Finite Doping Research Articles

Mottness at finite doping and charge-instabilities in cuprates.

The influence of the Mott physics on the doping-temperature phase diagram of copper oxides represents a major issue that is subject of intense theoretical and experimental effort. Here, we investigate the ultrafast electron dynamics in prototypical single-layer Bi-based cuprates at the energy scale of the O-2p→Cu-3d charge-transfer (CT) process. We demonstrate a clear evolution of the CT excitations from incoherent and localized, as in a Mott insulator, to coherent and delocalized, as in a conventional metal. This reorganization of the high-energy degrees of freedom occurs at the critical doping pcr ≈0.16 irrespective of the temperature, and it can be well described by dynamical mean field theory calculations. We argue that the onset of the low-temperature charge instabilities is the low-energy manifestation of the underlying Mottness that characterizes the p < pcr region of the phase diagram. This discovery sets a new framework for theories of charge order and low-temperature phases in underdoped copper oxides.

Hyperbolic Cooling of a Graphene on BN Transistor in the Zener-Klein Regime

Engineering of cooling mechanisms is a bottleneck in nanoelectronics. Whereas thermal exchanges in diffusive graphene are driven by defect-assisted supercollisions [1], the case of high-mobility graphene on hBN is radically different with a prominent contribution of remote phonons from the substrate. Here, we show that a bilayer graphene on hBN transistor can be driven in the Zener-Klein (ZK) tunnelling regime where current is fully saturated. Using sensitive GHz noise thermometry [2], we show that ZK-tunnelling triggers a new cooling pathway due to the emission of hyperbolic phonons polaritons (HPPs) in hBN by out-of-equilibrium electron-hole pairs (Figure 1). The most striking consequence is a reversal of the doping dependence of the electronic temperature due to the Pauli blocking of ZK-tunnelling at finite doping. HPP cooling is the most efficient mechanism in graphene and promotes graphene Zener-Klein transistors as a valuable route for RF power amplification. A. Betz et al., Nat. Phys., 9 (2013) 109 W. Yang et al., submitted (2016) Figure 1

Nonlinear optical conductivity of a generic two-band system with application to doped and gapped graphene

We present a general formulation to calculate the dynamic optical conductivity, beyond the linear response regime, of any electronic system whose quasiparticle dispersion is described by a two band model. Our phenomenological model is based on the optical Bloch equations. In the steady state regime it yields an analytic solution for the population inversion and the interband coherence, which are nonlinear in the optical field intensity, including finite doping and temperature effects. We explicitly show that the optical nonlinearities are controlled by a single dimensionless parameter which is directly proportional to the incident field strength and inversely proportional to the optical frequency. This identification leads to a unified way to study the dynamical conductivity and the differential transmission spectrum across a wide range of optical frequencies, and optical field strength. We use our formalism to analytically calculate the nonlinear optical conductivity of doped and gapped graphene, deriving the well known universal ac conductivity of $\sigma_0={e^2}/4\hbar$ in the linear response regime of low optical intensities (or equivalently high frequencies) and non-linear deviations from it which appear at high laser intensities (or low frequencies) including the impact of finite doping and band-gap opening.

Breakdown of the Nagaoka phase at finite doping

The Nagaoka ($U=\infty$) limit of the Hubbard model on a square lattice is mapped onto the itinerant-localized Kondo model at infinitely strong coupling. Such a model is well suited to perform quantum Monte Carlo (QMC) simulations to compute spin correlation functions. This model is shown to exhibit no short-range ferromagnetic (FM) spin correlations at any doping $\delta\ge 0.01$ and finite temperature, $T=0.1t$. Our simulations give no indication that there is a tendency towards ferromagnetic ordering in the ground state.

