- Letter
- Open Access
Thermoelectric transport properties of gapless pinned charge density waves
Phys. Rev. B 106, L041118 – Published 29 July, 2022
DOI: https://doi.org/10.1103/PhysRevB.106.L041118
Abstract
Quantum strongly correlated matter exhibits properties which are not easily explainable in the conventional framework of Fermi liquids. Universal effective field theory tools are applicable in these cases regardless of the microscopic details of the quantum system, since they are based on symmetries. It is necessary, however, to construct these effective tools in full generality, avoiding restrictions coming from particular microscopic descriptions which may inadequately constrain the coefficients that enter in the effective theory. In this work we demonstrate with explicit examples how the hydrodynamic coefficients, which have been recently reinstated in the effective theory of pinned charge density waves (CDWs), can affect the phenomenology of the thermoelectric transport in strongly correlated quantum matter. Our examples, based on two classes of holographic models with pinned CDW, have microscopics which are conceptually different from Fermi liquids. Therefore, the above transport coefficients are nonzero, contrary to the conventional approach. We show how these coefficients allow one to take into account the change of sign of the Seebeck coefficient and the low resistivity of the CDW phase of the cuprate high temperature superconductors, without referring to the effects of Fermi surface reconstruction.
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References (85)
- R. Arpaia and G. Ghiringhelli, Charge order at high temperature in cuprate superconductors, J. Phys. Soc. Jpn. 90, 111005 (2021).
- C. Collignon, A. Ataei, A. Gourgout, S. Badoux, M. Lizaire, A. Legros, S. Licciardello, S. Wiedmann, J.-Q. Yan, J.-S. Zhou et al., Thermopower across the phase diagram of the cuprate : Signatures of the pseudogap and charge density wave phases, Phys. Rev. B 103, 155102 (2021).
- M. Hucker, V. Kataev, J. Pommer, O. Baberski, W. Schlabitz, and B. Büchner, Consequences of stripe order for the transport properties of rare earth doped , J. Phys. Chem. Solids 59, 1821 (1998).
- Y. Nakamura and S. Uchida, Anisotropic transport properties of single-crystal : Effect of the structural phase transition, Phys. Rev. B 46, 5841 (1992).
- Q. Li, M. Hücker, G. D. Gu, A. M. Tsvelik, and J. M. Tranquada, Two-Dimensional Superconducting Fluctuations in Stripe-Ordered , Phys. Rev. Lett. 99, 067001 (2007).
- J. Chang, R. Daou, C. Proust, D. LeBoeuf, N. Doiron-Leyraud, F. Laliberté, B. Pingault, B. Ramshaw, R. Liang, D. Bonn et al., Nernst and Seebeck Coefficients of the Cuprate Superconductor : A study of Fermi Surface Reconstruction, Phys. Rev. Lett. 104, 057005 (2010).
- N. Doiron-Leyraud, S. Lepault, O. Cyr-Choiniere, B. Vignolle, G. Grissonnanche, F. Laliberté, J. Chang, N. Barišić, M. K. Chan, L. Ji et al., Hall, Seebeck, and Nernst Coefficients of Underdoped : Fermi-Surface Reconstruction in an Archetypal Cuprate Superconductor, Phys. Rev. X 3, 021019 (2013).
- S. Badoux, S. A. A. Afshar, B. Michon, A. Ouellet, S. Fortier, D. LeBoeuf, T. P. Croft, C. Lester, S.M. Hayden, H. Takagi et al., Critical Doping for the Onset of Fermi-Surface Reconstruction by Charge-Density-Wave Order in the Cuprate Superconductor , Phys. Rev. X 6, 021004 (2016).
- F. Laliberté, J. Chang, N. Doiron-Leyraud, E. Hassinger, R. Daou, M. Rondeau, B. Ramshaw, R. Liang, D. Bonn, W. Hardy et al., Fermi-surface reconstruction by stripe order in cuprate superconductors, Nat. Commun. 2, 432 (2011).
- B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen, From quantum matter to high-temperature superconductivity in copper oxides, Nature (London) 518, 179 (2015).
- T. J. Reber, X. Zhou, N. Plumb, S. Parham, J. Waugh, Y. Cao, Z. Sun, H. Li, Q. Wang, J. Wen et al., A unified form of low-energy nodal electronic interactions in hole-doped cuprate superconductors, Nat. Commun. 10, 5737 (2019).
- J. Ayres, M. Berben, M. Čulo, Y.-T. Hsu, E. van Heumen, Y. Huang, J. Zaanen, T. Kondo, T. Takeuchi, J. Cooper et al., Incoherent transport across the strange-metal regime of overdoped cuprates, Nature (London) 595, 661 (2021).
- A. Gourgout, G. Grissonnanche, F. Laliberté, A. Ataei, L. Chen, S. Verret, J.-S. Zhou, J. Mravlje, A. Georges, N. Doiron-Leyraud et al., Seebeck Coefficient in a Cuprate Superconductor: Particle-Hole Asymmetry in the Strange Metal Phase and Fermi Surface Transformation in the Pseudogap Phase, Phys. Rev. X 12, 011037 (2022).
