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Carbotte JP, Nicol EJ, Timusk T. Detecting Superconductivity in the High Pressure Hydrides and Metallic Hydrogen from Optical Properties. Phys Rev Lett 2018; 121:047002. [PMID: 30095968 DOI: 10.1103/physrevlett.121.047002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2018] [Revised: 04/23/2018] [Indexed: 06/08/2023]
Abstract
We present a new technique for measuring the critical temperature T_{c} in the high pressure, high T_{c} electron-phonon-driven superconducting hydrides. This technique does not require connecting leads to the sample. In the region of the absorption spectrum above the sum of the optical gap and maximum phonon energy, the reflectance mirrors the temperature variation of the superconducting order parameter. For an appropriately chosen value of fixed photon energy, the temperature dependence of the reflectance varies much more rapidly below T=T_{c} than above. It increases with increasing temperature in the superconducting state while it decreases in the normal state. Examining the temperature dependence of the reflectance at a fixed photon energy, there is a cusp at T=T_{c} which provides a measurement of the critical temperature. We discuss these issues within the context of the recently reported atomic metallic phase of hydrogen, but our proposed technique should prove useful for other hydrides with large coupling to high energy phonons.
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Affiliation(s)
- J P Carbotte
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
- The Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
| | - E J Nicol
- Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1, Canada
| | - T Timusk
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
- The Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
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Mukherjee SP, Carbotte JP. Anomalous DC Hall response in noncentrosymmetric tilted Weyl semimetals. J Phys Condens Matter 2018; 30:115702. [PMID: 29384496 DOI: 10.1088/1361-648x/aaac16] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Weyl nodes come in pairs of opposite chirality. For broken time reversal symmetry (TR) they are displaced in momentum space by [Formula: see text] and the anomalous DC Hall conductivity [Formula: see text] is proportional to [Formula: see text] at charge neutrality. For finite doping there are additive corrections to [Formula: see text] which depend on the chemical potential as well as on the tilt ([Formula: see text]) of the Dirac cones and on their relative orientation. If inversion symmetry (I) is also broken the Weyl nodes are shifted in energy by an amount [Formula: see text]. This introduces further changes in [Formula: see text] and we provide simple analytic formulas for these modifications for both type I ([Formula: see text]) and type II ([Formula: see text], overtilted) Weyl. For type I when the Weyl nodes have equal magnitude but oppositely directed tilts, the correction to [Formula: see text] is proportional to the chemical potential μ and completely independent of the energy shift [Formula: see text]. When instead the tilts are parallel, the correction is linear in [Formula: see text] and μ drops out. For type II the corrections involve both μ and [Formula: see text], are nonlinear and also involve a momentum cut off. We discuss the implied changes to the Nernst coefficient and to the thermal Hall effect of a finite [Formula: see text].
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Affiliation(s)
- S P Mukherjee
- Department of Physics and Astronomy, McMaster University, Hamiltion, Ontario, L8S 4M1, Canada
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Mukherjee SP, Carbotte JP. Optical response in Weyl semimetal in model with gapped Dirac phase. J Phys Condens Matter 2017; 29:425301. [PMID: 28749377 DOI: 10.1088/1361-648x/aa82a7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We study the optical properties of Weyl semimetal (WSM) in a model which features, in addition to the usual term describing isolated Dirac cones proportional to the Fermi velocity v F, a gap term m and a Zeeman spin-splitting term b with broken time reversal symmetry. Transport is treated within Kubo formalism and particular attention is payed to the modifications that result from a finite m and b. We consider how these modifications change when a finite residual scattering rate [Formula: see text] is included. For [Formula: see text] the A.C. conductivity as a function of photon energy [Formula: see text] continues to display the two quasilinear energy regions of the clean limit for [Formula: see text] below the onset of the second electronic band which is gapped at ([Formula: see text]). For [Formula: see text] of the order m little trace of two distinct linear energy scales remain and the optical response has evolved towards that for [Formula: see text]. Although some quantitative differences remain there are no qualitative differences. The magnitude of the D.C. conductivity [Formula: see text] at zero temperature ([Formula: see text]) and chemical potential ([Formula: see text]) is altered. While it remains proportional to [Formula: see text] it becomes inversely dependent on an effective Fermi velocity out of the Weyl nodes equal to [Formula: see text] which decreases strongly as the phase boundary between Weyl semimetal and gapped Dirac phase (GDSM) is approached at [Formula: see text]. The leading term in the approach to [Formula: see text] for finite [Formula: see text], [Formula: see text] and [Formula: see text] is found to be quadratic. The coefficient of these corrections tracks closely the [Formula: see text] dependence of the [Formula: see text] limit with differences largest near to the WSM-GDSM boundary.
