Effect of interlayer tunneling on the electronic structure of bilayer cuprates and quantum phase transitions in carrier concentration and high magnetic field

We present a theoretical study of the electronic structure of bilayer HTSC cuprates and its evolution under doping and in a high magnetic field. Analysis is based on the t-t′-t″-J* model in the generalized Hartree-Fock approximation. Possibility of tunneling between CuO2 layers is taken into account in the form of a nonzero integral of hopping between the orbitals of adjacent planes and is included in the scheme of the cluster form of perturbation theory. The main effect of the coupling between two CuO₂ layers in a unit cell is the bilayer splitting manifested in the presence of antibonding and bonding bands formed by a combination of identical bands of the layers themselves. A change in the doping level induces reconstruction of the band structure and the Fermi surface, which gives rise to a number of quantum phase transitions. A high external magnetic field leads to a fundamentally different form of electronic structure. Quantum phase transitions in the field are observed not only under doping, but also upon a variation of the field magnitude. Because of tunneling between the layers, quantum transitions are also split; as a result, a more complex sequence of the Lifshitz transitions than in single-layer structures is observed.     

Coulomb correlations do not fill the e<Superscript>′</Superscript><Subscript>g</Subscript> hole pockets in Na<Subscript>0.3</Subscript>CoO<Subscript>2</Subscript>

There exists presently considerable debate over the question whether local Coulomb interactions can explain the absence of the small e^′ _g Fermi surface hole pockets in photoemission studies of Na_0.3CoO₂. By comparing dynamical mean field results for different single particle Hamiltonians and exact diagonalization as well as quantum Monte Carlo treatments, we show that, for realistic values of the Coulomb energy U and Hund exchange J, the e^′ _g pockets can be slightly enhanced or reduced compared to band structure predictions, but they do not disappear.     

Angular studies of the magnetoresistance in the density wave state of the quasi-two-dimensional purple bronze KMo<Subscript>6</Subscript>O<Subscript>17</Subscript>

The purple molybdenum bronze KMo₆O₁₇ is a quasi-two-dimensional compound which shows a Peierls transition towards a commensurate metallic charge density wave (CDW) state. High magnetic field measurements have revealed several transitions at low temperature and have provided an unusual phase diagram “temperature-magnetic field”. Angular studies of the interlayer magnetoresistance are now reported. The results suggest that the orbital coupling of the magnetic field to the CDW is the most likely mechanism for the field induced transitions. The angular dependence of the magnetoresistance is discussed on the basis of a warped quasi-cylindrical Fermi surface and provides information on the geometry of the Fermi surface in the low temperature density wave state.     

First-principles study of high pressure phase transformations in Li<Subscript>3</Subscript>N

The lattice dynamics of lithium nitride (Li₃N) under high pressure are extensively investigated to probe its phase transformations by using the pseudopotential plane-wave method within the density functional theory. A new second order α↦α^′-Li₃N phase transition is identified for the first time. The newly proposed α^′-phase possesses a hexagonal symmetry with four ions in the unit cell having a space group of P-3m1. Further enthalpy and phonon calculations support the existence of this phase, which stabilizes in a narrow pressure range of 2.8 – 3.6 GPa at zero temperature. Upon further compression, transitions to denser packed phases of β-and γ-Li₃N are typical first order. The analysis of the electronic densities of states suggests that all the high pressure modifications of Li₃N are insulators and, interestingly, the typical behavior of compression is to broaden the band gap.     

Non-uniform doping across the Fermi surface of NbS<Subscript>2</Subscript> intercalates

Magnetic ordering of the first row transition metal intercalates of NbS₂ due to coupling between the conduction electrons and the intercalated ions has been explained in terms of Fermi surface nesting. We use angle-resolved photoelectron spectroscopy to investigate the Fermi surface topology and the valence band structure of the quasi-two-dimensional layer compounds Mn_1/3NbS₂ and Ni_1/3NbS₂. Charge transfer from the intercalant species to the host layer leads to non-uniform, pocket selective doping of the Fermi surface. The implication of our results on the nesting properties are discussed.     