- A. Georges and J. Mravlje, Skewed non-Fermi liquids and the Seebeck effect, Phys. Rev. Research 3, 043132 (2021).
- P. Chaikin and T. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 2000).
- L. V. Delacrétaz, B. Goutéraux, S. A. Hartnoll, and A. Karlsson, Bad metals from fluctuating density waves, SciPost Phys. 3, 025 (2017).
- L. V. Delacrétaz, B. Goutéraux, S. A. Hartnoll, and A. Karlsson, Theory of hydrodynamic transport in fluctuating electronic charge density wave states, Phys. Rev. B 96, 195128 (2017).
- L. V. Delacrétaz, B. Goutéraux, and V. Ziogas, Damping of Pseudo-Goldstone Fields, Phys. Rev. Lett. 128, 141601 (2022).
- J. Armas, A. Jain, and R. Lier, Approximate symmetries, pseudo-Goldstones, and the second law of thermodynamics, arXiv:2112.14373.
- G. Grüner, The dynamics of charge-density waves, Rev. Mod. Phys. 60, 1129 (1988).
- J. Zaanen, Y.-W. Sun, Y. Liu, and K. Schalm, Holographic Duality in Condensed Matter Physics (Cambridge University Press, Cambridge, 2015).
- S. A. Hartnoll, A. Lucas, and S. Sachdev, Holographic Quantum Matter (MIT Press, 2018).
- A. Amoretti, D. Areán, B. Goutéraux, and D. Musso, Effective holographic theory of charge density waves, Phys. Rev. D 97, 086017 (2018).
- B. Goutéraux, N. Jokela, and A. Pönni, Incoherent conductivity of holographic charge density waves, J. High Energy Phys. 07 (2018) 004.
- A. Donos, J. P. Gauntlett, T. Griffin, and V. Ziogas, Incoherent transport for phases that spontaneously break translations, J. High Energy Phys. 04 (2018) 053.
- A. Amoretti, D. Areán, B. Goutéraux, and D. Musso, Diffusion and universal relaxation of holographic phonons, J. High Energy Phys. 10 (2019) 068.
- M. Baggioli and B. Goutéraux, Effective and holographic theories of strongly-correlated phases of matter with broken translations, arXiv:2203.03298.
- J. Armas and A. Jain, Viscoelastic hydrodynamics and holography, J. High Energy Phys. 01 (2020) 126.
- J. Armas and A. Jain, Hydrodynamics for charge density waves and their holographic duals, Phys. Rev. D 101, 121901(R) (2020).
- H. Takagi, B. Batlogg, H. L. Kao, J. Kwo, R. J. Cava, J. J. Krajewski, and W. F. Peck, Jr., Systematic Evolution of Temperature-Dependent Resistivity in , Phys. Rev. Lett. 69, 2975 (1992).
- Y. Ando, G. S. Boebinger, A. Passner, T. Kimura, and K. Kishio, Logarithmic Divergence of both In-Plane and Out-of-Plane Normal-State Resistivities of Superconducting in the Zero-Temperature Limit, Phys. Rev. Lett. 75, 4662 (1995).
- R. Arpaia, E. Andersson, E. Trabaldo, T. Bauch, and F. Lombardi, Probing the phase diagram of cuprates with thin films and nanowires, Phys. Rev. Materials 2, 024804 (2018).
- F. Laliberté, W. Tabis, S. Badoux, B. Vignolle, D. Destraz, N. Momono, T. Kurosawa, K. Yamada, H. Takagi, N. Doiron-Leyraud et al., Origin of the metal-to-insulator crossover in cuprate superconductors, arXiv:1606.04491.
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.106.L041118 for the details of the two holographic models considered, the details of our fitting procedure, and a set of checks on the AC results, as well as some additional results in a holographic model based on helical Bianchi VII geometry.
- S. de Haro, S. N. Solodukhin, and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217, 595 (2001).
- B. Withers, Black branes dual to striped phases, Classical Quantum Gravity 30, 155025 (2013).
- A. Amoretti, D. Arean, D. K. Brattan, and N. Magnoli, Hydrodynamic magneto-transport in charge density wave states, J. High Energy Phys. 05 (2021) 027.
- A. Amoretti, D. Arean, D. K. Brattan, and L. Martinoia, Hydrodynamic magneto-transport in holographic charge density wave states, J. High Energy Phys. 11 (2021) 011.
- T. Andrade, M. Baggioli, and A. Krikun, Phase relaxation and pattern formation in holographic gapless charge density waves, J. High Energy Phys. 03 (2021) 292.
- P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A: Math. Theor. 45, 473001 (2012).
- M. Ammon, M. Baggioli, S. Gray, S. Grieninger, and A. Jain, On the hydrodynamic description of holographic viscoelastic models, Phys. Lett. B 808, 135691 (2020).
