Singular or non-Fermi liquids

Varma, C. M.; Nussinov, Zohar; Saarloos, Wim van

doi:10.1016/s0370-1573(01)00060-6

Cited by 350 publications

(420 citation statements)

References 279 publications

(470 reference statements)

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“…For example, if the Fermi quasiparticles are coupled to a gapless boson (as is the case in many field-theoretical constructions of non-Fermi liquids; see e.g. [1,[54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70] and references therein), small-momentum scattering is strongly preferred because of the larger phase space available to the gapless boson at smaller momenta. However, this small-momentum scattering does not degrade the current and so contributes differently to the conductivity than it does to the single-particle lifetime, meaning that the resistivity grows with temperature with a higher power than the single-particle scattering rate [64].…”

Section: Discussionmentioning

confidence: 99%

“…Since the mid 1980s, however, there has been an accumulation of metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory [1,2]. A prime example of these so-called non-Fermi liquids is the strange metal phase of the high T c cuprates, a funnel-shaped region in the phase diagram emanating from optimal doping at T ¼ 0, the understanding of which is believed to be essential for deciphering the mechanism for high T c superconductivity.…”

Section: Introductionmentioning

confidence: 99%

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Charge transport by holographic Fermi surfaces

Faulkner

Iqbal²,

Liu

et al. 2013

Phys. Rev. D

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We compute the contribution to the conductivity from holographic Fermi surfaces obtained from probe fermions in an AdS charged black hole. This requires calculating a certain part of the one-loop correction to a vector propagator on the charged black hole geometry. We find that the current dissipation is as efficient as possible and the transport lifetime coincides with the single-particle lifetime. In particular, in the case where the spectral density is that of a marginal Fermi liquid, the resistivity is linear in temperature.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Charge transport by holographic Fermi surfaces

Faulkner

Iqbal²,

Liu

et al. 2013

Phys. Rev. D

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“…The observation of a nearly quadratic increase as a function of energy at the nodal point indicates a Fermi liquid behavior and explains the quadratic temperature dependence of the inplane resistivity above the superconducting transition temperature [45]. The nearly linear increase at the antinodal point signals the proximity to a marginal Fermi liquid [46]. Near the center of the BZ, at k = ( 3π 8 , 0) the total life-time broadening amounts to 65 % of E B [see Fig.…”

mentioning

confidence: 95%

High-Energy Anomaly in the Angle-Resolved Photoemission Spectra ofNd2−xCexCuO4:

et al. 2014

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We used polarization-dependent angle-resolved photoemission spectroscopy (ARPES) to study the high-energy anomaly (HEA) in the dispersion of Nd2−xCexCuO4, (x = 0.123). We have found that at particular photon energies the anomalous, waterfalllike dispersion gives way to a broad, continuous band. This suggests that the HEA is a matrix element effect: it arises due to a suppression of the intensity of the broadened quasi-particle band in a narrow momentum range. We confirm this interpretation experimentally, by showing that the HEA appears when the matrix element is suppressed deliberately by changing the light polarization. Calculations of the matrix element using atomic wave functions and simulation of the ARPES intensity with one-step model calculations provide further proof for this scenario. The possibility to detect the full quasi-particle dispersion further allows us to extract the high-energy self-energy function near the center and at the edge of the Brillouin zone. One of the unique assets of angle-resolved photoemission spectroscopy (ARPES) is the ability to determine the spectral function A(ω, k) in energy and momentum space. The finite width and deviation of the dispersion from that calculated in an independent particle model are interpreted in the majority of cases in terms of manybody effects [1]. In the cuprate high-T c superconductors, various kinks in the dispersion have been discovered which were analyzed in terms of a coupling of the charge carriers to bosonic excitations possibly mediating high-T c superconductivity in these materials. Besides the kinks in the low binding energy (E B ) region (E B ≤ 0.1 eV) at E B = E H 0.3 eV the band appears to bend sharply and seems to proceed almost vertically towards the valence bands. This phenomenon has been termed "waterfall" or high-energy anomaly (HEA) [2]. The HEA has been observed in undoped cuprates [3] as well as in their hole-doped [2, 4-13], and electron-doped derivatives [4,[13][14][15]. In the latter two systems E H shows a d-wave momentum dependence being larger along the nodal direction and smaller near the antinodal point opposite to the momentum dependence of the d-wave superconducting gap [6,12,14]. The values of E H exhibit a difference of ≈ 0.4 eV between hole doped and electron doped cuprates [4]. This difference was interpreted in terms of a shift of the chemical potential [14]. The experimental studies were accompanied by numerous theoretical papers [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].For the phenomenon of the HEA, a number of explanations have been suggested including Mott-Hubbard models with a transition from the coherent quasi-particle dispersion to the incoherent lower Hubbard band [5,18,21,26,32], a disintegration of the low-energy branch into a holon and spinon band due to a spin charge separation [2], a coupling to spin fluctuations [9,17,19,29,33], a coupling to phonons [7], string excitations of spinpolarons [32], a bifurcation of the quasi-particle band due to an excitation of a bosonic mode of ...