Formula omitted] nonlinear sigma model vs strong electron correlations

The nonlinear sigma model targeted on the coset supermanifold CP1|1=SU(2|1)/U(1|1) is derived in an attempt to describe the quasiclassical low-energy effective action for the doped t−J model at the SUSY point, J=2t. In spite of the fact that the supermanifold CP1|1 indeed appears as the phase space of the strongly correlated electrons, the canonical CP1|1 nonlinear sigma model (NLSM) is unable to capture the physics of strong correlations displayed by the SUSY t−J model at any finite doping. This is due to the fact that, in this regime, the doping itself cannot be self-consistently incorporated into the CP1|1 NLSM.

Competition between Kondo effect and RKKY physics in graphene magnetism

The cooperative behavior of quantum impurities on 2D materials, such as graphene and bilayer graphene, is characterized by a non-trivial competition between screening (Kondo effect), and Ruderman-Kittel-Kasuya-Yosida (RKKY) magnetism. In addition, due to the small density of states at the Fermi level, impurities may not couple to the conduction electrons at all, behaving as free moments. Employing a recently developed {\em{exact}} numerical method to study multi-impurity lattice systems, we obtain non-perturbative results that dramatically depart from expectations based on the conventional RKKY theory. At half-filling and for weak coupling, impurities remain in the local moment regime when they are on opposite sublattices, up to a critical value of the interactions when they start coupling anti-ferromagnetically with correlations that decay very slowly with inter-impurity distance. At finite doping, away from half-filling, ferromagnetism is completely absent and the physics is dominated by a competition between anti-ferromagnetism and Kondo effect. In bilayer graphene, impurities on opposite layers behave as free moments, unless the interaction is of the order of the hopping or larger.

Synthesis of Biomass-Derived Mesoporous Carbon with Super Adsorption Performance by an Aqueous Cooperative Assemble Route

Exploring the suitable precursors that interact with the surfactant via hydrogen bonding is an important task for the green synthesis of mesoporous carbons (MCs). Boron-doped mesoporous carbon and its derived super adsorbent are synthesized by a reproducible and low-cost hydrothermal method. β-Cyclodextrins and boric acid were employed as the environmentally friendly carbon precursor and dopant, respectively, which give the mesoporous carbon a certain doping amount and super capture ability. This method not only permits the biomass-derived compounds to participate the self-assembly process but also reduces the potential industrial-scale production cost and avoids the employment of hazardous substances. Textural properties, mesostructured morphology, X-ray photoelectron spectroscopic and surface functional groups of products are characterized to describe synthetic mechanism. The obtained B-doped MCs show a developed mesostructure, a finite boron doping (around 2 wt %) and a high specific surface area (∼648...

Direct evidence of M2 phase during the monoclinic-tetragonal (rutile) phase transition of W-doped VO2 nanowires

Identifying different phases of VO2 during the metal−insulator phase transition is critical for device application due to the difference of electrical, mechanical and magnetic properties of phases. However, most studies so far were carried out using microprobe analyses, which lack the spatial resolution needed to identify nanoscale phases and changes. Taking advantage of in situ low temperature aberration-corrected scanning transmission electron microscopy, we observed the existence of M2 phase alongside M1 and R phase in the W-doped nanowires close to transition temperature. The localized stress caused by adding W in the structure results in the stabilization of nanosize grains of M2 phase in structure along with M1 and R phases. The observation of the metastable M2 phase even for unclamped nanowires suggests the possibility of finely modulating the phase diagram of VO2 through a combination of finite size and doping.

Spontaneous particle-hole symmetry breaking of correlated fermions on the Lieb lattice

We study spinless fermions with nearest-neighbor repulsive interactions ($t$-$V$ model) on the two-dimensional three-band Lieb lattice. At half-filling, the free electronic band structure consists of a flat band at zero energy and a single cone with linear dispersion. The flat band is expected to be unstable upon inclusion of electronic correlations, and a natural channel is charge order. However, due to the three-orbital unit cell, commensurate charge order implies an imbalance of electron and hole densities and therefore doping away from half-filling. Our numerical results show that below a finite-temperature Ising transition a charge density wave with one electron and two holes per unit cell and its partner under particle-hole transformation are spontaneously generated. Our calculations are based on recent advances in auxiliary-field and continuous-time quantum Monte Carlo simulations that allow sign-free simulations of spinless fermions at half-filling. It is argued that particle-hole symmetry breaking provides a route to access levels of finite doping, without introducing a sign problem.

