Underdoped Cuprates Research Articles

Incipient loop-current order in the underdoped cuprate superconductors

There are growing experimental evidence which indicate discrete symmetry breaking like time-reversal ($\mathcal{T}$), parity ($\mathcal{P}$) and C$_{4}$ lattice rotation in the pseudo-gap state of the under-doped copper-oxide based (cuprate) superconductors. The discrete symmetry breaking manifests a true phase transition to an ordered state. A detailed thermodynamic understanding of these orders can answer various puzzles related to the nature of the transition at the pseudo-gap temperature T$^*$. In this work, we investigate thermodynamic signature of $\mathcal{T-P}$ symmetry breaking considering superconductivity (SC) and bond-density wave (BDW) as two primary orders. The BDW can generate both modulating charge and current densities. This framework takes into account an intricate competition between the ubiquitous charge density wave and SC, which is prominent in various cuprates in the under-doped regime. We demonstrate that within mean-field approach of competing BDW and SC orders, a $\mathcal{T-P}$ breaking ground state of coexisting BDW and SC can be stabilized, provided the BDW itself breaks $\mathcal{T}-\mathcal{P}$. But this ground state ceases to occur at higher temperatures. However, we show that fluctuations in SC and BDW can drive emergence of a new unusual translational symmetry preserving order due to a preemptive phase transition by spontaneously breaking $\mathcal{T-P}$ at a higher temperature before the primary orders set in. We refer this order to be magneto-electric loop current (MELC) order. We present possible nature of phase transition for this new incipient MELC order and discuss some experimental relevance.

Origin of hour-glass magnetic dispersion in underdoped cuprate superconductors

In the present work we explain the hour-glass magnetic dispersion in underdoped cuprates. The dispersion arises due to the Lifshitz-type magnetic criticality. Superconductivity also plays a role, but the role is secondary. We list six major experimental observations related to the hour-glass and explain all of them. The theory provides a unified picture of the evolution of magnetic excitations in various cuprate families, including "hour-glass" and "wine-glass" dispersions and an emergent static incommensurate order. We propose the Lifshitz spin liquid "fingerprint" sum rule, and show that the latest data confirm the validity of the sum rule.

Bulk Superconductivity and Role of Fluctuations in the Iron-Based Superconductor FeSe at High Pressures.

The iron-based superconductor FeSe offers a unique possibility to study the interplay of superconductivity with purely nematic as well magnetic-nematic order by pressure (p) tuning. By measuring specific heat under p up to 2.36GPa, we study the multiple phases in FeSe using a thermodynamic probe. We conclude that superconductivity is bulk across the entire p range and competes with magnetism. In addition, whenever magnetism is present, fluctuations exist over a wide temperature range above both the bulk superconducting and the magnetic transitions. Whereas the magnetic fluctuations are likely temporal, the superconducting fluctuations may be either temporal or spatial. These observations highlight similarities between FeSe and underdoped cuprate superconductors.

Cooper pairing of incoherent electrons: An electron-phonon version of the Sachdev-Ye-Kitaev model

We introduce and solve a model of interacting electrons and phonons that is a natural generalization of the Sachdev-Ye-Kitaev-model and that becomes superconducting at low temperatures. In the normal state two Non-Fermi liquid fixed points with distinct universal exponents emerge. At weak coupling superconductivity prevents the onset of low-temperature quantum criticality, reminiscent of the behavior in several heavy-electron and iron-based materials. At strong coupling, pairing of highly incoherent fermions sets in deep in the Non-Fermi liquid regime, a behavior qualitatively similar to that in underdoped cuprate superconductors. The pairing of incoherent time-reversal partners is protected by a mechanism similar to Anderson's theorem for disordered superconductors. The superconducting ground state is characterized by coherent quasiparticle excitations and higher-order bound states thereof, revealing that it is no longer an ideal gas of Cooper pairs, but a strongly coupled pair fluid. The normal-state incoherency primarily acts to suppress the weight of the superconducting coherence peak and reduce the condensation energy. Based on this we expect strong superconducting fluctuations, in particular at strong coupling.

