arXiv subjects

J. P. Carbotte

Publications and source records attributed to J. P. Carbotte.

At least 109 records · Page 6Linked to original sources

arXiv2007

Role of magnetism and electron-lattice interactions in STM spectra of cuprates

The study of bosonic modes that couple to the charge carriers is a key element in understanding superconductivity. Lee et al. have used atomic-resolution scanning tunneling spectroscopy (STM) in an attempt to extract the spectrum of of these modes in the high temperature superconductor Bi2Sr2CaCu2O8+d and they found a mode whose frequency did not depend on doping but changed on 16O to 18O isotopic substitution leading them to suggest a role for lattice modes (phonons). A careful examination of their published data reveals a weaker but distinct feature that has all the characteristics of the magnetic excitation identified as the bosonic mode in other competing experiments. We suggest the lattice mode seen by Lee et al. is not relevant to superconductivity and is due to inelastic tunneling through the insulating oxide layer.

cond-mat.supr-con↗

arXiv2007

Magneto-optical conductivity in Graphene

Landau level quantization in graphene reflects the Dirac nature of its quasiparticles and has been found to exhibit an unusual integer quantum Hall effect. In particular the lowest Landau level can be thought as shared equally by electrons and holes and this leads to characteristic behaviour of the magneto-optical conductivity as a function of frequency $Ω$ for various values of the chemical potential $μ$. Particular attention is paid to the optical spectral weight under various absorption peaks and its redistribution as $μ$ is varied. We also provide results for magnetic field $B$ as well as chemical potential sweeps at selected fixed frequencies which can be particularly useful for possible measurements in graphene. Both diagonal and Hall conductivity are considered.

cond-mat.mes-hall↗

arXiv2007

Sum Rules for the Optical and Hall Conductivity in Graphene

Graphene has two atoms per unit cell with quasiparticles exhibiting the Dirac-like behavior. These properties lead to interband in addition to intraband optical transitions and modify the $f$-sum rule on the longitudinal conductivity. The expected dependence of the corresponding spectral weight on the applied gate voltage $V_g$ in a field effect graphene transistor is $\sim {const}- |V_g|^{3/2}$. For $V_g =0$, its temperature dependence is $T^3$ rather than the usual $T^2$. For the Hall conductivity, the corresponding spectral weight is determined by the Hall frequency $ω_H$ which is linear in the carrier imbalance density $ρ$, and hence proportional to $V_g$, and is different from the cyclotron frequency for Dirac quasiparticles.

cond-mat.mes-hall↗

arXiv2007

Anomalous Absorption Line in the Magneto-Optical Response of Graphene

The intensity as well as position in energy of the absorption lines in the infrared conductivity of graphene, both exhibit features that are directly related to the Dirac nature of its quasiparticles. We show that the evolution of the pattern of absorption lines as the chemical potential is varied encodes the information about the presence of the anomalous lowest Landau level. The first absorption line related to this level always appears with full intensity or is entirely missing, while all other lines disappear in two steps. We demonstrate that if a gap develops, the main absorption line splits into two provided that the chemical potential is greater than or equal to the gap.

cond-mat.str-el↗

arXiv2006

High energy scales in electronic self-energy imaged by optics

We use a new technique to directly extract an estimate of the quasiparticle self-energy from the optical conductivity which can be easily related to both theory and angle-resolved photoemission spectroscopy (ARPES) experiments. In the high Tc cuprate Bi-2212 we find evidence for a new high energy scale at 900 meV in addition to the two previously well known ones at roughly 50 and 400 meV. The intermediate scale at 400 meV has been recently seen in ARPES as a large kink which optics finds to be weaker and shifted. In YBCO, the three energy scales are shifted to lower energy relative to Bi-2212 and we observe the emergence of a possible fourth high energy feature at 600 meV.

cond-mat.supr-con↗

arXiv2006

Evolution of the Spin Susceptibility of High-$T_c$ Superconductors

We demonstrate that a new tool, a model independent numerical Eliashberg inversion of the optical self-energy, based on maximum entropy considerations can be used to extract the magnetic excitation spectra of high-transition-temperature superconductors. In Bi-2212 we explicitly show that the magnetic mode that dominates the self-energy at low temperatures directly evolves out of a smooth transfer of spectral weight to the mode from the continuum just above it. This redistribution starts already at 200 K in optimally doped materials but is much weaker in overdoped samples. This provides evidence for the magnetic origin of the superconductivity and presents a challenge to theories of the spin susceptibility and to neutron scattering experiments in high-temperature superconductors.

