Function Of Hole Doping Research Articles

Doped Mott insulators in the triangular-lattice Hubbard model

We investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping $\delta$ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping $\delta\lesssim 10\%$, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave-vector is observed, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well defined Fermi surface. On further doping, $\delta \approx 10\%\sim 20\%$ SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping $\delta \gtrsim 20\%$, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.

Magnetic excitations in hole-doped Sr2IrO4 : Comparison with electron-doped cuprates

We have studied the evolution of magnetic and orbital excitations as a function of hole-doping in single crystal samples of Sr2Ir(1-x)Rh(x)O4 (0.07 < x < 0.42) using high resolution Ir L3-edge resonant inelastic x-ray scattering (RIXS). Within the antiferromagnetically ordered region of the phase diagram (x < 0.17) we observe highly dispersive magnon and spin-orbit exciton modes. Interestingly, both the magnon gap energy and the magnon bandwidth appear to increase as a function of doping, resulting in a hardening of the magnon mode with increasing hole doping. As a result, the observed spin dynamics of hole-doped iridates more closely resemble those of the electron-doped, rather than hole-doped, cuprates. Within the paramagnetic region of the phase diagram (0.17 < x < 0.42) the low-lying magnon mode disappears, and we find no evidence of spin fluctuations in this regime. In addition, we observe that the orbital excitations become essentially dispersionless in the paramagnetic phase, indicating that magnetic order plays a crucial role in the propagation of the spin-orbit exciton.

Drude weight anisotropy in the doped iron pnictides: The primary role of orbital weight redistribution along the reconstructed Fermi surfaces

We explore the anisotropy in low frequency conductivity as a function of hole doping in multiorbital models of pnictides by analyzing the Drude weight in the $x$ and $y$ directions of a ($\pi$, 0) spin-density wave state. A reduction in the conductivity anisotropy with increased hole doping, and subsequent sign reversal, both observed in experiments, is found to be a common trend in these models. This behavior arises due to the interplay of low energy orbitally-resolved density of states and the geometrical features of the Fermi surface. An understanding of anisotropy in the electron doped regime, however, would require additional ingredients.

Evolution of superconducting gap anisotropy in hole‐doped 122 iron pnictides

AbstractMotivated by recent experimental findings, we investigate the evolution of the superconducting gap anisotropy in 122 iron pnictides as a function of hole doping. Employing both a functional and a weak coupling renormalization group approach (FRG and WRG), we analyze the Fermi surface instabilities of an effective 122 model band structure at different hole dopings x, and derive the gap anisotropy from the leading superconducting instability. In the transition regime from collinear magnetism to ‐wave, where strong correlations are present, we employ FRG to identify a non‐monotonous change of the gap anisotropy in qualitative agreement with new experimental findings. From the WRG, which is asymptotically exact in the weak coupling limit, we find an ‐wave to d‐wave transition as a function of hole doping, complementing previous findings from FRG [Thomale et al., Phys. Rev. Lett. 107, 117001 (2011)]. The gap anisotropy of the ‐wave monotonously increases towards the transition to d‐wave as a function of x.

Charge and spin quantum fluctuations in the doped strongly coupled Hubbard model on the honeycomb lattice

Field-theoretic methods are used to investigate the large-$U$ Hubbard model on the honeycomb lattice at half-filling and in the hole-doped regime. Within the framework of a functional-integral approach, we obtain the Lagrangian density associated with the charge and spin degrees of freedom. The Hamiltonian related to the charge degrees of freedom is exactly diagonalized. In the strong-coupling regime, we derive a perturbative low-energy theory suitable to describe the quantum antiferromagnetic phase (AF) as a function of hole doping. At half-filling, we deal with the underlying spin degrees of freedom of the quantum AF Heisenberg model by employing a second-order spin-wave analysis, in which case we have calculated the ground-state energy and the staggered magnetization; the results are in very good agreement with previous studies. Further, in the continuum, we derive a nonlinear $\ensuremath{\sigma}$ model with a topological Hopf term that describes the AF-VBS (valence bond solid) competition. Lastly, in the challenging doped regime, our approach allows the derivation of a $t\text{\ensuremath{-}}J$ Hamiltonian, and the analysis of the role played by charge and spin quantum fluctuations on the ground-state energy and, particularly, on the breakdown of the AF order at a critical hole doping; the results are benchmarked against recent Grassmann tensor product state simulations.