Superfluid stiffness in cuprates: Effect of Mott transition and phase competition

Superfluid stiffness $\rho_s$ is a defining characteristic of the superconducting state, allowing phase coherence and supercurrent. It is accessible experimentally through the penetration depth. Coexistence of $d$-wave superconductivity with other phases in underdoped cuprates, such as antiferromagnetism (AF) or charge-density waves (CDW), may drastically alter $\rho_s$. To shed light on this physics, the zero-temperature value of $\rho_s=\rho_{zz}$ along the $c$-axis was computed for different values of Hubbard interaction $U$ and different sets of tight-binding parameters describing the high-temperature superconductors YBCO and NCCO. We used Cellular Dynamical Mean-Field Theory for the one-band Hubbard model with exact diagonalization as impurity solver and state-of-the-art bath parametrization. We conclude that Mott physics plays a dominant role in determining the superfluid stiffness on the hole-doped side of the phase diagram. On the electron-doped side, antiferromagnetism wins over superconductivity near half-filling. But upon approaching optimal electron-doping, homogeneous coexistence between superconductivity and antiferromagnetism causes the superfluid stiffness to drop sharply. Hence, on the electron-doped side, it is competition between antiferromagnetism and $d$-wave superconductivity that plays a dominant role in determining the value of $\rho_{zz}$ near half-filling. At large overdoping, $\rho_{zz}$ behaves in a more BCS-like manner in both the electron- and hole-doped cases. We comment on some qualitative implications of these results for the superconducting transition temperature.

Bond particle theory for the pseudogap phase of underdoped cuprates

We present a theory for the lightly doped t-J model which is of possible relevance for the normal state of underdoped cuprates. Starting from an arbitrary dimer covering of the plane an exact representation of the t-J Hamiltonian in terms of bond bosons and fermions can be derived. Since all dimer coverings must give identical results for observable quantities we construct an approximate but translationally invariant Hamiltonian by averaging the bond particle Hamiltonian over all possible dimer coverings. Treating the resulting Hamiltonian in mean-field approximation we find fermi pockets centered near (pi/2,pi/2) with a total area of x/2 (with x the hole concentration) and a gapped spin-wave-like band of triplet excitations.

Tc and Other Cuprate Properties in Relation to Planar Charges as Measured by NMR

Nuclear magnetic resonance (NMR) in cuprate research is a prominent bulk local probe of magnetic properties. NMR also, as was shown over the last years, actually provides a quantitative measure of local charges in the CuO 2 plane. This has led to fundamental insights, e.g., that the maximum T c is determined by the sharing of the parent planar hole between Cu and O. Using bonding orbital hole contents on planar Cu and O measured by NMR, instead of the total doping x, the thus defined two-dimensional cuprate phase diagram reveals significant differences between the various cuprate materials. Even more importantly, the reflected differences in material chemistry appear to set a number of electronic properties as we discuss here, for undoped, underdoped and optimally doped cuprates. These relations should advise attempts at a theoretical understanding of cuprate physics as well as inspire material chemists towards new high- T c materials. Probing planar charges, NMR is also sensitive to charge variations or ordering phenomena in the CuO 2 plane. Thereby, local charge order on planar O in optimally doped YBCO could recently be proven. Charge density variations seen by NMR in both planar bonding orbitals with amplitudes between 1% to 5% appear to be omnipresent in the doped CuO 2 plane, i.e., not limited to underdoped cuprates and low temperatures.