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Affiliation(s)
- S P Mukherjee
- Department of Physics and Astronomy, McMaster University, Hamiltion, Ontario, L8S 4M1, Canada
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Capitani F, Langerome B, Brubach JB, Roy P, Drozdov A, Eremets M, Nicol EJ, Carbotte JP, Timusk T. Spectroscopic evidence of a new energy scale for superconductivity in H 3S. Nat Phys 2017; 13:859-863. [PMID: 28883888 PMCID: PMC5584662 DOI: 10.1038/nphys4156] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2016] [Accepted: 04/28/2017] [Indexed: 05/31/2023]
Abstract
The discovery of a superconducting phase in sulfur hydride under high pressure with a critical temperature above 200 K has provided fresh impetus to the search for superconductors at ever higher temperatures. Although this systems displays all the hallmarks of superconductivity, the mechanism through which it arises remains to be determined. Here we provide a first optical spectroscopy study of this superconductor. Experimental results for the optical reflectivity of H3S, under hydrostatic pressure of 150 GPa, for several temperatures and over the range 60 to 600 meV of photon energies, are compared with theoretical calculations based on Eliashberg theory. Two significant features stand out: some remarkably strong infrared active phonons at around 160 meV, and a band with a depressed reflectance in the superconducting state in the region from 450 meV to 600 meV. In this energy range H3S becomes more reflecting with increasing temperature, a change that is traced to superconductivity originating from the electron-phonon interaction. The shape, magnitude, and energy dependence of this band at 150 K agrees with our calculations. This provides strong evidence of a conventional mechanism. However, the unusually strong optical phonon suggests a contribution of electronic degrees of freedom.
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Affiliation(s)
- F. Capitani
- Synchrotron SOLEIL, AILES Beamline, Saint-Aubin, 91190, France
| | - B. Langerome
- Synchrotron SOLEIL, AILES Beamline, Saint-Aubin, 91190, France
| | - J.-B. Brubach
- Synchrotron SOLEIL, AILES Beamline, Saint-Aubin, 91190, France
| | - P. Roy
- Synchrotron SOLEIL, AILES Beamline, Saint-Aubin, 91190, France
| | - A. Drozdov
- Biogeochemistry Department, Max Planck Institute for Chemistry, PO Box 3060, 55020 Mainz, Germany
| | - M.I. Eremets
- Biogeochemistry Department, Max Planck Institute for Chemistry, PO Box 3060, 55020 Mainz, Germany
| | - E. J. Nicol
- Department of Physics, University of Guelph, Guelph, ON N1G 2W1, Canada
| | - J. P. Carbotte
- Department of Physics and Astronomy, McMaster University, Hamilton, ON L8S 4M1, Canada
- The Canadian Institute for Advanced Research, Toronto, ON M5G 1Z8, Canada
| | - T. Timusk
- Department of Physics and Astronomy, McMaster University, Hamilton, ON L8S 4M1, Canada
- The Canadian Institute for Advanced Research, Toronto, ON M5G 1Z8, Canada
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Abstract
We calculate the AC optical response of a line node semimetal with emphasis on characteristic behaviours which can be used to distinguish them from point node materials such as Dirac and Weyl semimetals. The interband optical background at zero temperature displays a flat region at small photon energies ([Formula: see text]) analogue to the universal background seen in graphene. However, in contrast to graphene, the height of the constant region is not universal but depends inversely on the Fermi velocity of the charge carriers and directly on the radius (b) in momentum space of the nodal circle. The parameter b is a defining energy scale and determines the range of photon energy over which the flat response persists. At high energies [Formula: see text], the interband response becomes linear in [Formula: see text] in agreement with the case for 3D-Dirac fermions with point node. The optical spectral weight contained in the interband or Drude conductivity shows the same two distinct regimes. At low temperature (T) (chemical potential (μ)), it rises linearly with [Formula: see text] and is proportional to b. At high temperature, [Formula: see text], a [Formula: see text] law is obtained, which is independent of b. At T = 0, the Lorentz number takes on the conventional value [Formula: see text] for all values of μ. It increases with increasing temperature to reach a first plateau of 2.4L o provided [Formula: see text] but [Formula: see text]. At high temperature, T > b, a second plateau of height 4.2L o emerges. The first plateau is characteristic of 2D-Dirac while the second corresponds to 3D-Dirac. The thermopower as a function of temperature also shows an evolution from a 2D to 3D behaviour.
