Abstract
We investigate holographic fermions in uni-directional striped phases, where the breaking of translational invariance can be generated either spontaneously or explicitly. We solve the Dirac equation for a probe fermion in the associated background geometry. When the spatial modulation effect becomes sufficiently strong, we see a spectral weight suppression whenever the Fermi surface is larger than the first Brillouin zone. This leads to the gradual disappearance of the Fermi surface along the symmetry breaking direction, in all of the cases we have examined. This effect appears to be a generic consequence of strong inhomogeneities, independently of whether translational invariance is broken spontaneously or explicitly. The resulting Fermi surface is segmented and has features reminiscent of Fermi arcs.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Henningson and K. Sfetsos, Spinors and the AdS/CFT correspondence, Phys. Lett.B 431 (1998) 63 [hep-th/9803251] [INSPIRE].
W. Mueck and K.S. Viswanathan, Conformal field theory correlators from classical field theory on anti-de Sitter space. 2. Vector and spinor fields, Phys. Rev.D 58 (1998) 106006 [hep-th/9805145] [INSPIRE].
S.-S. Lee, A Non-Fermi Liquid from a Charged Black Hole: A Critical Fermi Ball, Phys. Rev.D 79 (2009) 086006 [arXiv:0809.3402] [INSPIRE].
H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, Phys. Rev.D 83 (2011) 065029 [arXiv:0903.2477] [INSPIRE].
M. Cubrovic, J. Zaanen and K. Schalm, String Theory, Quantum Phase Transitions and the Emergent Fermi-Liquid, Science325 (2009) 439 [arXiv:0904.1993] [INSPIRE].
T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, Phys. Rev.D 83 (2011) 125002 [arXiv:0907.2694] [INSPIRE].
N. Iqbal, H. Liu and M. Mezei, Lectures on holographic non-Fermi liquids and quantum phase transitions, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 2010). String Theory and Its Applications: From meV to the Planck Scale, Boulder, Colorado, U.S.A., 1-25 June 2010, pp. 707-816 (2011) [https://doi.org/10.1142/9789814350525_0013] [arXiv:1110.3814] [INSPIRE].
A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys.9 (2013) 649 [arXiv:1212.2998] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP05 (2014) 101 [arXiv:1311.5157] [INSPIRE].
A. Bagrov, N. Kaplis, A. Krikun, K. Schalm and J. Zaanen, Holographic fermions at strong translational symmetry breaking: a Bianchi-VII case study, JHEP11 (2016) 057 [arXiv:1608.03738] [INSPIRE].
Y. Liu, K. Schalm, Y.-W. Sun and J. Zaanen, Lattice Potentials and Fermions in Holographic non Fermi-Liquids: Hybridizing Local Quantum Criticality, JHEP10 (2012) 036 [arXiv:1205.5227] [INSPIRE].
Y. Ling, C. Niu, J.-P. Wu, Z.-Y. Xian and H.-b. Zhang, Holographic Fermionic Liquid with Lattices, JHEP07 (2013) 045 [arXiv:1304.2128] [INSPIRE].
E. Fradkin, S.A. Kivelson and J.M. Tranquada, Colloquium: Theory of intertwined orders in high temperature superconductors, Rev. Mod. Phys.87 (2015) 457.
S. Cremonini, L. Li and J. Ren, Holographic Fermions in Striped Phases, JHEP12 (2018) 080 [arXiv:1807.11730] [INSPIRE].
M.R. Norman et al., Destruction of the Fermi Surface in Underdoped High Tc Superconductors, Nature392 (1998) 157 [cond-mat/9710163].
A. Kanigel et al., Evolution of the pseudogap from Fermi arcs to the nodal liquid, Nat. Phys.2 (2006) 447.
A. Kanigel et al., Protected Nodes and the Collapse of Fermi Arcs in High-T cCuprate Superconductors, Phys. Rev. Lett.99 (2007) 157001.
