations in conjunction with the core level studies suggest that oxygen vacancies play an important role for metallicity observed in the end compound. The exponent to the spectral line shape close to the Fermi level suggests the origin of pseudogap to be due to other contributions in addition to disorder in the case of BPBO70 and BPO. The core level studies also show that as one goes from x = 0.70 to 1.0, there occurs chemical potential shift towards the valence band suggesting hole doping. Our results open the venue to further study these compounds as a function of particle size, nature of carriers for its transport behaviour, electronic structure below TC , composition at the grain boundaries and microscopic origin of pseudogap in the non-superconducting phase. We believe that our results call for a revision of the temperature-doping phase diagram of BPBO to include the pseudogap phase.

Coexistence of antiferromagnetism and unconventional superconductivity in a quasi-one-dimensional flat-band system: Creutz lattice

We study the coexistence of antiferromagnetism and unconventional superconductivity on the Creutz lattice which shows strictly flat bands in the noninteracting regime. The famous renormalized mean-field theory is used to deal with strong electron–electron repulsive Hubbard interaction in the effective low-energy t–J model, the superfluid weight of the unconventional superconducting state has been calculated via the linear response theory. An unconventional superconducting state with both spin-singlet and staggered spin-triplet pairs emerges beyond a critical antiferromagnetic coupling interaction, while antiferromagnetism accompanies this state. The superconducting state with only spin-singlet pairs is dominant with paramagnetic phase. The A phase is analogous to the pseudogap phase, which shows that electrons go to form pairs but do not cause a supercurrent. We also show the superfluid behavior of the unconventional superconducting state and its critical temperature. It is proven directly that the flat band can effectively raise the critical temperature of superconductivity. It is implementable to simulate and control strongly-correlated electrons’ behavior on the Creutz lattice in the ultracold atoms experiment or other artificial structures. Our results may help the understanding of the interplay between unconventional superconductivity and magnetism.

Spin-momentum locking and quantum anomalous Hall effect in d+id-density wave ordered pseudo gap phase of Bi2212

We model Bi 2 Sr 2 CaCu 2 O 8 + δ (Bi2212) bilayer system by a time reversal symmetry (TRS) and inversion symmetry (IS) broken Bloch Hamiltonian H. The pseudo-gap phase of the bilayer is assumed to be chiral d-density wave ordered. One of the focal points of the paper is the theoretical study of the spin-momentum locking (SML), due to the presence of a strong spin–orbit coupling in Bi2212, reported earlier in this phase in a spin-and angle-resolved photoemission spectroscopic measurement. The non-trivial spin texture in k -space, which is an outcome of the broken IS for the bilayer system, is found tuneable by electric field (and also by intercalation). We also show that this system exhibits anomalous quantum Hall effect due to the broken TRS and the presence of a strong spin–orbit coupling. • The emergent quantum anomalous Hall state due to the time reversal asymmetry. • The tuneable non-trivial spin-texture by electric field and intercalation. • The CDDW order is the raison d’etre of the freezing of anti-nodal quasi-particles. • The spin current density is a skew matrix only at the anti-nodal points. • The Majorana zero mode exists for the Zeeman field ⩾ a critical value.

Temperature and carrier concentration dependence of Fermi arcs in moderately underdoped Bi2Sr2CaCu2O8+δ cuprate high-temperature superconductors: A joint density of states perspective

Employing an autocorrelation analysis of angle resolved photoemission spectroscopy data, we have investigated the evolution of the joint density of states (JDOS) in the pseudogap phase of slightly underdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}(\mathrm{Bi}2212)$ cuprate high temperature superconductors for different temperatures $(T'\mathrm{s})$ and carrier concentrations $(\ensuremath{\delta}'\mathrm{s})$. Our JDOS analysis show that the Fermi arcs expand with increasing $T$ at a fixed $\ensuremath{\delta}$ and with increasing $\ensuremath{\delta}$ at a specific $T$. Qualitatively, these observations are consistent with the theoretical scenarios of the pseudogap phase being a phase incoherent $d$-wave superconductor, in which the Fermi arcs are described in terms of a subtle balance between temperature-dependent lifetime broadening of the single-particle excitations and the magnitude of the pairing gap.

Thermal evolution of the single-particle spectral function in the half-filled Hubbard model and pseudogap

In the half-filled one-orbital Hubbard model on a square lattice, we find pseudogap-like features in the form of two-peak structures associated with the momentum-resolved spectral function. These features exist within the temperature window ${T}_{N}\ensuremath{\lesssim}T\ensuremath{\lesssim}{T}^{*}$, where ${T}_{N}$ is the N\'eel temperature and ${T}^{*}$ is the temperature below which there exists a well-formed dip in the density of state. Inside the window ${T}_{N}\ensuremath{\lesssim}T\ensuremath{\lesssim}{T}^{*}$, the peak-to-peak separation in the two-peak structure of the momentum-resolved spectral function grows on moving away from the point ($\ensuremath{\pi}/2,\ensuremath{\pi}/2$) along the normal state Fermi surface toward $(\ensuremath{\pi},0)$, a behavior with remarkable similarities to what is observed in the $d$-wave state and pseudogap phase of high-${T}_{c}$ cuprates. We unveil these features by using a parallelized cluster-based Monte Carlo method for simulating the magnetic order parameter fields on a superlattice. The method enables us to access the momentum-resolved single-particle spectral function corresponding to a lattice size of $\ensuremath{\approx}240 \ifmmode\times\else\texttimes\fi{}$ 240 with an almost negligible finite-size effect.

Local pairs in high-temperature superconductors: The concept of pseudogap

The origin of the high-temperature superconductivity of cuprates remains a subject of debate after almost four decades of investigation. One of the main questions — what is the physics behind the mechanism of superconducting pairing, which makes it possible to obtain real Cooper pairs at temperatures much higher than 100 K, remains open. It is believed that the answer can be obtained by the studying the properties of cuprates in the normal state above Tc, where the pseudogap (PG) opens at T* >> Tc. The number of papers devoted to the study of PG is extraordinarily large, but its physics also remains in question. In cuprates, the question arises whether the pseudogap phase arises exclusively due to antiferromagnetic fluctuations, spin or charge density waves, or whether it can be explained by the formation below T* of specific paired fermions, the so-called local pairs. We review studies on both approaches to PG that should clarify this issue. In addition to theoretical considerations, we analyze and discuss various experimental results of fluctuation conductivity and PG measurements, as well as magnetic measurements, in an attempt to prove the decisive role of local pairs in the formation of the PG state. Accordingly, various types of supposed magnetic interactions can be considered as possible mechanisms of superconducting pairing in high-temperature superconductors.

Unified intermediate coupling description of pseudogap and strange metal phases of cuprates

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.