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Affiliation(s)
- J P Carbotte
- Department of Physics, McMaster University, Hamilton, Ontario, L8S 4M1, Canada. Canadian Institute for Advance Research, Toronto, Ontario, M5G 1Z8, Canada
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Hwang J, Carbotte JP, Min BH, Kwon YS, Timusk T. Electron-boson spectral density of LiFeAs obtained from optical data. J Phys Condens Matter 2015; 27:055701. [PMID: 25612554 DOI: 10.1088/0953-8984/27/5/055701] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We analyze existing optical data in the superconducting state of LiFeAs at T = 4 K, to recover its electron-boson spectral density. A maximum entropy technique is employed to extract the spectral density I(2)χ(ω) from the optical scattering rate. Care is taken to properly account for elastic impurity scattering which can importantly affect the optics in an s-wave superconductor, but does not eliminate the boson structure. We find a robust peak in I(2)χ(ω) centered about Ω(R) ≅ 8.0 meV or 5.3 k(B)Tc (with Tc = 17.6 K). Its position in energy agrees well with a similar structure seen in scanning tunneling spectroscopy (STS). There is also a peak in the inelastic neutron scattering (INS) data at this same energy. This peak is found to persist in the normal state at T = 23 K. There is evidence that the superconducting gap is anisotropic as was also found in low temperature angular resolved photoemission (ARPES) data.
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Affiliation(s)
- J Hwang
- Department of Physics, Sungkyunkwan University, Suwon, Gyeonggi-do 440-746, Republic of Korea
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Tabert CJ, Carbotte JP. Magnetization of the metallic surface states in topological insulators. J Phys Condens Matter 2015; 27:015008. [PMID: 25427753 DOI: 10.1088/0953-8984/27/1/015008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We calculate the magnetization of the helical metallic surface states of a topological insulator. We account for the presence of a small sub-dominant Schrödinger piece in the Hamiltonian in addition to the dominant Dirac contribution. This breaks particle-hole symmetry. The cross-section of the upper Dirac cone narrows while that of the lower cone broadens. The sawtooth pattern seen in the magnetization of the pure Dirac limit as a function of chemical potential (μ) is shifted; but, the quantization of the Hall plateaus remains half integral. This is verified by taking the derivative of the magnetization with respect to μ. We compare our results with those when the non-relativistic piece dominates over the relativistic contribution and the quantization is integral. Analytic results for the magnetic oscillations are obtained where we include a first order correction in the ratio of non-relativistic to relativistic magnetic energy scales. Our fully quantum mechanical derivations confirm the expectation of semiclassical theory except for a small correction to the expected phase. There is a change in the overall amplitude of the magnetic oscillations. The Dingle and temperature factors are modified.