Pseudogap and Fermi arcs in underdoped cuprates

The proposed loop-current order in cuprates cannot give the observed pseudogap and the Fermi-arcs because it preserves translation symmetry. A modification to a periodic arrangement of the four possible orientations of the order parameter with a large period of between about 12 to 30 lattice constants is proposed and shown in a simple and controlled calculation to give one-particle spectra with every feature as in the ARPES experiments. The results follow from (1) the currents at the boundaries of the periodic domains with similar topology as the Affleck-Marston flux phase, and (2) the mixing introduced by the boundary currents between the states near the erstwhile Fermi-surface and the ghost Fermi-surfaces which are displaced from it by mini-reciprocal vectors. The proposed idea can be ruled out or verified by high resolution diffraction or imaging experiments. It does not run afoul of the variety of different experiments consistent with the loop-current order as well as the theory of the marginal Fermi-liquid and d-wave superconductivity based on quantum-critical fluctuations of the loop current order.

Sign change of polarization rotation under time or space inversion in magnetoelectric YbAl3(BO3)4

Materials with optical activity can rotate the polarization plane of transmitted light. The most typical example is the natural optical activity, which has the symmetry property of changing sign after space inversion but being invariant to time inversion. Faraday rotation exhibits the opposite: it is invariant to space inversion but changes sign after time reversal. Here, we demonstrate that in a magnetoelectric material, another type of polarization rotation is possible. This effect is investigated in magnetoelectric YbAl3(BO3)4 under the viewpoint of time and space inversion symmetry arguments. We observe the sign change of the rotation sense under either time or space reversal. This investigation proves that the polarization rotation in YbAl3(BO3)4 must be classified as gyrotropic birefringence, which has been discussed within the idea of time-reversal breaking in underdoped cuprates. The diagonal terms in the magnetoelectric susceptibility are responsible for the observed signal of gyrotropic birefringence. Further analysis of the experimental spectra reveals a substantial contribution of the natural optical activity to the polarization rotation. We also demonstrate that the observed activity originates from the magnetoelectric susceptibility.

Single origin of the nodal and antinodal gaps in cuprates

Recent angle-resolved photoemission electron spectroscopy (ARPES) experiments demonstrate that the momentum dependence of the spectral gap in underdoped cuprates does not follow a pure d-wave form (Anzai H. et al., Nat. Commun., 4 (2013) 1815). This deviation is highly controversial. It has often been interpretated as a proof of the non-superconducting origin of the antinodal gap in the underdoped regime. In this paper, we show that the measured angular dependence of the spectral gap can be explained by the basic nature of pairs in high-Tc cuprates. Hole pairs, or pairons, form as a result of the local antiferromagnetic environment on the scale , the magnetic coherence length. The spatial extension of the pairon wave function beyond first nearest neighbours gives rise to the anomalous angular dependence of the gap, in quantitative agreement with experiments. This simple interpretation strongly indicates the common origin of the nodal and antinodal gaps.

Consideration of thermal Hall effect in undoped cuprates

A recent observation of thermal Hall effect of magnetic origin in underdoped cuprates calls for critical re-examination of low-energy magnetic dynamics in undoped antiferromagnetic compound on square lattice, where traditional, renormalized spin-wave theory was believed to work well. Using Holstein-Primakoff boson formalism, we find that magnon-based theories can lead to finite Berry curvature in the magnon band once the Dzyaloshinskii-Moriya spin interaction is taken into account explicitly, but fail to produce non-zero thermal Hall conductivity. Assuming accidental doping by impurities and magnon scattering off of such impurity sites fails to predict skew scattering at the level of Born approximation. Local formation of skyrmion defects is also found incapable of generating magnon thermal Hall effect. Turning to spinon-based scenario, we write down a simple model by adding spin-dependent diagonal hopping to the well-known {\pi}-flux model of spinons. The resulting two-band model has Chern number in the band structure, and generates thermal Hall conductivity whose magnetic field and temperature dependences mimic closely the observed thermal Hall signals. In disclaimer, there is no firm microscopic basis of this model and we do not claim to have found an explanation of the data, but given the unexpected nature of the experimental observation, it is hoped this work could serve as a first step towards reaching some level of understanding.