Growth of arsenic doped ZnO films using a finite surface doping source by metal organic chemical vapor deposition

Arsenic doped ZnO films are prepared using a pre-deposited GaAs finite surface source on sapphire substrates by a MOCVD method. Their conductivity and optical properties are closely related to the annealing process. The as-grown ZnO film shows n-type conductivity with weak FA emission. The in situ annealed sample shows p-type conductivity. The AsZn–2VZn acceptor level is confirmed by low-temperature photoluminescence measurement. The post annealed ZnO film appears to be n-type, which is attributed to the arsenic surface enrichment and the compensation of introduced donor like defects. Our method could be widely used in fabricating arsenic doped p-type ZnO related photoelectric devices.

Charge dynamics of the antiferromagnetically ordered Mott insulator

We introduce a slave-fermion formulation in which to study the charge dynamics of the half-filled Hubbard model on the square lattice. In this description, the charge degrees of freedom are represented by fermionic holons and doublons and the Mott-insulating characteristics of the ground state are the consequence of holon–doublon bound-state formation. The bosonic spin degrees of freedom are described by the antiferromagnetic Heisenberg model, yielding long-ranged (Néel) magnetic order at zero temperature. Within this framework and in the self-consistent Born approximation, we perform systematic calculations of the average double occupancy, the electronic density of states, the spectral function and the optical conductivity. Qualitatively, our method reproduces the lower and upper Hubbard bands, the spectral-weight transfer into a coherent quasiparticle band at their lower edges and the renormalisation of the Mott gap, which is associated with holon–doublon binding, due to the interactions of both quasiparticle species with the magnons. The zeros of the Green function at the chemical potential give the Luttinger volume, the poles of the self-energy reflect the underlying quasiparticle dispersion with a spin-renormalised hopping parameter and the optical gap is directly related to the Mott gap. Quantitatively, the square-lattice Hubbard model is one of the best-characterised problems in correlated condensed matter and many numerical calculations, all with different strengths and weaknesses, exist with which to benchmark our approach. From the semi-quantitative accuracy of our results for all but the weakest interaction strengths, we conclude that a self-consistent treatment of the spin-fluctuation effects on the charge degrees of freedom captures all the essential physics of the antiferromagnetic Mott–Hubbard insulator. We remark in addition that an analytical approximation with these properties serves a vital function in developing a full understanding of the fundamental physics of the Mott state, both in the antiferromagnetic insulator and at finite temperatures and dopings.

Erratum: Optical and transport properties in three-dimensional Dirac and Weyl semimetals [Phys. Rev. B93, 085426 (2016)

Within a Kubo formalism, we study dc transport and ac optical properties of 3D Dirac and Weyl semimetals. Emphasis is placed on the approach to charge neutrality and on the differences between Dirac and Weyl materials. At charge neutrality, the zero-temperature limit of the dc conductivity is not universal and also depends on the residual scattering model employed. However, the Lorenz number L retains its usual value L_0. With increasing temperature, the Wiedemann-Franz law is violated. At high temperatures, L exhibits a new plateau at a value dependent on the details of the scattering rate. Such details can also appear in the optical conductivity, both in the Drude response and interband background. In the clean limit, the interband background is linear in photon energy and always extrapolates to the origin. This background can be shifted to the right through the introduction of a massless gap. In this case, the extrapolation can cut the axis at a finite photon energy as is observed in some experiments. It is also of interest to differentiate between the two types of Weyl semimetals: those with broken time-reversal symmetry and those with broken spatial-inversion symmetry. We show that, while the former will follow the same behaviour as the 3D Dirac semimetals, for the zero magnetic field properties discussed here, the latter type will show a double step in the optical conductivity at finite doping and a single absorption edge at charge neutrality. The Drude conductivity is always finite in this case, even at charge neutrality.