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Affiliation(s)
- C J Tabert
- Department of Physics, University of Guelph, 50 Stone Road East, Guelph, Ontario N1G 2W1, Canada. Guelph-Waterloo Physics Institute, University of Guelph, 50 Stone Road East, Guelph, Ontario N1G 2W1, Canada
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Hwang J, Carbotte JP. Deriving the electron-phonon spectral density of MgB2 from optical data, using maximum entropy techniques. J Phys Condens Matter 2014; 26:165702. [PMID: 24695073 DOI: 10.1088/0953-8984/26/16/165702] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We use maximum entropy techniques to extract an electron-phonon density from optical data for the normal state at T = 45 K of MgB2. Limiting the analysis to a range of phonon energies below 110 meV, which is sufficient for capturing all phonon structures, we find a spectral function that is in good agreement with that calculated for the quasi-two-dimensional σ-band. Extending the analysis to higher energies, up to 160 meV, we find no evidence for any additional contributions to the fluctuation spectrum, but find that the data can only be understood if the density of states is taken to decrease with increasing energy.
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Affiliation(s)
- J Hwang
- Department of Physics, Sungkyunkwan University, Suwon, Gyeonggi-do 440-746, Korea
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9
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Abstract
We use a maximum entropy technique to obtain the electron-boson spectral density from optical scattering rate data across the underdoped region of the Bi2Sr(2-x)La(x)CuO6 (Bi-2201) phase diagram. Our method involves a generalization of previous work which explicitly includes finite temperature and the opening of a pseudogap which modifies the electronic structure. We find that the mass enhancement factor λ associated with the electron-boson spectral density increases monotonically with reduced doping and closer proximity to the Mott antiferromagnetic insulating state. This observation is consistent with increased coupling to the spin fluctuations. At the same time the system has reduced metallicity because of increased pseudogap effects which we model with a reduced effective density of states around the Fermi energy with the range of the modifications in energy set by the pseudogap scale.
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Affiliation(s)
- Jungseek Hwang
- Department of Physics, Sungkyunkwan University, Suwon, Gyeonggi-do, Republic of Korea.
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10
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Carbotte JP, Schachinger E. Interlayer penetration depth in the pseudogap phase of cuprate superconductors. J Phys Condens Matter 2013; 25:165702. [PMID: 23553656 DOI: 10.1088/0953-8984/25/16/165702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
The opening of a pseudogap in the electronic structure of the underdoped high Tc cuprates has a profound effect on superconducting properties. Here we consider the c-axis penetration depth. A phenomenological model of the pseudogap due to Yang, Rice, and Zhang (YRZ) is used. It is based on the idea of a resonating valence bond spin liquid. A simplifying limit, the arc model, is also considered as it provides useful analytic formulas. The zero temperature value of the superfluid density n(s)(T = 0) is greatly reduced with increasing values of the pseudogap (Δpg). This value reflects the reconstruction of the Fermi surface from the large contour of Fermi liquid theory to ever smaller Luttinger pockets as Δpg becomes larger. Also, as temperature is increased the ratio n(s)(T)/n(s)(0) as a function of the reduced temperature t = T/T(c) decreases more rapidly than in the corresponding Fermi liquid (Δpg = 0) as states which have both superconducting and pseudogap become more significantly sampled.
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Affiliation(s)
- J P Carbotte
- Department of Physics and Astronomy, McMaster University, Hamilton, ON, Canada
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11
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Abstract
In highly correlated systems one can define an optical self-energy in analogy to its quasiparticle (QP) self-energy counterpart. This quantity provides useful information on the nature of the excitations involved in inelastic scattering processes. Here we calculate the self-energy of the intraband optical transitions in graphene originating in the electron-electron interaction (EEI) as well as electron-phonon interaction (EPI). Although optics involves an average over all momenta (k) of the charge carriers, the structure in the optical self-energy is nevertheless found to mirror mainly that of the corresponding quasiparticles for k equal to or near the Fermi momentum k(F). Consequently, plasmaronic structures which are associated with momenta near the Dirac point at k = 0 are not important in the intraband optical response. While the structure of the electron-phonon interaction (EPI) reflects the sharp peaks of the phonon density of states, the excitation spectrum associated with the electron-electron interaction is in comparison structureless and flat and extends over an energy range which scales linearly with the value of the chemical potential. We introduce a method whereby detailed quantitative information on such excitation spectra can be extracted from optical data. Modulations seen on the edge of the interband optical conductivity as it rises towards its universal background value are traced to structure in the quasiparticle self-energies around k(F) of the lower Dirac cone associated with the occupied states.
