arXiv subjects

E. J. Nicol

Publications and source records attributed to E. J. Nicol.

At least 37 records · Page 2Linked to original sources

arXiv2011

Optical properties of the pseudogap state in underdoped cuprates

Recent optical measurements of deeply underdoped cuprates have revealed that a coherent Drude response persists well below the end of the superconducting dome. In addition, no large increase in optical effective mass has been observed, even at dopings as low as 1%. We show that this behavior is consistent with the resonating valence bond spin-liquid model proposed by Yang, Rice, and Zhang. In this model, the overall reduction in optical conductivity in the approach to the Mott insulating state is caused not by an increase in effective mass, but by a Gutzwiller factor, which describes decreased coherence due to correlations, and by a shrinking of the Fermi surface, which decreases the number of available charge carriers. We also show that in this model, the pseudogap does not modify the low-temperature, low-frequency behavior, though the magnitude of the conductivity is greatly reduced by the Gutzwiller factor. Similarly, the profile of the temperature dependence of the microwave conductivity is largely unchanged in shape, but the Gutzwiller factor is essential in understanding the observed difference in magnitude between ortho-I and -II YBa$_2$Cu$_3$O$_y$.

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arXiv2010

Effects of a particle-hole asymmetric pseudogap on Bogoliubov quasiparticles

We show that in the presence of a pseudogap, the spectral function in the superconducting state of the underdoped cuprates exhibits additional Bogoliubov quasiparticle peaks at both positive and negative energy which are revealed by the particle-hole asymmetry of the pseudogapped energy bands. This provides direct information on the unoccupied band via measurement of the occupied states. When sufficiently close, these Bogoliubov peaks will appear to merge with existing peaks leading to the anomalous observation, seen in experiment, that the carrier spectral density broadens with reduced temperature in the superconducting state. Using the resonating valence bond (RVB) spin liquid model in conjunction with recent angle-resolved photoemission spectroscopy (ARPES) data allows for an empirical determination of the temperature dependence of the pseudogap suggesting that it opens only very gradually below the pseudogap onset temperature $T^*$.

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arXiv2010

Specific heat across the superconducting dome in the cuprates

The specific heat of the superconducting cuprates is calculated over the entire phase diagram. A d-wave BCS approach based on the large Fermi surface of Fermi liquid and band structure theory provides a good description of the overdoped region. At underdoping it is essential to include the emergence of a second energy scale, the pseudogap and its associated Gutzwiller factor, which accounts for a reduction in the coherent piece of the electronic Green's function due to increased correlations as the Mott insulating state is approached. In agreement with experiment, we find that the slope of the linear in T dependence of the low temperature specific heat rapidly increases above optimum doping while it is nearly constant below optimum. Our theoretical calculations also agree with recent data on Bi$_2$Sr$_{2-\rm x}$La$_{\rm x}$CuO$_{6+δ}$ for which the normal state is accessed through the application of a large magnetic field. A quantum critical point is located at a doping slightly below optimum.

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arXiv2010

Signature of pseudogap formation in the density of states of underdoped cuprates

The resonating valence bond spin liquid model for the underdoped cuprates has as an essential element, the emergence of a pseudogap. This new energy scale introduces asymmetry in the quasiparticle density of states because it is associated with the antiferromagnetic Brillouin zone. By contrast, superconductivity develops on the Fermi surface and this largely restores the particle-hole symmetry for energies below the superconducting energy gap scale. In the highly underdoped regime, these two scales can be separately identified in the density of states and also partial density of states for each fixed angle in the Brillouin zone. From the total density of states, we find that the pseudogap energy scale manifests itself differently as a function of doping for positive and negative bias. Furthermore, we find evidence from recent scanning tunneling spectroscopy data for asymmetry in the positive and negative bias of the extracted $Δ(θ)$ which is in qualitative agreement with this model. Likewise, the slope of the linear low energy density of states is nearly constant in the underdoped regime while it increases significantly with overdoping in agreement with the data.