Y. Ling, P. Liu, C. Niu, J.-P. Wu and Z.-Y. Xian, Holographic fermionic system with dipole coupling on Q-lattice, JHEP12 (2014) 149 [arXiv:1410.7323] [INSPIRE].
G. Vanacore, S.T. Ramamurthy and P.W. Phillips, Evolution of Holographic Fermi Arcs from a Mott Insulator, JHEP09 (2018) 009 [arXiv:1508.02390] [INSPIRE].
S. Chakrabarti, D. Maity and W. Wahlang, Probing the Holographic Fermi Arc with scalar field: Numerical and analytical study, JHEP07 (2019) 037 [arXiv:1902.08826] [INSPIRE].
C. Cosnier-Horeau and S.S. Gubser, Holographic Fermi surfaces at finite temperature in top-down constructions, Phys. Rev.D 91 (2015) 066002 [arXiv:1411.5384] [INSPIRE].
S. Franco, A. Garcia-Garcia and D. Rodriguez-Gomez, A General class of holographic superconductors, JHEP04 (2010) 092 [arXiv:0906.1214] [INSPIRE].
F. Aprile and J.G. Russo, Models of Holographic superconductivity, Phys. Rev.D 81 (2010) 026009 [arXiv:0912.0480] [INSPIRE].
R.-G. Cai, S. He, L. Li and L.-F. Li, Entanglement Entropy and Wilson Loop in Stúckelberg Holographic Insulator/Superconductor Model, JHEP10 (2012) 107 [arXiv:1209.1019] [INSPIRE].
E. Kiritsis and L. Li, Holographic Competition of Phases and Superconductivity, JHEP01 (2016) 147 [arXiv:1510.00020] [INSPIRE].
M. Headrick, S. Kitchen and T. Wiseman, A New approach to static numerical relativity and its application to Kaluza-Klein black holes, Class. Quant. Grav.27 (2010) 035002 [arXiv:0905.1822] [INSPIRE].
S. Cremonini, L. Li and J. Ren, Holographic Pair and Charge Density Waves, Phys. Rev.D 95 (2017) 041901 [arXiv:1612.04385] [INSPIRE].
S. Cremonini, L. Li and J. Ren, Intertwined Orders in Holography: Pair and Charge Density Waves, JHEP08 (2017) 081 [arXiv:1705.05390] [INSPIRE].
R.-G. Cai, L. Li, Y.-Q. Wang and J. Zaanen, Intertwined Order and Holography: The Case of Parity Breaking Pair Density Waves, Phys. Rev. Lett.119 (2017) 181601 [arXiv:1706.01470] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic charge density waves, Phys. Rev.D 87 (2013) 126008 [arXiv:1303.4398] [INSPIRE].
Y. Ling, C. Niu, J. Wu, Z. Xian and H.-b. Zhang, Metal-insulator Transition by Holographic Charge Density Waves, Phys. Rev. Lett.113 (2014) 091602 [arXiv:1404.0777] [INSPIRE].
S.S. Gubser and J. Ren, Analytic fermionic Green’s functions from holography, Phys. Rev.D 86 (2012) 046004 [arXiv:1204.6315] [INSPIRE].
T. Andrade and A. Krikun, Commensurate lock-in in holographic non-homogeneous lattices, JHEP03 (2017) 168 [arXiv:1701.04625] [INSPIRE].
A. Krikun, Holographic discommensurations, JHEP12 (2018) 030 [arXiv:1710.05801] [INSPIRE].
P. Bak, Commensurate phases, incommensurate phases and the devil’s staircase, Rept. Prog. Phys.45 (1982) 587.
N. Gnezdilov, A. Krikun, K. Schalm and J. Zaanen, Isolated zeros in the spectral function as signature of a quantum continuum, Phys. Rev.B 99 (2019) 165149 [arXiv:1810.10429] [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: 1906.02753
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Cremonini, S., Li, L. & Ren, J. Spectral weight suppression and Fermi arc-like features with strong holographic lattices. J. High Energ. Phys. 2019, 14 (2019). https://doi.org/10.1007/JHEP09(2019)014
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2019)014