Lifshits quantum phase transitions and rearrangement of the Fermi surface upon a change in the hole concentration in high-temperature superconductors

Changes in the electronic structure in the normal phase of high-T _c superconductors (HTSCs), viz., layered cuprates, are considered. The results of LDA + GTB calculations of the electron structure and the Fermi surface of La_{2 − x} Sr _x CuO₄ one-layer cuprates with allowance for strong correlations are compared with ARPES and quantum oscillations data. Two critical points x _c1 and x _c2 are discovered at which the rear-rangement of the Fermi surface takes place. In the vicinity of these points, changes in the thermodynamic properties at low temperatures are determined using the Lifshits ideology concerning 2.5-order quantum phase transitions. A singularity δ(C/T) ∝ (x − x _e )^1/2 in the electron heat capacity agrees well with the available experimental data in the vicinity of x _c1 ≈ 0.15. Sign reversal of the Hall constant upon doping is also considered qualitatively.     

Doping-dependent electronic structure of cuprates studied using angle-scanned photoemission

Full k -maps of the electronic structure near the Fermi level of differently doped cuprates measured with angle-scanned photoelectron spectroscopy are presented. The valence band maximum of the antiferromagnetic insulator Sr₂CuO₂Cl₂, which is taken as a representative of an undoped cuprate, and the Fermi surfaces of overdoped, optimally doped and underdoped Bi₂Sr₂CaCu₂O_8+δ high-temperature superconductors are mapped in the normal state. The results confirm the existence of large Luttinger Fermi surfaces at high doping with a Fermi surface volume proportional to (1+x), where x is the hole concentration. At very low doping, however, we find that this assumption based on Luttinger's theorem is not fulfilled. This implies a change in the topology of the Fermi surface. Furthermore the intensity of the shadow bands observed on the Fermi surface of Bi₂Sr₂CaCu₂O_8+δ as a function of the doping is discussed. Received 12 October 1999 and Received in final form 12 April 2000     

Pseudogap behavior in Bi<Subscript>2</Subscript>Ca<Subscript>2</Subscript>SrCu<Subscript>2</Subscript>O<Subscript>8</Subscript>: Results of the generalized dynamical mean-field approach

Pseudogap phenomena are observed for the normal underdoped phase of different high-T _c cuprates. Among others, the Bi₂Sr₂CaCu₂O_{8 − δ} (Bi2212) compound is one of the most studied experimentally. To describe the pseudogap regime in Bi2212, we use a novel generalized ab initio LDA + DMFT + Σ_k hybrid scheme. This scheme is based on the strategy of one of the most powerful computational tools for real correlated materials: the local density approximation (LDA) + dynamical mean-field theory (DMFT). Conventional LDA + DMFT equations are here supplied with an additional (momentum-dependent) self-energy Σ_k in the spirit of our recently proposed DMFT + Σ_k approach taking into account pseudogap fluctuations. In the present model, Σ_k describes nonlocal correlations induced by short-range collective Heisenberg-like antiferromagnetic spin fluctuations. The effective single-impurity problem of the DMFT is solved by the numerical renormalization group (NRG) method. Material-specific model parameters for the effective x ² − y ² orbital of Cu-3d shell of the Bi2212 compound, e.g., the values of intra-and interlayer hopping integrals between different Cu sites, the local Coulomb interaction U, and the pseudogap potential Δ were obtained within the LDA and LDA + DMFT schemes. Here, we report on the theoretical LDA + DMFT + Σ_k quasiparticle band dispersion and damping, Fermi surface renormalization, momentum anisotropy of (quasi)static scattering, densities of states, spectral densities, and angular-resolved photoemission (ARPES) spectra, taking into account pseudogap and bilayer splitting effects for normal (slightly) underdoped Bi2212 (δ = 0.15). We show that LDA + DMFT + Σ_k successfully describes strong (pseudogap) scattering close to Brillouin zone boundaries. Our calculated LDA + DMFT + Σ_k Fermi surfaces and ARPES spectra in the presence of pseudogap fluctuations are almost insensitive to the bilayer splitting strength. However, our LDA-calculated value of bilayer splitting is rather small to describe the experimentally observed peak-dip-hump structure. The results obtained are in good semiquantitative agreement with various recent ARPES experiments. The article was submitted by the authors in English.     