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arXiv2009

Signatures of Fermi surface reconstruction in Raman spectra of underdoped cuprates

We have calculated the Raman B$_{1g}$ and B$_{2g}$ spectra as a function of temperature, as well as doping, for the underdoped cuprates, using a model based on the resonating valence-bond spin-liquid. We discuss changes in intensity and peak position brought about by the presence of a pseudogap and the implied Fermi surface reconstruction, which are elements of this model. Signatures of Fermi surface reconstruction are evident as a sharp rise in the doping dependence of the antinodal to nodal peak ratio which occurs below the quantum critical point. The temperature dependence of the B$_{1g}$ polarization can be used to determine if the superconducting gap is limited to the Fermi pocket, as seen in angle resolved photoemission spectroscopy, or extends beyond. We find that the slope of the linear low energy B$_{2g}$ spectrum maintains its usual d-wave form, but with an effective gap which reflects the gap amplitude projected on the Fermi pocket. Our calculations capture the main qualitative features revealed in the extensive data set available on the HgBa$_2$CuO$_{4+δ}$ (Hg-1201) cuprate.

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arXiv2009

Effect of pseudogap formation on the penetration depth of underdoped high $T_c$ cuprates

The penetration depth is calculated over the entire doping range of the cuprate phase diagram with emphasis on the underdoped regime. Pseudogap formation on approaching the Mott transition, for doping below a quantum critical point, is described within a model based on the resonating valence bond spin liquid which provides an ansatz for the coherent piece of the Green's function. Fermi surface reconstruction, which is an essential element of the model, has a strong effect on the superfluid density at T=0 producing a sharp drop in magnitude, but does not change the slope of the linear low temperature variation. Comparison with recent data on Bi-based cuprates provides validation of the theory and shows that the effects of correlations, captured by Gutzwiller factors, are essential for a qualitative understanding of the data. We find that the Ferrell-Glover-Tinkham sum rule still holds and we compare our results with those for the Fermi arc and the nodal liquid models.

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arXiv2009

Effect of electron-phonon interaction on spectroscopies in graphene

We calculate the effect of the electron-phonon interaction on the electronic density of states (DOS), the quasiparticle properties and on the optical conductivity of graphene. In metals with DOS constant on the scale of phonon energies, the electron-phonon renormalizations drop out of the dressed DOS, however, due to the Dirac nature of the electron dynamics in graphene, the band DOS is linear in energy and phonon structures remain, which can be emphasized by taking an energy derivative. There is a shift in the chemical potential and in the position in energy of the Dirac point. Also, the DOS can be changed from a linear dependence out of value zero at the Dirac point to quadratic out of a finite value. The optical scattering rate $1/τ$ sets the energy scale for the rise of the optical conductivity from its universal DC value $4e^2/πh$ (expected in the simplest theory when chemical potential and temperature are both $\ll 1/2τ$) to its universal AC background value $(σ_0=πe^2/2h)$. As in ordinary metals the DC conductivity remains unrenormalized while its AC value is changed. The optical spectral weight under the intraband Drude is reduced by a mass renormalization factor as is the effective scattering rate. Optical weight is transferred to an Holstein phonon-assisted side band. Due to Pauli blocking the interband transitions are sharply suppressed, but also nearly constant, below twice the value of renormalized chemical potential and also exhibit a phonon-assisted contribution. The universal background conductivity is reduced below $σ_0$ at large energies.

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arXiv2009

Phonon spectroscopy through the electronic density of states in graphene

We study how phonon structure manifests itself in the electronic density of states of graphene. A procedure for extracting the value of the electron-phonon renormalization $λ$ is developed. In addition, we identify direct phonon structures. With increasing doping, these structures, along with $λ$, grow in amplitude and no longer display particle-hole symmetry.

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arXiv2009

Specific heat of underdoped cuprates: RVB versus Fermi arcs

A recent microscopic model of the pseudogap state, based on the resonating valence bond (RVB) spin liquid, has provided a simple ansatz for the electronic self energy in which a gap forms on the antiferromagnetic Brillouin zone as the limit of a Mott insulator is approached in the underdoped regime. Here, the ansatz is employed to calculate the electronic specific heat when a superconducting gap is also included. We find qualitative agreement with all experimental observations in the underdoped regime of the cuprates. We explore the relationship of the theory to two other purely phenomenological approaches, the nodal liquid and the Fermi arc model, and provide justification for their use on experimental data in light of this microscopic RVB theory.