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Affiliation(s)
- J Hwang
- Department of Physics, Sungkyunkwan University, Suwon, Gyeonggi-do, Republic of Korea
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Muschler B, Prestel W, Schachinger E, Carbotte JP, Hackl R, Ono S, Ando Y. An electron-boson glue function derived from electronic Raman scattering. J Phys Condens Matter 2010; 22:375702. [PMID: 21403206 DOI: 10.1088/0953-8984/22/37/375702] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Raman scattering cross sections depend on photon polarization. In the cuprates, nodal and antinodal directions are weighted more strongly in B(2g) and B(1g) symmetries, respectively. On the other hand, in angle-resolved photoemission spectroscopy (ARPES), electronic properties are measured along well-defined directions in momentum space rather than their weighted averages being taken. In contrast, the optical conductivity involves a momentum average over the entire Brillouin zone. Newly measured Raman response data on high-quality Bi(2)Sr(2)CaCu(2)O(8 + δ) single crystals up to high energies have been inverted using a modified maximum entropy inversion technique to extract from B(1g) and B(2g) Raman data corresponding electron-boson spectral densities (glue), and these are compared to the results obtained with known ARPES and optical inversions. We find that the B(2g) spectrum agrees qualitatively with nodal direction ARPES while the B(1g) results look more like the optical spectrum. A large peak around 30-40 meV in B(1g) and a much less prominent one in B(2g) are taken as support for the importance of (π, π) scattering at this frequency.
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Affiliation(s)
- B Muschler
- Walther Meissner Institut, Bayerische Akademie der Wissenschaften, Garching, Germany
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Yang J, Hüvonen D, Nagel U, Rõõm T, Ni N, Canfield PC, Bud'ko SL, Carbotte JP, Timusk T. Optical spectroscopy of superconducting Ba0.55K0.45Fe2As2: evidence for strong coupling to low-energy bosons. Phys Rev Lett 2009; 102:187003. [PMID: 19518902 DOI: 10.1103/physrevlett.102.187003] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2008] [Indexed: 05/27/2023]
Abstract
Normal state optical spectroscopy on single crystals of the new iron arsenide superconductor Ba0.55K0.45Fe2As2 shows that the infrared spectrum consists of two major components: a strong metallic Drude band and a well-separated midinfrared absorption centered at 0.7 eV. It is difficult to separate the two components unambiguously but several fits using Lorentzian peaks suggest a model with a Drude peak having a plasma frequency of 1.6 to 2.1 eV and a midinfrared peak with a plasma frequency of 2.5 eV. Detailed analysis of the frequency dependent scattering rate shows that the charge carriers interact with a broad bosonic spectrum extending beyond 100 meV with a very large coupling constant lambda=3.4 at low temperature. As the temperature increases this coupling weakens to lambda=0.78 at ambient temperature. This suggests a bosonic spectrum that is similar to what is seen in the lower Tc cuprates.
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Affiliation(s)
- J Yang
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
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14
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Yang J, Hwang J, Schachinger E, Carbotte JP, Lobo RPSM, Colson D, Forget A, Timusk T. Exchange boson dynamics in cuprates: optical conductivity of HgBa_2CuO_4+delta. Phys Rev Lett 2009; 102:027003. [PMID: 19257311 DOI: 10.1103/physrevlett.102.027003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2008] [Indexed: 05/27/2023]
Abstract
The electron-boson spectral density function I;{2}chi(Omega) responsible for carrier scattering of the high temperature superconductor HgBa_{2}CuO_{4+delta} (T_{c}=90 K) is calculated from new data on the optical scattering rate. A maximum entropy technique is used. Published data on HgBa_{2}Ca_{2}Cu_{3}O_{8+delta} (T_{c}=130 K) are also inverted and these new results are put in the context of other known cases. All spectra (with two notable exceptions) show a peak at an energy (Omega_{r}) proportional to the superconducting transition temperature Omega_{r} approximately 6.3k_{B}T_{c}. This charge channel relationship follows closely the magnetic resonance seen by polarized neutron scattering, Omega_{r};{neutron} approximately 5.4k_{B}T_{c}. The amplitudes of both peaks decrease strongly with increasing temperature. In some cases, the peak at Omega_{r} is weak and the spectrum can have additional maxima and a background extending up to several hundred meV.