Stabilization of antiferromagnetic phase under hydrostatic pressure in layered perovskite cobaltites Nd1-xCaxBaCo2O5.5 (x = 0–0.06)

Magnetic measurements have been performed under pressure of 0–9.7 kbar and in the temperature range of 5–300 K for the hole-doped Nd1-xCaxBaCo2O5.5 system over the composition range x = 0–0.06, where a strong competition between antiferromagnetic and ferrimagnetic phases is present. The dependence of TN, i.e., of the temperature of a first order phase transition from the antiferromagnetic to the ferrimagnetic state, and of TC, i.e., of the temperature of the second order phase transition from the ferrimagnetic to the paramagnetic state on hydrostatic pressure was found to be a function of hole doping. The large pressure-induced increase of TN becomes enhanced with increasing of the hole doping level, while a small pressure-induced increase of TC is suppressed by increasing the hole doping level. This finding shows that the hydrostatic pressure stabilizes the antiferromagnetic phase, whereas the hole doping alone suppresses the antiferromagnetic phase. All investigated compounds have revealed the existence of a certain fraction of ferrimagnetic phase at temperatures much below TN. An increase of a magnetization observed in high magnetic field of 50 kOe at temperatures much below TN was explained as the high-field induced polarization of Nd3+ magnetic moments, appearing in the magnetic field exceeding the strength of Nd-Co antiferromagnetic exchange interactions.

Vortex lattice melting andHc2in underdoped YBa2Cu3Oy

Vortices in a type-II superconductor form a lattice structure that melts when the thermal displacement of the vortices is an appreciable fraction of the distance between vortices. In an anisotropic high-Tc superconductor, such as YBa2Cu3Oy, the magnetic field value where this melting occurs can be much lower than the mean-field critical field Hc2. We examine this melting transition in YBa2Cu3Oy with oxygen content y from 6.45 to 6.92, and fit the data to a theory of vortex-lattice melting. The quality of the fits indicates that the transition to a resistive state is indeed the vortex lattice melting transition, with the shape of the melting curves being consistent with the known change in penetration depth anisotropy from underdoped to optimally doped YBa2Cu3Oy. From the fits we extract Hc2(T = 0) as a function of hole doping. The unusual doping dependence of Hc2(T =0) points to some form of electronic order competing with superconductivity around 0.12 hole doping.

GINZBURG–LANDAU LIKE THEORY OF HIGH TEMPERATURE SUPERCONDUCTIVITY IN THE CUPRATES: EMERGENT d-WAVE ORDER

High temperature superconductivity in the cuprates remains one of the most widely investigated, constantly surprising and poorly understood phenomena in physics. Here, we describe briefly a new phenomenological theory inspired by the celebrated description of superconductivity due to Ginzburg and Landau and believed to describe its essence. This posits a free energy functional for the superconductor in terms of a complex order parameter characterizing it. We propose that there is, for superconducting cuprates, a similar functional of the complex, in plane, nearest neighbor spin singlet bond (or Cooper) pair amplitude ψij. Further, we suggest that a crucial part of it is a (short range) positive interaction between nearest neighbor bond pairs, of strength J′. Such an interaction leads to nonzero long wavelength phase stiffness or superconductive long range order, with the observed d-wave symmetry, below a temperature Tc~z J′ where z is the number of nearest neighbors; d-wave superconductivity is thus an emergent, collective consequence. Using the functional, we calculate a large range of properties, e.g., the pseudogap transition temperature T* as a function of hole doping x, the transition curve Tc(x), the superfluid stiffness ρs(x, T), the specific heat (without and with a magnetic field) due to the fluctuating pair degrees of freedom and the zero temperature vortex structure. We find remarkable agreement with experiment. We also calculate the self-energy of electrons hopping on the square cuprate lattice and coupled to electrons of nearly opposite momenta via inevitable long wavelength Cooper pair fluctuations formed of these electrons. The ensuing results for electron spectral density are successfully compared with recent experimental results for angle resolved photo emission spectroscopy (ARPES), and comprehensively explain strange features such as temperature dependent Fermi arcs above Tc and the "bending" of the superconducting gap below Tc.