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arXiv2009

Non-BCS behavior of optical properties across the cuprate phase diagram

The finite-frequency optical properties of the underdoped cuprates, in both the normal and superconducting state, display features which go beyond a Fermi liquid and a BCS description. We provide an understanding of these properties within a simplified analytical model, which has been evolved out of the Hubbard model and ideas based on a resonating valence bond spin liquid. We find that: 1) in underdoped samples, the missing area integrals reveal a second energy scale due to the pseudogap, not present at optimum or overdoping; 2) the real part of the optical self-energy shows a large sharp peak, that emerges with the opening of the pseudogap which exists within the superconducting state and persists in the normal state; and 3) the amount of optical spectral weight which is transferred to the condensate is greatly reduced by the presence of the pseudogap as compared to the Fermi liquid case. These non-BCS features of the superconducting state are in good qualitative agreement with a body of experimental work on different cuprate systems and provide strong evidence from optical conductivity that they are all a manifestation of the pseudogap energy scale.

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arXiv2008

Signatures of superconducting gap inhomogeneities in optical properties

Scanning tunneling spectroscopy applied to the high-$T_{c}$ cuprates has revealed significant spatial inhomogeneity on the nanoscale. Regions on the order of a coherence length in size show variations of the magnitude of the superconducting gap of order $\pm20%$ or more. An important unresolved question is whether or not these variations are also present in the bulk, and how they influence superconducting properties. As many theories and data analyses for high-$T_{c}$ superconductivity assume spatial homogeneity of the gap magnitude, this is a pressing question. We consider the far-infrared optical conductivity and evaluate, within an effective medium approximation, what signatures of spatial variations in gap magnitude are present in various optical quantities. In addition to the case of d-wave superconductivity, relevant to the high-$T_c$ cuprates, we have also considered s-wave gap symmetry in order to provide expected signatures of inhomogeneities for superconductors in general. While signatures of gap inhomogeneities can be strongly manifested in s-wave superconductors, we find that the far-infrared optical conductivity in d-wave is robust against such inhomogeneity.

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arXiv2008

Optical conductivity of bilayer graphene with and without an asymmetry gap

When a bilayer of graphene is placed in a suitably configured field effect device, an asymmetry gap can be generated and the carrier concentration made different in each layer. This provides a tunable semiconducting gap, and the valence and the conductance band no longer meet at the two Dirac points of the graphene Brillouin zone. We calculate the optical conductivity of such a semiconductor with particular emphasis on the optical spectral weight redistribution brought about by changes in gap and chemical potential due to charging. We derive an algebraic formula for arbitrary value of the chemical potential for the case of the bilayer conductivity without a gap.

cond-mat.mes-hall↗

arXiv2008

The unusual thickness dependence of superconductivity in $α$-MoGe thin films

Thin films of $α$-MoGe show progressively reduced $T_{c}$'s as the thickness is decreased below 30 nm and the sheet resistance exceeds 100 $Ω/\Box$. We have performed far-infrared transmission and reflection measurements for a set of $α$-MoGe films to characterize this weakened superconducting state. Our results show the presence of an energy gap with ratio $2Δ_0/k_BT_{c} = 3.8 \pm 0.1$ in all films studied, slightly higher than the BCS value, even though the transition temperatures decrease significantly as film thickness is reduced. The material properties follow BCS-Eliashberg theory with a large residual scattering rate except that the coherence peak seen in the optical scattering rate is found to be strongly smeared out in the thinner superconducting samples. A peak in the optical mass renormalization at $2Δ_0$ is predicted and observed for the first time.

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arXiv2008

Optical self-energy of superconducting Pb in the THz region

New THz data on the optical conductivity of Pb are presented as well as a detailed Eliashberg analysis with particular emphasis on phonon-assisted processes not included in a BCS approach. Consideration of the optical self-energy instead of the conductivity itself helps highlight the differences with BCS predictions. Predicted coherence peaks are observed in the optical scattering rates. Impurities enhance the optical effective mass at zero frequency by an order of magnitude and induce a large peak at twice the gap in agreement with theory. This work illustrates the usefulness of the optical self-energy for the analysis of data.

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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.

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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.

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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.

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arXiv2005

Optical Response for the d-density wave model

We have calculated the optical conductivity and the Raman response for the d-density wave model, proposed as a possible explanation for the pseudogap seen in high Tc cuprates. The total optical spectral weight remains approximately constant on opening of the pseudogap for fixed temperature. This occurs because there is a transfer of weight from the Drude peak to interband transitions across the pseudogap. The interband peak in the optical conductivity is prominent but becomes progressively reduced with increasing temperature, with impurity scattering, which distributes it over a larger energy range, and with ineleastic scattering which can also shift its position, making it difficult to have a direct determination of the value of the pseudogap. Corresponding structure is seen in the optical scattering rate, but not necessarily at the same energies as in the conductivity.

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