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“…The bulk of the large theoretical literature [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50] dealing with this subject that evolved since then departs from an assumption dating back to the seminal work of Herz in the 1970's [51]. This involves the nature of the ultraviolet: at some relatively short time scale where the electron system has closely approached a Fermi-liquid the influence of the critical order parameter fluctuations become noticable.…”

Section: Introductionmentioning

confidence: 99%

BCS superconductivity in quantum critical metals

She

Zaanen

2009

Phys. Rev. B

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[file: qcbcs-arxiv2])We present a simple phenomenological scaling theory for the pairing instability of a quantum critical metal. It can be viewed as a minimal generalization of the classical Bardeen-Cooper-Schrieffer theory of superconductivity for normal Fermi-liquid metals. We assume that attractive interactions are induced in the fermion system by an external 'bosonic glue' that is strongly retarded. Resting on the small Migdal parameter, all the required information from the fermion system needed to address the superconductivity enters through the pairing susceptibility. Asserting that the normal state is a strongly interacting quantum critical state of fermions, the form of this susceptibility is governed by conformal invariance and one only has the scaling dimension of the pair operator as free parameter. Within this scaling framework, conventional BCS theory appears as the 'marginal' case but it is now easily generalized to the (ir)relevant scaling regimes. In the relevant regime an algebraic singularity takes over from the BCS logarithm with the obvious effect that the pairing instability becomes stronger. However, it is more surprising that this effect is strongest for small couplings and small Migdal parameters, highlighting an unanticipated important role of retardation. Using exact forms for the finite temperature pair susceptibility from 1+1D conformal field theory as models, we study the transition temperatures, finding that the gap to transition temperature ratio's are generically large compared to the BCS case, showing however an opposite trend as function of the coupling strength compared to conventional Migdal-Eliashberg theory. We show that our scaling theory naturally produces the superconducting 'domes' surrounding the quantum critical points, even when the coupling to the glue itself is not changing at all. We argue that hidden relations will exist between the location of the cross-over lines to the Fermi-liquids away from the quantum critical points , and the detailed form of the dome when the glue strength is independent of the zero temperature control parameter. Finally, we discuss the behavior of the orbital limited upper critical magnetic field as function of the zero temperature coupling constant. Compared to the variation of the transition temperature, the critical field might show a much stronger variation pending the value of the dynamical critical exponent.

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Singular or non-Fermi liquids

Cited by 350 publications

References 279 publications

Charge transport by holographic Fermi surfaces

Charge transport by holographic Fermi surfaces

High-Energy Anomaly in the Angle-Resolved Photoemission Spectra ofNd2−xCexCuO4:

BCS superconductivity in quantum critical metals

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