Pseudogap and superconductivity in two-dimensional doped charge-transfer insulators

High-temperature superconductivity emerges in the CuO$_2$ plane upon doping a Mott insulator. To ascertain the influence of Mott physics plus short-range correlations, we solve a three-band copper-oxide model in the charge-transfer regime using cellular dynamical mean-field theory with continuous-time quantum Monte Carlo as an impurity solver. We report the normal and superconducting phase diagram of this model as a function of doping, interaction strength and temperature. Upon hole doping of the charge-transfer insulator, the phase boundary between pseudogap and correlated metal consists of a first-order transition line at finite doping ending at a critical point, as in the one-band model. Beyond the endpoint, the phase boundary continues as a Widom crossover line, across which thermodynamic quantities peak. This phase boundary determines changes in the pairing mechanism and is an emergent phenomenon characteristic of doped Mott insulators, independent of many microscopic details. Broader implications are discussed.

Inelastic vibrational signals in electron transport across graphene nanoconstrictions

We present calculations of the inelastic vibrational signals in the electrical current through a graphene nanoconstriction. We find that the inelastic signals are only present when the Fermi-level position is tuned to electron transmission resonances, thus, providing a fingerprint which can link an electron transmission resonance to originate from the nanoconstriction. The calculations are based on a novel first-principles method which includes the phonon broadening due to coupling with phonons in the electrodes. We find that the signals are modified due to the strong coupling to the electrodes, however, still remain as robust fingerprints of the vibrations in the nanoconstriction. We investigate the effect of including the full self-consistent potential drop due to finite bias and gate doping on the calculations and find this to be of minor importance.

Impurity effects on electrical conductivity of doped bilayer graphene in the presence of a bias voltage

We address the electrical conductivity of bilayer graphene as a function of temperature, impurity concentration, and scattering strength in the presence of a finite bias voltage at finite doping, beginning with a description of the tight-binding model using the linear response theory and Green’s function approach. Our results show a linear behavior at high doping for the case of high bias voltage. The effects of electron doping on the electrical conductivity have been studied via changing the electronic chemical potential. We also discuss and analyze how the bias voltage affects the temperature behavior of the electrical conductivity. Finally, we study the behavior of the electrical conductivity as a function of the impurity concentration and scattering strength for different bias voltages and chemical potentials respectively. The electrical conductivity is found to be monotonically decreasing with impurity scattering strength due to the increased scattering among electrons at higher impurity scattering strength.

Optical and transport properties in three-dimensional Dirac and Weyl semimetals

Within a Kubo formalism, we study dc transport and ac optical properties of 3D Dirac and Weyl semimetals. Emphasis is placed on the approach to charge neutrality and on the differences between Dirac and Weyl materials. At charge neutrality, the zero-temperature limit of the dc conductivity is not universal and also depends on the residual scattering model employed. However, the Lorenz number $L$ retains its usual value ${L}_{0}$. With increasing temperature, the Wiedemann-Franz law is violated. At high temperatures, $L$ exhibits a new plateau at a value dependent on the details of the scattering rate. Such details can also appear in the optical conductivity, both in the Drude response and interband background. In the clean limit, the interband background is linear in photon energy and always extrapolates to the origin. This background can be shifted to the right through the introduction of a massless gap. In this case, the extrapolation can cut the axis at a finite photon energy as is observed in some experiments. It is also of interest to differentiate between the two types of Weyl semimetals: those with broken time-reversal symmetry and those with broken spatial-inversion symmetry. We show that, while the former will follow the same behavior as the 3D Dirac semimetals, for the zero magnetic field properties discussed here, the latter type will show a double step in the optical conductivity at finite doping and a single absorption edge at charge neutrality. The Drude conductivity is always finite in this case, even at charge neutrality.