Gapless spin excitations in superconducting La2−xCa1+xCu2O6 with Tc up to 55 K

We report inelastic neutron scattering on single crystals of the bilayer cuprate family La$_{2-x}$Ca$_{1+x}$Cu$_{2}$O$_{6+\delta}$, including two crystals made superconducting (transitions at 45 and 55 K) by high-pressure annealing in an oxygen-containing atmosphere. The magnetic excitations in the non-superconducting crystal have a similar temperature-dependence as those in weakly hole-doped cuprates. In the superconducting crystals, there is a near-uniform suppression of the magnetic spectral weight with increasing temperature; in particular, there are no signs of a spin gap or "resonance" peak. This is different from the temperature dependence seen in many optimally-doped cuprates but similar to the behavior seen in certain underdoped cuprates. We discuss the possible connection with pair-density-wave superconductivity.

Distinctive Features of Metal-Insulator Transitions, Multiscale Phase Separation, and Related Effects in Hole-Doped Cuprates

We study the distinctive features of the metal-insulator transitions, multiscale phase separation, and evolution of coexisting insulating and metallic/superconducting phases in hole-doped cuprates. We show how these interrelated phenomena and related effects manifest themselves in a wide doping range from the lightly doped to optimally doped regime in these systems, where the localized and mobile hole carriers reside in hole-poor (insulating) and hole-rich (metallic or superconducting) regions. We argue that small hole-rich regions (i.e. narrow nanoscale metallic islands or stripes) can persist in the insulating phase of the lightly doped cuprates, while the competing insulating, metallic, and superconducting phases would coexist in the under-doped cuprates. When the doping level is increased further, the hole-poor regions (or insulating zones) gradually narrow from macroscale to nanoscale insulating stripes and disappear in the optimally doped cuprates. We demonstrate clearly that the metal-insulator transitions and the coexisting insulating and metallic/superconducting phases are manifested in the suppression of superconductivity in underdoped cuprates and in the different temperature-dependent behaviors of the magnetic susceptibility and c-axis resistivity of lightly to optimally doped cuprates.

Enhanced nematic fluctuations near an antiferromagnetic Mott insulator and possible application to high-Tc cuprates

Motivated by the widespread experimental observations of nematicity in strongly underdoped cuprate superconductors, we investigate the possibility of enhanced nematic fluctuations in the vicinity of a Mott insulator that displays Néel-type antiferromagnetic order. By performing a strong-coupling expansion of an effective model that contains both Cu-d and O-p orbitals on the square lattice, we demonstrate that quadrupolar fluctuations in the p-orbitals inevitably generate a biquadratic coupling between the spins of the d-orbitals. The key point revealed by our classical Monte-Carlo simulations and large-N calculations is that the biquadratic term favors local stripe-like magnetic fluctuations, which result in an enhanced nematic susceptibility that onsets at a temperature scale determined by the effective Heisenberg exchange J. We discuss the impact of this type of nematic order on the magnetic spectrum and outline possible implications on our understanding of nematicity in the cuprates.

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.

Competition between spin-induced charge instabilities in underdoped cuprates

We study the static charge correlation function in an one-band model on a square lattice. The Hamiltonian consist of effective hoppings of the electrons between the lattice sites and the Heisenberg Hamiltonian. Approximating the irreducible charge correlation function by a single bubble yields the ladder approximation for the charge correlation function. In this approximation one finds in general three charge instabilities, two of them are due to nesting, the third one is the flux phase instability. Since these instabilities cannot explain the experiments in hole-doped cuprates we have included in the irreducible charge correlation function also Aslamasov-Larkin (AL) diagrams where charge fluctuations interact with products of spin fluctuations. We then find at high temperatures a nematic or $d$-wave Pomeranchuk instability with a very small momentum. Its transition temperature decreases roughly linearly with doping in the underdoped region and vanishes near optimal doping. Decreasing the temperature further a secondary axial charge-density wave (CDW) instability appears with mainly $d$-wave symmetry and a wave vector somewhat larger than the distance between nearest neighbor hot spots. At still lower temperatures the diagonal flux phase instability emerges. A closer look shows that the AL diagrams enhance mainly axial and not diagonal charge fluctuations in our one-band model. This is the main reason why axial and not diagonal instabilities are the leading ones in agreement with experiment. The two instabilities due to nesting vanish already at very low temperatures and do not play any major role in the phase diagram. Remarkable is that the nematic and the axial CDW instabilities show a large reentrant behavior.