Electronic structure and properties of high-T c superconducting cuprates in the normal and superconducting phases within the LDA + GTB approach

Theoretical investigations of the properties of high-T _c superconducting cuprates within the LDA + GTB method taking into account the magnetic and phonon pairing mechanisms have been reviewed. These properties are the concentration-dependent electronic structure, quantum phase transitions with a change in the topology of the Fermi surface, and the superconducting phase of the $d_{x^2 - y^2 }$ symmetry.     

Effect of hole doping on the electronic structure and the Fermi surface in the Hubbard model within norm-conserving cluster pertubation theory

The concentration dependences of the band structure, spectral weight, density of states, and Fermi surface in the paramagnetic state are studied in the Hubbard model within cluster pertubation theory with 2 × 2 clusters. Representation of the Hubbard X operators makes it possible to control conservation of the spectral weight in constructing cluster perturbation theory. The calculated value of the ground-state energy is in good agreement with the results obtained using nonperturbative methods such as the quantum Monte Carlo method, exact diagonalization of a 4 × 4 cluster, and the variational Monte Carlo method. It is shown that in the case of hole doping, the states in the band gap (in-gap states) lie near the top of the lower Hubbard band for large values of U and near the bottom of the upper band for small U. The concentration dependence of the Fermi surface strongly depends on hopping to second (t′) and third (t″) neighbors. For parameter values typical of HTSC cuprates, the existence of three concentration regions with different Fermi surfaces is demonstrated. It is shown that broadening of the spectral electron density with an energy resolution typical of contemporary ARPES leads to a pattern of arcs with a length depending on the concentration. Only an order-of-magnitude decrease in the linewidth makes it possible to obtain the true Fermi surface from the spectral density. The kinks associated with strong electron correlations are detected in the dispersion relation below the Fermi level.     

Common features in high Tc cuprates and diborides

The normal state of magnesium diboride, the simplest metallic system showing the macroscopic quantum coherence at high temperature (high T_c superconductivity––HTcS) shows some features that are common with the cuprates, shedding light on the pairing mechanism for T_c amplification in HTcS: (1) two or more electronic components associated with multiple Fermi surface portions; (2) crossing of electronic topological transitions (ETT) where the Fermi surface changes its topology and (3) phonon softening in extended Kohn anomalies (EKA) over a large wave-vector range.     

Reconstruction of the Fermi surface of HTSC cuprates in a high magnetic field

The effect of a high magnetic field on the electronic structure of HTSC cuprates is considered. The study is performed in the t-t′-t″-J* model, and the high magnetic field effect is taken into account not only as the Zeeman splitting of the one-electron levels, but also in the occupation numbers of the states with different spin projections and in the formation of the spin correlation functions. The field is assumed to be high enough to align all of the spins along the field. As a result, the Fermi surface reconstruction is obtained from four hole pockets about the nodal point (π/2, π/2) in the paramagnetic phase to a large hole pocket about the point (π, π) in the ferromagnetic phase. As the magnetic field strength decreases, a number of quantum phase transitions are revealed; they are manifested in the changed Fermi surface topology. The Fermi surface reconstruction with a decreasing field is qualitatively the same as that with an increasing doping degree in the absence of a magnetic field.     