Pauli limiting and metastability regions of superconducting graphene and intercalated graphite superconductors

We present a study of metastability regions in the in-plane magnetic field versus temperature phase diagram of graphene and intercalated graphite superconductors. Due to the vanishing density of states, undoped graphene requires a finite BCS interaction ${V}_{c}$ to become superconducting (any finite doping drives this critical value to zero). Above ${V}_{c}$, superconducting graphene under in-plane magnetic field displays the conventional low temperature first-order transition (FOT) to the normal phase, but the width of the associated metastability region (normalized to the zero-temperature critical field) vanishes when doping goes to zero and the interaction approaches ${V}_{c}$. In the case of intercalated graphite superconductors, modeled as two-dimensional two-band superconductors (a graphene-like band and a metallic interlayer band), a critical graphene intraband interaction is required for the appearance of a second metastability region in the superconducting region of the phase diagram. The width of this metastability region also goes to zero as the graphene intraband interaction approaches, from above, its critical value and the metastability region vanishes at the zero-temperature supercooling field associated with the metallic interlayer band. Slightly above this critical value, the low-temperature FOT line bifurcates at an intermediate temperature into a FOT line and a second-order transition line.

Phonon enhancement of electronic order and negative isotope effect in the Hubbard-Holstein model on a square lattice

Looking for superconductors with higher transition temperature requires a guiding principle. In conventional superconductors, electrons pair up into Cooper pairs via the retarded attraction mediated by electron-phonon coupling. Higher-frequency phonon (or smaller atomic mass) leads to higher superconducting transition temperature, known as the isotope effect. Furthermore, superconductivity is the only instability channel of the metallic normal state. In correlated systems, the above simple scenario could be easily violated. The strong local interaction is poorly screened, and this conspires with a featured Fermi surface to promote various competing electronic orders, such as spin-density-wave, charge-density-wave and unconventional superconductivity. On top of the various phases, the effect of electron-phonon coupling is an intriguing issue. Using the functional renormalization group, here we investigated the interplay between the electron correlation and electron-phonon coupling in a prototype Hubbard-Holstein model on a square lattice. At half-filling, we found spin-density-wave and charge-density-wave phases and the transition between them, while no superconducting phase arises. Upon finite doping, d-wave/s-wave superconductivity emerges in proximity to spin-density-wave/charge-density-wave phases. Surprisingly, lower-frequency Holstein-phonons are either less destructive, or even beneficial, to the various phases, resulting in a negative isotope effect. We discuss the underlying mechanism behind and the implications of such anomalous effects.

Spin-orbit coupling and proximity effects in metallic carbon nanotubes

We study spin-orbit coupling in metallic carbon nanotubes (CNTs) within the many-body Tomonaga-Luttinger liquid (TLL) framework. For a well defined sub-class of metallic CNTs, that contains both achiral zig-zag as well as a sub-set of chiral tubes, an effective low energy field theory description is derived. We aim to describe system at finite dopings, but close to the charge neutrality point (commensurability). A new regime is identified where spin-orbit coupling leads to an inverted hierarchy of mini-gaps of bosonic modes. We then add a proximity coupling to a superconducting (SC) substrate and show that the only order parameter that is supported within the novel, spin-orbit induced phase is a topologically trivial s-SC.

Quasiparticle properties of the nonlinear Holstein model at finite doping and temperature

We use determinant quantum Monte Carlo to study the single particle properties of quasiparticles and phonons in a variant of the two-dimensional Holstein model that includes an additional non-linear electron-phonon (e-ph) interaction. We find that a small positive non-linear interaction reduces the effective coupling between the electrons and the lattice, suppresses charge-density wave (CDW) correlations, and hardens the effective phonon frequency. Conversely, a small negative non-linear interaction can enhance the e-ph coupling resulting in heavier quasiparticles, an increased tendency towards a CDW phase at all fillings, and a softened phonon frequency. An effective linear model with a renormalized interaction strength and phonon frequency can qualitatively capture this physics; however, the quantitative effects of the non-linearity on both the electronic and phononic degrees of freedom cannot be captured by such a model. These results are significant for typical non-linear coupling strengths found in real materials, indicating that non-linearity can have a significant influence on the physics of many e-ph coupled systems.