E. J. Nicol
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
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Research Interests
E. J. Nicol has a total of 21 co-authors. Here are the top co-authors by number of shared publications:
- J. P. Carbotte
Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1
17 shared publications J. P. Carbotte
7 shared publications- James P. F. LeBlanc
Memorial University of Newfoundland
3 shared publications - Douglas J. Scalapino
Department of Physics, University of California, Santa Barbara, California 93106-9530
2 shared publications A. Knigavko
Department of Physics Brock University St. Cathrine L25 3A1 Ontario Canada
1 shared publicationA. Perez Gonzalez
Department of Physics, McMaster University, Hamilton, Ontario, Canada L8S 4M1
1 shared publication
Latest Publications
- 18 July 2016
- Published by American Physical Society (APS) in Physical Review B
- Vol. 94 (3) , 039901
Erratum: Optical and transport properties in three-dimensional Dirac and Weyl semimetals [Phys. Rev. B93, 085426 (2016)]
DOI:http://dx.doi.org/10.1103/PhysRevB.94.039901
- 18 July 2016
- Published by American Physical Society (APS) in Physical Review B
- Vol. 94 (3) , 039901
Erratum: Optical and transport properties in three-dimensional Dirac and Weyl semimetals [Phys. Rev. B93, 085426 (2016)]
DOI:http://dx.doi.org/10.1103/PhysRevB.94.039901
- 25 October 2011
- Published by American Physical Society (APS) in Physical Review B
- Vol. 84 (16)
Effect of electron-phonon coupling on energy and density of states renormalizations of dynamically screened graphene
Electronic screening strongly renormalizes the linear bands that occur near the Dirac crossing in graphene. The single bare Dirac crossing is split into two individual Dirac-like points, which are separated in energy but still at zero momentum relative to the K point. A diamond-like structure occurs in between as a result of the formation of plasmarons. In this work, we explore the combined effect of electron-electron and electron-phonon couplings on the renormalized energy dispersion, the spectral function, and the electronic density of states. We find that distinct signatures of the plasmaron structure are observable in the density of states with the split Dirac points presenting themselves as minima with quadratic dependence on energy about such points. By examining the slopes of both the density of states and the renormalized dispersion near the Fermi level, we illustrate how one can separate - and -dependent renormalizations and suggest how this might allow for the isolation of the renormalization due to the electron-phonon interaction from that of the electron-electron interaction. DOI: http://dx.doi.org/10.1103/PhysRevB.84.165448 ©2011 American Physical Society- 25 October 2011
- Published by American Physical Society (APS) in Physical Review B
- Vol. 84 (16)
Effect of electron-phonon coupling on energy and density of states renormalizations of dynamically screened graphene
Electronic screening strongly renormalizes the linear bands that occur near the Dirac crossing in graphene. The single bare Dirac crossing is split into two individual Dirac-like points, which are separated in energy but still at zero momentum relative to the K point. A diamond-like structure occurs in between as a result of the formation of plasmarons. In this work, we explore the combined effect of electron-electron and electron-phonon couplings on the renormalized energy dispersion, the spectral function, and the electronic density of states. We find that distinct signatures of the plasmaron structure are observable in the density of states with the split Dirac points presenting themselves as minima with quadratic dependence on energy about such points. By examining the slopes of both the density of states and the renormalized dispersion near the Fermi level, we illustrate how one can separate - and -dependent renormalizations and suggest how this might allow for the isolation of the renormalization due to the electron-phonon interaction from that of the electron-electron interaction. DOI: http://dx.doi.org/10.1103/PhysRevB.84.165448 ©2011 American Physical Society- 24 August 2011
- Published by American Physical Society (APS) in Physical Review B
- Vol. 84 (8)
Effects of electron-phonon coupling on Landau levels in graphene
We calculate the density of states (DOS) in graphene for electrons coupled to a phonon in an external magnetic field. We find that coupling to an Einstein mode of frequency not only shifts and broadens the Landau levels (LLs), but radically alters the DOS by introducing a new set of peaks at energies , where is the energy of the th LL. If one of these new peaks lies sufficiently close to an LL, it causes the LL to split in two; if the system contains an energy gap, an LL may be split in three. The new peaks occur outside the interval , leaving the LLs in that interval largely unaffected. If the chemical potential is greater than the phonon frequency, the zeroth LL lies outside the interval and can be split, eliminating its association with a single Dirac point. We find that coupling to an extended phonon distribution such as a Lorentzian or Debye spectrum does not qualitatively alter these results. DOI: http://dx.doi.org/10.1103/PhysRevB.84.085125 ©2011 American Physical Society- 24 August 2011
- Published by American Physical Society (APS) in Physical Review B
- Vol. 84 (8)
Effects of electron-phonon coupling on Landau levels in graphene