Hole spectral functions in lightly doped quantum antiferromagnets

We study the hole and magnon spectral functions as a function of hole doping in the two-dimensional (2D) t-J and t-t'-t"-J models working within the limits of the spin-wave theory, by linearizing the hole-spin-deviation interaction and by adapting the non-crossing approximation (NCA). We find that the staggered magnetization decreases rather rapidly with doping and it goes to zero at a few percent of hole concentration in both t-J and the t-t'-t"-J model. We find that with doping, the residue of the quasiparticle peak at G=(pi/2,pi/2) decreases rapidly with doping and the spectral function is in agreement with high resolution angle-resolved photo-emission spectroscopy (ARPES) studies of the copper-oxide superconductors. The observed large shift of the chemical potential inside the Mott gap is found to be a result of broadening of the quasiparticle peak. We find pockets centered at G, similar to those observed by quantum oscillation measurements, (i) with an elliptical shape with large eccentricity along the anti-nodal direction in the case of the t-J model, and (ii) with an almost circular shape in the case of the t-t'-t"-J model. We also find that the spectral intensity distribution in the doped antiferromagnet has a waterfall-like patten along the nodal direction of the Brillouin zone, a feature that is also seen in ARPES measurements.

Oxygen Isotope Effect in Cuprates Results from Polaron-induced Superconductivity

The planar oxygen isotope effect coefficient measured as a function of hole doping in the Pr- and La-doped YBa2Cu3O7 (YBCO) and the Ni-doped La1.85Sr0.15CuO4 (LSCO) superconductors quantitatively and qualitatively follows the form originally proposed by Kresin and Wolf [Phys. Rev. B 49, 3652 (1994)], which was derived for polarons perpendicular to the superconducting planes. Interestingly, the inverse oxygen isotope effect coefficient at the pseudogap temperature also obeys the same formula. These findings allow the conclusion that the superconductivity in YBCO and LSCO results from polarons or rather bipolarons in the CuO2 plane. The original formula, proposed for the perpendicular direction only, is obviously more generally valid and accounts for the superconductivity in the CuO2 planes.

New superconductivity induced by d-density wave in high-temperature superconductors

We present a self-consistent theory of the interplay between the d-density wave (DDW) and superconductivity on the basis of the fluctuation-exchange (FLEX) approximation for the two-dimensional (2D) Hubbard model with the nearest-neighbor hopping t and on-site Coulomb repulsion U. In order to stabilize the DDW state with respect to phase separation at lower dopings a small nearest-neighbor Coulomb repulsion V is included within the Hartree–Fock approximation. The competition between the DDW and superconductivity can generically result in the appearance of a new superconducting state, which has the π-pairing order parameter. We solve the gap equations for competing DDW, BCS, and π-pairing order parameters with d-wave symmetry, together with calculating the FLEX interaction self-consistently, and calculating the corresponding three transition temperatures T ⁎, T c , and T c ⁎ as a function of hole doping. The calculated phase diagram has a quantum critical point (QCP) separating a pure BCS superconducting state at large dopings δ> δ 0 from a coexisting DDW and π-pairing state at lower dopings δ< δ 0. Remarkable is the much higher value of the T c ⁎ for the π-pairing superconductivity as compared with the pure BCS superconductivity.