cond-mat.supr-con↗

arXiv2006

Optical Sum Rule in Finite Bands

In a single finite electronic band the total optical spectral weight or optical sum carries information on the interactions involved between the charge carriers as well as on their band structure. It varies with temperature as well as with impurity scattering. The single band optical sum also bears some relationship to the charge carrier kinetic energy and, thus, can potentially provide useful information, particularly on its change as the charge carriers go from normal to superconducting state. Here we review the considerable advances that have recently been made in the context of high $T_c$ oxides, both theoretical and experimental.

cond-mat.supr-con↗

arXiv2006

Inversion techniques for optical conductivity data

Optical data is encoded with information on the microscopic interaction between charge carriers. For an electron-phonon system, the Eliashberg equations apply and a Kubo formula can be used to get the infrared conductivity. The task of extracting the electron-phonon spectral density $α^2F(ω)$ from data is rather complicated and, thus, simplified but approximate expressions for the conductivity have often been used. We test the accuracy of such simplifications and also discuss the advantages and disadvantages of various numerical methods needed in the inversion process. Normal and superconducting state are considered as well as boson exchange mechanisms which might be applicable to the High-$T_c$ oxides.

cond-mat.supr-con↗

arXiv2006

Superfluid density and competing orders in d-wave superconductors

We derive expressions for the superfluid density $ρ_s$ in the low-temperature limit $T \to 0$ in d-wave superconductors, taking into account the presence of competing orders such as spin-density waves, $i d_{xy}$-pairing, etc. Recent experimental data for the thermal conductivity and for elastic neutron scattering in La$_{2-x}$Sr$_x$CuO$_4$ suggest there are magnetic field induced anomalies that can be interpreted in terms of competing orders. We consider the implications of these results for the superfluid density and show in the case of competing spin-density wave order that the usual Volovik-like $\sqrt{H}$ depletion of $ρ_s(H)$ is replaced by a slower dependence on applied magnetic field. We find that it is crucial to include the competing order parameter in the self-consistent equation for the impurity scattering rate.

cond-mat.supr-con↗

arXiv2006

Temperature Dependence of the Conductivity Sum Rule in the Normal State due to Inelastic Scattering

We examine the temperature dependence of the optical sum rule in the normal state due to interactions. To be concrete we adopt a weak coupling approach which uses an electron-boson exchange model to describe inelastic scattering of the electrons with a boson, in the Migdal approximation. While a number of recent works attribute the temperature dependence in the normal state to that which arises in a Sommerfeld expansion, we show that in a wide parameter regime this contribution can be quite small. Instead, most of the temperature dependence arises from the zeroth order term in the `expansion', through the temperature dependence of the spectral function, and the interaction parameters contained therein. For low boson frequencies this circumstance causes a linear T-dependence in the sum rule. We develop some analytical expressions and understanding of the temperature dependence.

cond-mat.str-el↗

arXiv2006

Unusual Microwave Response of Dirac Quasiparticles in Graphene

Recent experiments have proven that the quasiparticles in graphene obey a Dirac equation. Here we show that microwaves are an excellent probe of their unusual dynamics. When the chemical potential is small the intraband response can exhibit a cusp around zero frequency $Ω$ and this unusual lineshape changes to Drude-like by increasing the chemical potential $|μ|$, with width also increasing linearly with $μ$. The interband contribution at T=0 is a constant independent of $Ω$ with a lower cutoff at $2 μ$. Distinctly different behavior occurs if interaction-induced phenomena in graphene cause an opening of a gap $Δ$. At large magnetic field $B$, the diagonal and Hall conductivities at small $Ω$ become independent of $B$ but remain nonzero and show structure associated with the lowest Landau level. This occurs because in the Dirac theory the energy of this level, $E_0 = \pm Δ$, is field independent in sharp contrast to the conventional case.

cond-mat.str-el↗

arXiv2006

Impurity effects on optical response in a finite band electronic system coupled to phonons

The concepts, which have traditionally been useful in understanding the effects of the electron--phonon interaction in optical spectroscopy, are based on insights obtained within the infinite electronic band approximation and no longer apply in finite band metals. Impurity and phonon contributions to electron scattering are not additive and the apparent strength of the coupling to the phonon degrees of freedom is substantially reduced with increased elastic scattering. The optical mass renormalization changes sign with increasing frequency and the optical scattering rate never reaches its high frequency quasiparticle value which itself is also reduced below its infinite band value.

