Abstract
Motivated by the overwhelming evidence some type of quantum criticality underlies the power-law for the optical conductivity and T−linear resistivity in the cuprates, we demonstrate here how a scale-invariant or unparticle sector can lead to a unifying description of the observed scaling forms. We adopt the continuous mass formalism or multi band (flavor) formalism of the unparticle sector by letting various microscopic parameters be mass-dependent. In particular, we show that an effective mass that varies with the flavor index as well as a running band edge and lifetime capture the AC and DC transport phenomenology of the cuprates. A key consequence of the running mass is that the effective dynamical exponent can differ from the underlying bare critical exponent, thereby providing a mechanism for realizing the fractional values of the dynamical exponent required in a previous analysis [1]. We also predict that regardless of the bare dynamical exponent, z, a non-zero anomalous dimension for the current is required. Physically, the anomalous dimension arises because the charge depends on the flavor, mass or energy. The equivalent phenomenon in a d + 1 gravitational construction is the running of the charge along the radial direction. The nature of the superconducting instability in the presence of scale invariant stuff shows that the transition temperature is not necessarily a monotonic function of the pairing interaction.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.A. Hartnoll and A. Karch, Scaling theory of the cuprate strange metals, Phys. Rev. B 91 (2015) 155126 [arXiv:1501.03165] [INSPIRE].
C.M. Varma, P.B. Littlewood, S. Schmitt-Rink, E. Abrahams and A.E. Ruckenstein, Phenomenology of the normal state of Cu-O high-temperature superconductors, Phys. Rev. Lett. 63 (1989) 1996 [INSPIRE].
S. Chakravarty, B.I. Halperin and D.R. Nelson, Two-dimensional quantum Heisenberg antiferromagnet at low temperatures, Phys. Rev. B 39 (1989) 2344 [INSPIRE].
Y. Ando et al., Quantum phase transitions in the cuprate superconductor Bi2Sr2−x La x CuO6+δ , Phys. Rev. Lett. 92 (2004) 247004 [cond-mat/0402025].
F.F. Balakirev et al., Signature of optimal doping in Hall-effect measurements on a high-temperature superconductor, Nature 424 (2003) 912.
T. Valla et al., Evidence for quantum critical behavior in the optimally doped cuprate Bi2Sr2CaCu2O8+Δ, Science 285 (1999) 2110.
C. Panagopoulos et al., Exposing the spin-glass ground state of the nonsuperconducting La2−x Sr x Cu1−y Zn y O4 high-T c oxide, Phys. Rev. B 69 (2004) 144510.
D. van der Marel et al., Quantum critical behaviour in a high-T c superconductor, Nature 425 (2003) 271 [INSPIRE].
P.W. Anderson, Infrared conductivity of cuprate metals: detailed fit using Luttinger-liquid theory, Phys. Rev. B 55 (1997) 11785.
A. El Azrak et al., Infrared properties of YBa2Cu3O7 and Bi2Sr2Ca n−1Cu n O2n+4 thin films, Phys. Rev. B 49 (1994) 9846.
Z. Schlesinger et al., Superconducting energy gap and normal-state conductivity of a single-domain YBa2Cu3O7 crystal, Phys. Rev. Lett. 65 (1990) 801.
J. Hwang, T. Timusk and G.D. Gu, Doping dependent optical properties of Bi2Sr2CaCu2O8+δ , J. Phys. Cond. Matter 19 (2007) 125208 [cond-mat/0607653].
D.N. Basov, R.D. Averitt, D. van der Marel, M. Dressel and K. Haule, Electrodynamics of correlated electron materials, Rev. Mod. Phys. 83 (2011) 471 [arXiv:1106.2309].
P. Phillips and C. Chamon, Breakdown of one-parameter scaling in quantum critical scenarios for high-temperature copper-oxide superconductors, Phys. Rev. Lett. 95 (2005) 107002 [cond-mat/0412179].
X.-G. Wen, Scaling theory of conserved current and universal amplitudes at anisotropic critical points, Phys. Rev. B 46 (1992) 2655.
A.A. Patel, P. Strack and S. Sachdev, Hyperscaling at the spin density wave quantum critical point in two dimensional metals, Phys. Rev. B 92 (2015) 165105 [arXiv:1507.05962] [INSPIRE].
H. Georgi, Unparticle physics, Phys. Rev. Lett. 98 (2007) 221601 [hep-ph/0703260] [INSPIRE].
P.W. Phillips, B.W. Langley and J.A. Hutasoit, Un-Fermi liquids: unparticles in strongly correlated electron matter, Phys. Rev. B 88 (2013) 115129 [arXiv:1305.0006] [INSPIRE].
P.W. Phillips, Beyond particles: unparticles in strongly correlated electron matter, in Quantum criticality in condensed matter, J. Jedrzejewski ed., World Scientific, Singapore (2015), pg. 133 [arXiv:1412.1098] [INSPIRE].
A. Karch, Multiband models for field theories with anomalous current dimension, JHEP 07 (2015) 021 [arXiv:1504.02478] [INSPIRE].
K. Limtragool and P. Phillips, Power-law optical conductivity from unparticles: application to the cuprates, Phys. Rev. B 92 (2015) 155128 [arXiv:1506.00649] [INSPIRE].
J. Terning, Gauging nonlocal Lagrangians, Phys. Rev. D 44 (1991) 887 [INSPIRE].
G. Cacciapaglia, G. Marandella and J. Terning, Colored unparticles, JHEP 01 (2008) 070 [arXiv:0708.0005] [INSPIRE].
R. Basu, D. Choudhury and H.S. Mani, Fermionic un-particles, gauge interactions and the β-function, Eur. Phys. J. C 61 (2009) 461 [arXiv:0803.4110] [INSPIRE].
S.K. Domokos and G. Gabadadze, Unparticles as the holographic dual of gapped AdS gravity, Phys. Rev. D 92 (2015) 126011 [arXiv:1509.03285] [INSPIRE].
D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of massive gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].
R.A. Davison, Momentum relaxation in holographic massive gravity, Phys. Rev. D 88 (2013) 086003 [arXiv:1306.5792] [INSPIRE].
N.G. Deshpande and X.-G. He, Unparticle realization through continuous mass scale invariant theories, Phys. Rev. D 78 (2008) 055006 [arXiv:0806.2009] [INSPIRE].
A.V. Balatsky, Superconducting instability in a non-Fermi liquid scaling approach, Phil. Mag. Lett. 68 (1993) 251 [cond-mat/9308008].
J.P.F. LeBlanc and A.G. Grushin, Unparticle mediated superconductivity, New J. Phys. 17 (2015) 033039 [arXiv:1407.8492] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1511.02868
Guggenheim Fellow. (Philip W. Phillips)
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Karch, A., Limtragool, K. & Phillips, P.W. Unparticles and anomalous dimensions in the cuprates. J. High Energ. Phys. 2016, 175 (2016). https://doi.org/10.1007/JHEP03(2016)175
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2016)175