Coexistence of magnetism and superconductivity in at−Jbilayer

We investigate coexistence of antiferromagnetic and superconducting correlations in bilayered materials using a two-dimensional $t\text{\ensuremath{-}}J$ model with couplings across the layers using variational Monte Carlo calculations. It is found that the underdoped regime supports a coexisting phase, beyond which the ($d$-wave) superconducting state becomes stable. Further, the effects of interplanar coupling parameters on the magnetic and superconducting correlations as a function of hole doping are studied in detail. The magnetic correlations are found to diminish with increasing interplanar hopping away from half filling, while the exchange across the layers strengthens interplanar antiferromagnetic correlations both at and away from half filling. The superconducting correlations show more interesting features where larger interplanar hopping considerably reduces planar correlations at optimal doping, while an opposite behavior, i.e., stabilization of the superconducting state, is realized in the overdoped regime, with the interplanar exchange all the while playing a dormant role.

Diamagnetism of doped two-leg ladders and probing the nature of their commensurate phases

We study the magnetic orbital effect of a doped two-leg ladder in the presence of a magnetic field component perpendicular to the ladder plane. Combining both low-energy approach (bosonization) and numerical simulations (density-matrix renormalization group) on the strong coupling limit ($t\text{\ensuremath{-}}J$ model), a rich phase diagram is established as a function of hole doping and magnetic flux. Above a critical flux, the spin gap is destroyed and a Luttinger liquid phase is stabilized. Above a second critical flux, a reentrance of the spin gap at high magnetic flux is found. Interestingly, the phase transitions are associated with a change of sign of the orbital susceptibility. Focusing on the small magnetic field regime, the spin-gapped superconducting phase is robust, but immediately acquires algebraic transverse (i.e., along rungs) current correlations which are commensurate with the $4{k}_{F}$ density correlations. In addition, we have computed the zero-field orbital susceptibility for a large range of doping and interaction ratio $J∕t$: we found strong anomalies at low $J∕t$ only in the vicinity of the commensurate fillings corresponding to $\ensuremath{\delta}=1∕4$ and $1∕2$. Furthermore, the behavior of the orbital susceptibility reveals that the nature of these insulating phases is different: while for $\ensuremath{\delta}=1∕4$ a $4{k}_{F}$ charge density wave is confirmed, the $\ensuremath{\delta}=1∕2$ phase is shown to be a bond order wave.

DopedAB2Hubbard chain: Spiral, Nagaoka and resonating-valence-bond states, phase separation, and Luttinger-liquid behavior

We present an extensive numerical study of the Hubbard model on the doped $A{B}_{2}$ chain, both in the weak coupling and the infinite-$U$ limit. Due to the special unit-cell topology, this system displays a rich variety of phases as a function of hole doping $(\ensuremath{\delta})$ away from half-filling. Near half-filling spiral states develop in the weak-coupling regime, while Nagaoka itinerant ferromagnetism is observed in the infinite-$U$ limit. For higher doping, the system phase-separates before reaching a Mott insulating phase of short-range resonating-valence-bond states at $\ensuremath{\delta}=1∕3$. Moreover, for $\ensuremath{\delta}&gt;1∕3$ we observe a crossover, which anticipates the Luttinger-liquid behavior for $\ensuremath{\delta}&gt;2∕3$.

Doping properties of the two-orbital model in manganites

We study the two-orbital model as a function of hole doping in single-layered manganites in the ferromagnetic phase. Numerical results are presented which are appropriate for the large bandwidth La 1 - x Sr x MnO 3 compound. We calculate the hopping integrals exactly using a mean-field scheme which incorporates the proper geometrical factors, effective nuclear charges and lattice parameters. For suitable values of the Hund's rule coupling the spin derived e g bands are found to be partially polarized for small doping levels, indicating that these compounds are not half-metallic, in total accordance with recent spin polarization experiments in single crystals.

Electronic Structure of Strongly Correlatedd-Wave Superconductors

We study the electronic structure of a strongly correlated d-wave superconducting state. Combining a renormalized mean field theory with direct calculation of matrix elements, we obtain explicit analytical results for the nodal Fermi velocity upsilon(F), the Fermi wave vector k(F), and the momentum distribution n(k) as a function of hole doping in a Gutzwiller projected d-wave superconductor. We calculate the energy dispersion E(k) and spectral weight of the Gutzwiller-Bogoliubov quasiparticles and find that the spectral weight associated with the quasiparticle excitation at the antinodal point shows a nonmonotonic behavior as a function of doping. Results are compared to angle resolved photoemission spectroscopy of the high-temperature superconductors.