Physical quantities for two coupled Hubbard planes and comparison with experiments on Bilayer high-Tc cuprates

For a bilayer model of the high-T_c cuprates consisting of two coupled Hubbard planes we calculate within the FLEX (fluctuation exchange) approximation the quasiparticle self-energies and dynamic spin susceptibilities. We consider a Fermi surface similar to those of the YBaCuO cuprates, an on-site Coulomb repulsion U = 6 t (where t is the intraplane hopping), and interplane hoppings t’ up to t’ = 0.7 t. For sufficiently large t'(?0.3 t) the spin susceptibility gC^? due to transitions between the bonding and antibonding states becomes much larger than the susceptibility gC⁺ for transitions within the same band. The spectral density Im gC^?(q, ω) exhibits a peak centered at the antiferromagnetic wavevector q = Q = (π, π) and at the antiparamagnon frequency ω = ω_sf. For decreasing temperature T and increasing t’ the peak becomes more and more pronounced. We calculate the Fermi lines of the bonding and antibonding bands for different t'. The superconducting transition temperature T_c for d_x ²?y²-wave pairing decreases as t' increases. Our results are in qualitative agreement with magnetic neutron scattering, magnetic resonance, and photoemission experiments on bilayer YBaCuO cuprates. They are also consistent with the results of quantum Monte Carlo simulations.     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

Electronic and magnetic structure of a possible iron based superconductor BaFe<Subscript>2</Subscript>Se<Subscript>3</Subscript>

We present results of LDA calculations (band structure, densities of states, Fermi surfaces) for possible iron based superconductor BaFe₂Se₃ (Ba123) in normal (paramagnetic) phase. Results are briefly compared with similar data on prototype BaFe₂As₂ and (K,Cs)Fe₂Se₂ superconductors. Without doping this system is anti-ferromagnetic with T _N^exp ∼ 250 K and rather complicated magnetic structure. Neutron diffraction experiments indicated the possibility of two possible spin structures (antiferromagnetically ordered “plaquettes” or “zigzags”), indistinguishable by neutron scattering. Using LSDA calculated exchange parameters we estimate Neel temperatures for both spin structures within the molecular field approximation and show τ₁ (plaquettes) spin configuration to be more favorable than τ₂ (zigzags).     

Ab initio probing of the electronic band structure and Fermi surface of fluorine-doped WO<Subscript>3</Subscript> as a novel low-<Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">C</Emphasis></Subscript> superconductor

Ab initio calculations were performed to investigate the electronic structure and the Fermi surface of the newly discovered low-temperature superconductor: fluorine-doped WO₃. We find that F doping provides the transition of the insulating tungsten trioxide into a metallic-like phase WO_{3 − x} F _x , where the near-Fermi states are formed mainly from W 5d with admixture of O 2p orbitals. The cooperative effect of fluorine additives in WO₃ consists in change of electronic concentration as well as the lattice constant. At probing their influence on the near-Fermi states separately, the dominant role of the electronic factor for the transition of tungsten oxyfluoride into superconducting state was established. The volume of the Fermi surface gradually increases with the increase of the doping. In the sequence WO₃ → WO_2.5F_0.5 the effective atomic charges of W and O ions decrease, but much less, than it is predicted within the idealized ionic model—owing to presence of the covalent interactions W-O and W-F.     

Near doping-independent pocket area from an antinodal Fermi surface instability in underdoped high temperature superconductors

Fermi surface models applied to the underdoped cuprates predict the small pocket area to be strongly dependent on doping whereas quantum oscillations in YBa(2)Cu(3)O(6+x) find precisely the opposite to be true--seemingly at odds with the Luttinger volume. We show that such behavior can be explained by an incommensurate antinodal Fermi surface nesting-type instability--further explaining the doping-dependent superstructures seen in cuprates using scanning tunneling microscopy. We develop a Fermi surface reconstruction scheme involving orthogonal density waves in two dimensions and show that their incommensurate behavior requires momentum-dependent coupling. A cooperative modulation of the charge and bond strength is therefore suggested.     