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Affiliation(s)
- J Yang
- Department of Physics and Astronomy, McMaster University, Hamilton, ON L8S 4M1, Canada
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Hwang J, Carbotte JP, Timusk T. Evidence for a pseudogap in underdoped Bi{2}Sr_{2}CaCu{2}O{8+delta} and YBa2Cu3O6.50 from in-plane optical conductivity measurements. Phys Rev Lett 2008; 100:177005. [PMID: 18518327 DOI: 10.1103/physrevlett.100.177005] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2007] [Indexed: 05/26/2023]
Abstract
The real part of the in-plane optical self-energy data in underdoped Bi_{2}Sr_{2}CaCu_{2}O_{8+delta} (Bi-2212) and ortho II YBa2Cu3O6.5 contains new and important information on the pseudogap. Using a theoretical model approach, a major new finding is that states lost below the pseudogap Delta_{pg} are accompanied by a pileup of states just above this energy. The pileup along with a sharp mode in the bosonic spectral function leads to an unusually rapid increase in the optical scattering rate as a function of frequency and a characteristically sloped peak in the real part of the optical self-energy. These features are not found in optimally doped and overdoped samples and represent the clearest signature so far in the in-plane optical conductivity of the opening of a pseudogap.
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Affiliation(s)
- J Hwang
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada.
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16
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Hwang J, Schachinger E, Carbotte JP, Gao F, Tanner DB, Timusk T. Bosonic spectral density of epitaxial thin-film La1.83Sr0.17CuO4 superconductors from infrared conductivity measurements. Phys Rev Lett 2008; 100:137005. [PMID: 18517991 DOI: 10.1103/physrevlett.100.137005] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2007] [Indexed: 05/26/2023]
Abstract
We use optical spectroscopy to investigate the excitations responsible for the structure in the optical self-energy of thin epitaxial films of La(1.83)Sr(0.17)CuO(4). Using Eliashberg's formalism to invert the optical spectra we extract the electron-boson spectral function and find that at low temperature it has a two component structure closely matching the spin excitation spectrum recently measured by magnetic neutron scattering. We contrast the temperature evolution of the spectral density and the two-peak behavior in La(2-Sr(x)CuO(4) with another high temperature superconductor Bi(2)Sr(2)CaCu(2)O(8+delta). The bosonic spectral functions of the two materials account for the low T(c) of LSCO as compared to Bi-2212.
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Affiliation(s)
- J Hwang
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1Canada.
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Hwang J, Nicol EJ, Timusk T, Knigavko A, Carbotte JP. High energy scales in the optical self-energy of the cuprate superconductors. Phys Rev Lett 2007; 98:207002. [PMID: 17677731 DOI: 10.1103/physrevlett.98.207002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2006] [Indexed: 05/16/2023]
Abstract
Using optical spectroscopy with a derivative technique, we find for the high Tc cuprate Bi2Sr2CaCu2O8+delta (Bi-2212) evidence for a new high energy scale at 900 meV beyond the two previously well-known ones at roughly 50 and 400 meV. The intermediate scale at 400 meV has recently been seen in angle-resolved photoemission spectroscopy experiments along the nodal direction as a large kink. In YBa2Cu3O6.50, the three energy scales are shifted to lower energy relative to Bi-2212 and we observe the emergence of a possible new high energy feature at 600 meV.
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Affiliation(s)
- J Hwang
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario N1G 2W1, Canada
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Gusynin VP, Sharapov SG, Carbotte JP. Anomalous absorption line in the magneto-optical response of graphene. Phys Rev Lett 2007; 98:157402. [PMID: 17501382 DOI: 10.1103/physrevlett.98.157402] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2006] [Indexed: 05/15/2023]
Abstract
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.