Investigation of activated transport in hole doped rare earth manganites in the high temperature paramagnetic regime

Electronic transport in the high temperature paramagnetic regime of the colossal magnetoresistive oxides, La 1− x A x MnO 3, A=Ca, Sr, Ba, x≃0.1–0.3, has been investigated using resistivity measurements. The main motivation for this work is to relook into the actual magnitude of the activation energy for transport in a number of manganites and study its variation as a function of hole doping ( x), average A-site cation radius (〈 r A〉), cationic disorder ( σ 2) and strain ( ε zz ). We show that contrary to current practice, the description of a single activation energy in this phase is not entirely accurate. Our results clearly reveal a strong dependence of the activation energy on the hole doping as well as disorder. Comparing the results across different substituent species with different 〈 r A〉 reveals the importance of σ 2 as a metric to qualify any analysis based on 〈 r A〉.

Isospin model for suppression of charge order in hole-doped NaV 2O 5

The layered perovskite compound NaV 2O 5 exhibits charge ordering (CO) and spin-gap formation which is driven by inter-site Coulomb forces and exchange dimerisation. Experimentally it was found that charge ordering is rapidly suppressed by doping. CO in NaV 2O 5 has a quasi-1D character due to inter-ladder frustration in the Trellis lattice. Based on an extended isospin ( T=1) approach for hole-doped NaV 2O 5 ladders we construct an Ising-like model that explains qualitatively the destruction of the CO phase as function of hole doping δ and show how the CO parameter depends on δ and the ratio of Coulomb and hopping energies.

Phase separation and stripes in a boson version of a doped quantum antiferromagnet

A theoretical investigation of boson versions of the $t\ensuremath{-}J$ and $t\ensuremath{-}{J}_{z}$ models on the square lattice is carried out, by means of Green's function Monte Carlo simulations. Accurate ground-state energy estimates as a function of hole doping are obtained, allowing one to investigate the stability of the uniform phase against separation of the system into hole-rich and hole-free phases. In the boson $t\ensuremath{-}{J}_{z}$ model, such a separation is found to occur for arbitrarily small values of ${J}_{z},$ at sufficiently low hole doping. Phase separation is suppressed in the boson $t\ensuremath{-}J$ model, which features a uniform ground state at any doping, for $J/t\ensuremath{\lesssim}1.5.$ Relevance of this study to the corresponding fermion models is discussed. Fermi statistics enhances the tendency toward phase separation; in particular, phase separation at low doping is predicted in the fermion $t\ensuremath{-}{J}_{z}$ model at any ${J}_{z}&gt;0.$ The possible formation of stripes of holes is investigated for systems featuring both periodic and cylindrical boundary conditions. No evidence of a striped ground state is found in either the $t\ensuremath{-}J$ or $t\ensuremath{-}{J}_{z}$ boson models.

Magnetic coupling in the insulating and metallic ferromagneticLa1−xCaxMnO3

Low-energy spin excitations play an essential role in determining the characteristics of the phase transitions in the colossal magnetoresistant manganese-oxides (manganites). Inelastic neutron scattering has been utilized to study the spin excitations of the ferromagnetic (FM) ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{MnO}}_{3}$ (LCMO) as a function of hole doping x (0.2, 0.25, and 0.30) and temperature, above and below the Curie temperature ${T}_{C}.$ While the spin-diffusion coefficients $\ensuremath{\Lambda}(T)$ and ${T}_{C}$'s increase smoothly with doping concentration x, the spin-stiffness constant $D(T)$ for the insulating LCMO is 3 times smaller than that of the metallic LCMO. Furthermore, the paramagnetic-to-ferromagnetic phase transitions in LCMO manganites investigated have nonvanishing extrapolated values of $D(T)$ as $\stackrel{\ensuremath{\rightarrow}}{T}{T}_{C}$ and nondiverging spin-correlation lengths at ${T}_{C}.$ These results present a serious challenge to the understanding of these materials using models such as Heisenberg ferromagnetism, double exchange, or modified double exchange.