We calculate the density of states (DOS) in graphene for electrons coupled to a phonon in an external magnetic field. We find that coupling to an Einstein mode of frequency not only shifts and broadens the Landau levels (LLs), but radically alters the DOS by introducing a new set of peaks at energies , where is the energy of the th LL. If one of these new peaks lies sufficiently close to an LL, it causes the LL to split in two; if the system contains an energy gap, an LL may be split in three. The new peaks occur outside the interval , leaving the LLs in that interval largely unaffected. If the chemical potential is greater than the phonon frequency, the zeroth LL lies outside the interval and can be split, eliminating its association with a single Dirac point. We find that coupling to an extended phonon distribution such as a Lorentzian or Debye spectrum does not qualitatively alter these results. DOI: http://dx.doi.org/10.1103/PhysRevB.84.085125 ©2011 American Physical Society- 16 May 2011
- Published by American Physical Society (APS) in Physical Review B
- Vol. 83 (18)
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 spin liquid model in conjunction with recent angle-resolved photoemission spectroscopy 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 . DOI: http://dx.doi.org/10.1103/PhysRevB.83.184506 ©2011 American Physical Society- 16 May 2011
- Published by American Physical Society (APS) in Physical Review B
- Vol. 83 (18)
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 spin liquid model in conjunction with recent angle-resolved photoemission spectroscopy 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 . DOI: http://dx.doi.org/10.1103/PhysRevB.83.184506 ©2011 American Physical Society- 25 January 2010
- Published by American Physical Society (APS) in Physical Review B
- Vol. 81 (1)
Effect of pseudogap formation on the penetration depth of underdoped high-cupratesThe 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.
- 25 January 2010
- Published by American Physical Society (APS) in Physical Review B
- Vol. 81 (1)
Effect of pseudogap formation on the penetration depth of underdoped high-cupratesThe 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.
- 19 January 2010
- Published by American Physical Society (APS) in Physical Review B
- Vol. 81 (4) , 045419
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 sets the energy scale for the rise of the optical conductivity from its universal dc value (expected in the simplest theory when chemical potential and temperature are both ) to its universal ac background value . 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 at large energies.- 19 January 2010
- Published by American Physical Society (APS) in Physical Review B
- Vol. 81 (4) , 045419
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 sets the energy scale for the rise of the optical conductivity from its universal dc value (expected in the simplest theory when chemical potential and temperature are both ) to its universal ac background value . 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 at large energies.- Open Access
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 $1/\tau$ sets the energy scale for the rise of the optical conductivity from its universal DC value $4e^2/\pi h$ (expected in the simplest theory when chemical potential and temperature are both $\ll 1/2\tau$) to its universal AC background value $(\sigma_0=\pi e^2/2h)$. 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 $\sigma_0$ at large energies.Open AccessEffect 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 $1/\tau$ sets the energy scale for the rise of the optical conductivity from its universal DC value $4e^2/\pi h$ (expected in the simplest theory when chemical potential and temperature are both $\ll 1/2\tau$) to its universal AC background value $(\sigma_0=\pi e^2/2h)$. 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 $\sigma_0$ at large energies. - 6 March 2009
- Published by American Physical Society (APS) in Physical Review B
- Vol. 79 (10) , 100505
Non-Bardeen-Cooper-Schrieffer behavior of optical properties across the phase diagram of cuprate superconductors
The finite-frequency optical properties of the underdoped cuprates, in both the normal and superconducting states, display features which go beyond a Fermi liquid and a Bardeen-Cooper-Schrieffer (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.
- 6 March 2009
- Published by American Physical Society (APS) in Physical Review B
- Vol. 79 (10) , 100505
Non-Bardeen-Cooper-Schrieffer behavior of optical properties across the phase diagram of cuprate superconductors
The finite-frequency optical properties of the underdoped cuprates, in both the normal and superconducting states, display features which go beyond a Fermi liquid and a Bardeen-Cooper-Schrieffer (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.
- 28 May 2008
- Published by American Physical Society (APS) in Physical Review B
- Vol. 77 (17) , 174515
Optical self-energy of superconducting Pb in the terahertz region
New terahertz 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.
- 28 May 2008
- Published by American Physical Society (APS) in Physical Review B
- Vol. 77 (17) , 174515
Optical self-energy of superconducting Pb in the terahertz region
New terahertz 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.
- 7 April 2008
- Published by American Physical Society (APS) in Physical Review B
- Vol. 77 (15) , 155409
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 conductance bands 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 an arbitrary value of the chemical potential for the case of the bilayer conductivity without a gap.
- 7 April 2008
- Published by American Physical Society (APS) in Physical Review B
- Vol. 77 (15) , 155409
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 conductance bands 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 an arbitrary value of the chemical potential for the case of the bilayer conductivity without a gap.