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Affiliation(s)
- V P Gusynin
- Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine
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Abstract
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 Omega and this unusual line shape changes to Drude-like by increasing the chemical potential |mu|, with width linear in mu. The interband contribution at T=0 is a constant independent of Omega with a lower cutoff at 2mu. Distinctly different behavior occurs if interaction-induced phenomena in graphene cause an opening of a gap Delta. At a large magnetic field B, the diagonal and Hall conductivities at small Omega become independent of B but remain nonzero and show a structure associated with the lowest Landau level. This occurs because in the Dirac theory the energy of this level, E0 = +/-Delta, is field independent in sharp contrast to the conventional case.
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Affiliation(s)
- V P Gusynin
- Bogolyubov Institute for Theoretical Physics, Metrologicheskaya Street 14-b, Kiev, 03143, Ukraine
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Zhu JX, Kim W, Ting CS, Carbotte JP. Quasiparticle states around a nonmagnetic impurity in a d-density-wave state of high-T(c) cuprates. Phys Rev Lett 2001; 87:197001. [PMID: 11690444 DOI: 10.1103/physrevlett.87.197001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2001] [Indexed: 05/23/2023]
Abstract
The electronic structure around a single nonmagnetic impurity in the d-density-wave (DDW) ordering is studied. It is found that a single subgap resonance peak appears in the local density of states around the impurity. In the unitary limit, the position of this resonance peak shifts away from the Fermi energy in accord with the chemical potential. This result is dramatically different from the case of the pure superconducting state for which the impurity resonant energy is approximately pinned at the Fermi level. This can be used to probe the existence of the DDW ordering in cuprates.
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Affiliation(s)
- J X Zhu
- Texas Center for Superconductivity, University of Houston, Houston, Texas 77204, USA
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Schachinger E, Carbotte JP. Thermodynamic properties of strong coupling superconductors with energy-dependent electronic density of states. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0305-4608/13/12/017] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Carbotte JP, Schachinger E, Basov DN. Coupling strength of charge carriers to spin fluctuations in high-temperature superconductors. Nature 1999; 401:354-6. [PMID: 16862106 DOI: 10.1038/43843] [Citation(s) in RCA: 194] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/1999] [Accepted: 07/27/1999] [Indexed: 11/09/2022]
Abstract
In conventional superconductors, the most direct evidence of the mechanism responsible for superconductivity comes from tunnelling experiments, which provide a clear picture of the underlying electron-phonon interactions. As the coherence length in conventional superconductors is large, the tunnelling process probes several atomic layers into the bulk of the material; the observed structure in the current-voltage characteristics at the phonon energies gives, through inversion of the Eliashberg equations, the electron-phonon spectral density alpha2F(omega). The situation is different for the high-temperature copper oxide superconductors, where the coherence length (particularly for c-axis tunnelling) can be very short. Because of this, methods such as optical spectroscopy and neutron scattering provide a better route for investigating the underlying mechanism, as they probe bulk properties. Accurate reflection measurements at infrared wavelengths and precise polarized neutron-scattering data are now available for a variety of the copper oxides, and here we show that the conducting carriers (probed by infrared spectroscopy) are strongly coupled to a resonance structure in the spectrum of spin fluctuations (measured by neutron scattering). The coupling strength inferred from those results is sufficient to account for the high transition temperatures of the copper oxides, highlighting a prominent role for spin fluctuations in driving superconductivity in these materials.
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Affiliation(s)
- J P Carbotte
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
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Abstract
We compute the single-particle inverse lifetime, along with the
conductivity-derived scattering rate, for a metallic system in an s-wave
superconducting state. When both electron–phonon and electron-impurity
scattering are included, we find that while these scattering rates are in
qualitative agreement, in general quantitative agreement is lacking. We also
derive results for the quasiparticle lifetime within the BCS framework with
impurity scattering, which makes it clear that impurity scattering is
suppressed for electrons near the Fermi surface in the superconducting state.
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Abstract
We review the effect of elastic and inelastic scattering on the normal state
infrared conductivity, and describe modifications to the real and imaginary
parts which result from a transition to an s-wave superconducting state. The
zero frequency limit of the imaginary part is related to the
temperature-dependent penetration depth and, at finite frequency, provides
information about the superconducting gap. In the high
Tc cuprates the gap appears to
have d-wave symmetry. This profoundly modifies both the real and the imaginary
parts of the optical conductivity. After describing these modifications we
introduce the conductivity-derived scattering rate, which directly probes the
inelastic scattering processes, and is much larger in the oxides than in
conventional superconductors. This quantity is also significantly modified by
the d-wave symmetry of the gap.