Topological Structures in Unconventional Scenario for 2D Cuprates

Numerous experimental data point to cuprates as d-d charge transfer unstable systems whose description implies the inclusion of the three many-electron valence states CuO $_{4}^{7-,6-,5-}$ (nominally Cu1+,2+,3+) on an equal footing as a well-defined charge triplet. We introduce a minimal model to describe the charge degree of freedom in cuprates with the on-site Hilbert space reduced to only the three states and make use of the S = 1 pseudospin formalism. The formalism constitutes a powerful method to study complex phenomena in interacting quantum systems characterized by the coexistence and competition of various ordered states. Overall, such a framework provides a simple and systematic methodology to predict and discover new kinds of orders. In particular, the pseudospin formalism provides the most effective way to describe different topological structures, in particular, due to a possibility of a geometrical two-vector description of the on-site states. We introduce and analyze effective pseudospin Hamiltonian with on-site and inter-site charge correlations, two types of a correlated one-particle transfer and two-particle, or the composite boson transfer. The latter is of a principal importance for the HTSC perspectives. The 2D S = 1 pseudospin system is prone to a creation of different topological structures, which form topologically protected inhomogeneous distributions of the eight local S = 1 pseudospin order parameters. We present a short overview of localized topological structures, typical for S = 1 (pseudo)spin systems, focusing on unexpected antiphase domain walls in parent cuprates and so-called quadrupole skyrmion, which are believed to be candidates for a topological charge excitation in parent or underdoped cuprates. Puzzlingly, these unconventional structures can be characterized by an uniform distribution of the mean on-site charge, that makes these invisible for X-rays. Quasi-classical approximation and computer simulation are applied to analyze localized topological defects and evolution of the domain structures in “negative-U” model under charge order-superfluid phase transition.

Nature of the spin liquid in underdoped cuprate superconductors

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 $\lambda$ which drives magnetic criticality at low doping $x$. Hence we derive the zero temperature $\lambda-x$ phase diagram of the model. It is argued that all underdoped cuprates are close to the quantum tricritical point $x=0$, $\lambda=1$. The three phases "meet" at the tricritical point: (i) N\'eel antiferromagnet, (ii) spin spiral with antinodal direction of the spiral wave vector, (iii) algebraic spin liquid. We argue that underdoped cuprates belong either to the spin liquid phase or they are on the borderline between the spin liquid and the spin spiral. We calculate the energy position $E_{cross}$ of the inelastic neutron scattering response maximum at ${\bm q}=(\pi,\pi)$ and compare our results with experiments. We also explain softening of magnons in the intermediate regime observed in inelastic neutron scattering.

Metal-insulator transitions and nanoscale phase separation in various underdoped cuprates

Metal-insulator transitions and nanoscale phase separation in various underdoped cuprates

The coexisting of insulating and metallic/superconducting phases and their competing effects in various underdoped cuprates

We show that the unconventional electron–phonon interactions and polaronic effects, charge inhomogeneity and charge ordering in underdoped cuprates result in the nanoscale phase separation and the occurrence of competing and coexisting of insulating and metallic/superconducting phases. We identify possible types of localized and mobile charge carriers in these systems, which segregate into insulating (carrier-poor) and metallic/superconducting (carrier-rich) regions as a result of their specific ordering. We found that the coexistence of two competing insulating and metallic phases can persist in the lightly doped cuprates on a local scale, while the coexistence of three competing insulating, metallic and superconducting phases is expected in the underdoped cuprates on a global scale. We demonstrated that the competing effects of these coexisting insulating and metallic/superconducting phases are manifested in the unusual temperature dependences of the magnetic susceptibility and resistivity and in the suppression of superconductivity in various underdoped cuprates.