Electronic structure,topological phase transitions and superconductivity in (K,Cs)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Fe<Subscript>2</Subscript>Se<Subscript>2</Subscript>

We present LDA band structure of novel hole doped high temperature superconductors (T _c ∼ 30 K) K _x Fe₂Se₂ and Cs _x Fe₂Se₂ and compare it with previously studied electronic structure of isostructural FeAs superconductor BaFe₂As₂ (Ba122). We show that stoichiometric KFe₂Se₂ and CsFe₂Se₂ have rather different Fermi surfaces as compared with Ba122. However at about 60% of hole doping Fermi surfaces of novel materials closely resemble those of Ba122. In between these dopings we observe a number of topological Fermi surface transitions near the Γ point in the Brillouin zone. Superconducting transition temperature T _c of new systems is apparently governed by the value of the total density of states (DOS) at the Fermi level.     

Quantum oscillations of the resistivity and hall coefficient and the quantum limit in Bi<Subscript>0.93</Subscript>Sb<Subscript>0.07</Subscript> alloys in a magnetic field along the trigonal axis

The dependences of the electrical resistivity ρ and the Hall coefficient R on the magnetic field have been measured for single-crystal samples of the n-Bi_0.93Sb_0.07 semiconductor alloys with electron concentrations in the range 1 × 10¹⁶ cm⁻³ < n < 2 × 10¹⁸ cm⁻³. It has been found that the measured dependences exhibit Shubnikov-de Haas quantum oscillations. The magnetic fields corresponding to the maxima of the quantum oscillations of the electrical resistivity are in good agreement with the calculated values of the magnetic fields in which the Landau quantum level with the number N intersects the Fermi level. The quantum oscillations of the Hall coefficient with small numbers are characterized by a significant spin splitting. In a magnetic field directed along the trigonal axis, the quantum oscillations of the resistivity ρ and the Hall coefficient R are associated with electrons of the three-valley semiconductor and are in phase with the magnetic field. In the case of a magnetic field directed parallel to the binary axis, the quantum oscillations associated both with electrons of the secondary ellipsoids in weaker magnetic fields and with electrons of the main ellipsoid in strong magnetic fields (after the overflow of electrons from the secondary ellipsoids to the main ellipsoid) are also in phase. In magnetic fields of the quantum limit ħω _c /2 ≥ E _F, the electrical conductivity increases with an increase in the magnetic field: σ₂₂(H) ∼ H ^k . A theoretical evaluation of the exponent in this expression for a nonparabolic semiconductor leads to values of k close to the experimental values in the range 4 ≤ k ≤ 4.6, which were obtained for samples of the semiconductor alloys with different electron concentrations. A further increase in the magnetic field results in a decrease of the exponent k and in the transition to the inequality σ₂₂(H) ≤ σ₂₁(H).     

Magnetic phase diagram of the dimerized spin S = 1/2 ladder

The ground-state magnetic phase diagram of a spin S=1/2 two-leg ladder with alternating rung exchange J_⊥(n)=J_⊥[1 + (-1)ⁿ δ] is studied using the analytical and numerical approaches. In the limit where the rung exchange is dominant, we have mapped the model onto the effective quantum sine-Gordon model with topological term and identified two quantum phase transitions at magnetization equal to the half of saturation value from a gapped to the gapless regime. These quantum transitions belong to the universality class of the commensurate-incommensurate phase transition. We have also shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. We also present a detailed numerical analysis of the low energy excitation spectrum and the ground state magnetic phase diagram of the ladder with rung-exchange alternation using Lanczos method of numerical diagonalizations for ladders with number of sites up to N = 28. We have calculated numerically the magnetic field dependence of the low-energy excitation spectrum, magnetization and the on-rung spin-spin correlation function. We have also calculated the width of the magnetization plateau and show that it scales as δ^ν, where critical exponent varies from ν = 0.87±0.01 in the case of a ladder with isotropic antiferromagnetic legs to ν = 1.82±0.01 in the case of ladder with ferromagnetic legs. Obtained numerical results are in an complete agreement with estimations made within the continuum-limit approach.