cond-mat.mtrl-sci↗

arXiv2006

Observation of phonon structure in electron density of states of normal metal

Within standard treatments of the interacting electron--phonon system the electron density of states (EDOS) shows no sign of the phonons when the system is in the normal state. On the other hand, emergence of a fine energy scale in the superconducting state makes the phonons readily observable in the EDOS and other spectroscopic quantities. Here we wish to re-examine the conditions under which phonon structure might be present in the normal state. Accounting for a finite, i.e. non-infinite, electronic bandwidth results in easily distinguishable phonon structure in the EDOS. We argue that for narrow band metals, the resolution of photoemission spectroscopy is sufficient for resolving these structures. Manifestations of finite band effects in $K_3C_{60}$ are discussed.

cond-mat.mtrl-sci↗

arXiv2006

Effect of gap suppression by superfluid current on nonlinear microwave response of d-wave superconductors

Recently several works have focused on the intrinsic nonlinear current in passive microwave filters as a tool for identifying d-wave order parameter symmetry in the high Tc cuprates. Evidence has been found for d-wave pairing in YBCO and further work has ensued. Most of the theoretical work has been limited to low temperature because it has not included the effect of the superfluid current on the energy gap. We find that this effect leads to important corrections above T~0.2Tc, while leaving the 1/T low temperature behavior intact. A twofold increase in the nonlinear coefficient at temperatures of order ~0.75 Tc is found, and as T->Tc the nonlinearity comes entirely from the effects of the superfluid current on the gap. Impurity scattering has been included and, in addition, signatures for the case of d+s-wave are presented.

cond-mat.supr-con↗

arXiv2005

Nonlinear current response of one- and two-band superconductors

We have calculated the nonlinear current of a number of single band s-wave electron-phonon superconductors. Among issues considered were those of dimensionality, strong electron-phonon coupling, impurities, and comparison with BCS. For the case of two bands, particular attention is paid to the role of anisotropy, the integration effects of the off-diagonal electron-phonon interaction, as well as inter- and intraband impurities. For the specific case of MgB2, we present results based on the known microscopic parameters of band theory.

cond-mat.supr-con↗

arXiv2005

Effects of energy dependence in the quasiparticle density of states on far-infrared absorption in the pseudogap state

We derive a relationship between the optical conductivity scattering rate 1/τ(ω) and the electron-boson spectral function α^2F(Ω) valid for the case when the electronic density of states, N(ε), cannot be taken as constant in the vicinity of the Fermi level. This relationship turned out to be useful for analyzing the experimental data in the pseudogap state of cuprate superconductors.

cond-mat.str-el↗

arXiv2005

Optical sum in Nearly Antiferromagnetic Fermi Liquid Model

We calculate the optical sum (OS) and the kinetic energy (KE) for a tight binding band in the Nearly Antiferromagnetic Fermi Liquid (NAFFL) model which has had some success in describing the electronic structure of the high $T_c$ cuprates. The interactions among electrons due to the exchange of spin fluctuations profoundly change the probability of occupation $(n_{{\bf k},σ})$ of states of momentum {\bf k} and spin $σ$ which is the central quantity in the calculations of OS and KE. Normal and superconducting states are considered as a function of temperature. Both integrals are found to depend importantly on interactions and an independent electron model is inadequate.

cond-mat.supr-con↗

arXiv2005

The a-axis optical conductivity of detwinned ortho-II YBa_2Cu_3O_6.50

The a-axis optical properties of a detwinned single crystal of YBa_2Cu_3O_6.50 in the ortho II phase (Ortho II Y123, T_c= 59 K) were determined from reflectance data over a wide frequency range (70 - 42 000 cm^-1) for nine temperature values between 28 and 295 K. Above 200 K the spectra are dominated by a broad background of scattering that extends to 1 eV. Below 200 K a shoulder in the reflectance appears and signals the onset of scattering at 400 cm^-1. In this temperature range we also observe a peak in the optical conductivity at 177 cm^-1. Below 59 K, the superconducting transition temperature, the spectra change dramatically with the appearance of the superconducting condensate. Its spectral weight is consistent, to within experimental error, with the Ferrell-Glover-Tinkham (FGT) sum rule. We also compare our data with magnetic neutron scattering on samples from the same source that show a strong resonance at 31 meV. We find that the scattering rates can be modeled as the combined effect of the neutron resonance and a bosonic background in the presence of a density of states with a pseudogap. The model shows that the decreasing amplitude of the neutron resonance with temperature is compensated for by an increasing of the bosonic background yielding a net temperature independent scattering rate at high frequencies. This is in agreement with the experiments.

cond-mat.supr-con↗