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Branch D, Carbotte JP. Doping and van Hove singularity dependence of Raman background in dx2-y2 superconductors. Phys Rev B Condens Matter 1996; 54:13288-13294. [PMID: 9985192 DOI: 10.1103/physrevb.54.13288] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Jiang C, Schachinger E, Carbotte JP, Basov D, Timusk T. Imaginary part of the infrared conductivity of a dx2-y2 superconductor. Phys Rev B Condens Matter 1996; 54:1264-1272. [PMID: 9985398 DOI: 10.1103/physrevb.54.1264] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Jiang C, Carbotte JP. Raman electronic continuum in a dx2-y2 superconductor: Inelastic scattering. Phys Rev B Condens Matter 1996; 53:11868-11876. [PMID: 9982817 DOI: 10.1103/physrevb.53.11868] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Marsiglio F, Carbotte JP, Puchkov A, Timusk T. Imaginary part of the optical conductivity of Ba1-xKxBiO3. Phys Rev B Condens Matter 1996; 53:9433-9441. [PMID: 9982448 DOI: 10.1103/physrevb.53.9433] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Rendell JM, Carbotte JP. Effects of gap and band anisotropy on spin susceptibility in the oxide superconductors. Phys Rev B Condens Matter 1996; 53:5889-5900. [PMID: 9984198 DOI: 10.1103/physrevb.53.5889] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Marsiglio F, Carbotte JP. Signatures of the electron-phonon interaction in the far-infrared. Phys Rev B Condens Matter 1995; 52:16192-16198. [PMID: 9981003 DOI: 10.1103/physrevb.52.16192] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Atkinson WA, Carbotte JP. Effect of proximity coupling of chains and planes on the penetration-depth anisotropy in YBa2Cu3O7. Phys Rev B Condens Matter 1995; 52:10601-10609. [PMID: 9980113 DOI: 10.1103/physrevb.52.10601] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Atkinson WA, Carbotte JP. Critical Josephson current in a model Pb/YBa2Cu3O7- delta junction. Phys Rev B Condens Matter 1995; 52:6894-6902. [PMID: 9981919 DOI: 10.1103/physrevb.52.6894] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Branch D, Carbotte JP. Raman electronic continuum in a spin-fluctuation model for superconductivity. Phys Rev B Condens Matter 1995; 52:603-614. [PMID: 9979640 DOI: 10.1103/physrevb.52.603] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Atkinson WA, Carbotte JP. Penetration-depth calculations in the ab and c directions in a layered S/N superconductor. Phys Rev B Condens Matter 1995; 51:16371-16379. [PMID: 9978620 DOI: 10.1103/physrevb.51.16371] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Carbotte JP, Jiang C, Basov DN, Timusk T. Evidence for d-wave superconductivity in YBa2Cu3O7- delta from far-infrared conductivity. Phys Rev B Condens Matter 1995; 51:11798-11805. [PMID: 9977921 DOI: 10.1103/physrevb.51.11798] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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O'Donovan C, Branch D, Carbotte JP, Preston JS. Josephson current in an anisotropic d-wave model. Phys Rev B Condens Matter 1995; 51:6588-6593. [PMID: 9977193 DOI: 10.1103/physrevb.51.6588] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Nicol EJ, Carbotte JP. Effect of Abrikosov-Gor'kov impurities on Raman shifts and changes in phonon widths. Phys Rev B Condens Matter 1994; 50:10243-10249. [PMID: 9975107 DOI: 10.1103/physrevb.50.10243] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Jiang C, Carbotte JP. Phonon self-energy in a d-wave superconductor with retardation, finite temperature, and impurities. Phys Rev B Condens Matter 1994; 50:9449-9455. [PMID: 9974997 DOI: 10.1103/physrevb.50.9449] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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