- A. Amoretti, D. Areán, B. Goutéraux, and D. Musso, Universal Relaxation in a Holographic Metallic Density Wave Phase, Phys. Rev. Lett. 123, 211602 (2019).
- R. A. Davison and B. Goutéraux, Dissecting holographic conductivities, J. High Energy Phys. 09 (2015) 090.
- R. A. Davison, B. Goutéraux, and S. A. Hartnoll, Incoherent transport in clean quantum critical metals, J. High Energy Phys. 10 (2015) 112.
- R. A. Davison, S. A. Gentle, and B. Goutéraux, Slow Relaxation and Diffusion in Holographic Quantum Critical Phases, Phys. Rev. Lett. 123, 141601 (2019).
- R. A. Davison, S. A. Gentle, and B. Goutéraux, Impact of irrelevant deformations on thermodynamics and transport in holographic quantum critical states, Phys. Rev. D 100, 086020 (2019).
- M. Ammon, M. Baggioli, and A. Jiménez-Alba, A unified description of translational symmetry breaking in holography, J. High Energy Phys. 09 (2019) 124.
- A. Donos, D. Martin, C. Pantelidou, and V. Ziogas, Incoherent hydrodynamics and density waves, Class. Quantum Grav. 37, 045005 (2020).
- T. Andrade and A. Krikun, Coherent vs incoherent transport in holographic strange insulators, J. High Energy Phys. 05 (2019) 119.
- M. Baggioli, Homogeneous holographic viscoelastic models and quasicrystals, Phys. Rev. Research 2, 022022(R) (2020).
- M. Baggioli and M. Landry, Effective field theory for quasicrystals and phasons dynamics, SciPost Phys. 9, 062 (2020).
- C. P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A: Math. Theor. 42, 343001 (2009).
- S. A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quantum Grav. 26, 224002 (2009).
- R. Flauger, E. Pajer, and S. Papanikolaou, A striped holographic superconductor, Phys. Rev. D 83, 064009 (2011).
- Y. Liu, K. Schalm, Y.-W. Sun, and J. Zaanen, Lattice potentials and fermions in holographic non Fermi-liquids: Hybridizing local quantum criticality, J. High Energy Phys. 10 (2012) 036.
- G. T. Horowitz, J. E. Santos, and D. Tong, Optical conductivity with holographic lattices, J. High Energy Phys. 07 (2012) 168.
- G. T. Horowitz, J. E. Santos, and D. Tong, Further evidence for lattice-induced scaling, J. High Energy Phys. 11 (2012) 102.
- A. Donos and J. P. Gauntlett, The thermoelectric properties of inhomogeneous holographic lattices, J. High Energy Phys. 01 (2015) 035.
- M. Rangamani, M. Rozali, and D. Smyth, Spatial modulation and conductivities in effective holographic theories, J. High Energy Phys. 07 (2015) 024.
- B. W. Langley, G. Vanacore, and P. W. Phillips, Absence of power-law mid-infrared conductivity in gravitational crystals, J. High Energy Phys. 10 (2015) 163.
- A. Donos, Striped phases from holography, J. High Energy Phys. 05 (2013) 059.
- B. Withers, The moduli space of striped black branes, arXiv:1304.2011.
- A. Donos and J. P. Gauntlett, On the thermodynamics of periodic AdS black branes, J. High Energy Phys. 10 (2013) 038.
- A. Krikun, Holographic discommensurations, J. High Energy Phys. 12 (2018) 030.
- T. Andrade, A. Krikun, K. Schalm, and J. Zaanen, Doping the holographic Mott insulator, Nat. Phys. 14, 1049 (2018).
- T. Andrade and A. Krikun, Commensurate lock-in in holographic non-homogeneous lattices, J. High Energy Phys. 03 (2017) 168.
- T. Andrade and B. Withers, A simple holographic model of momentum relaxation, J. High Energy Phys. 05 (2014) 101.
- A. Donos and J. P. Gauntlett, Holographic Q-lattices, J. High Energy Phys. 04 (2014) 040.
- M. Baggioli and O. Pujolas, Electron-Phonon Interactions, Metal-Insulator Transitions, and Holographic Massive Gravity, Phys. Rev. Lett. 114, 251602 (2015).
- L. Alberte, M. Baggioli, A. Khmelnitsky, and O. Pujolas, Solid holography and massive gravity, J. High Energy Phys. 02 (2016) 114.
- M. Baggioli, K.-Y. Kim, L. Li, and W.-J. Li, Holographic Axion model: a simple gravitational tool for quantum matter, Sci. China: Phys., Mech. Astron. 64, 270001 (2021).
- S. Nakamura, H. Ooguri, and C.-S. Park, Gravity dual of spatially modulated phase, Phys. Rev. D 81, 044018 (2010).
- H. Ooguri and C.-S. Park, Holographic end-point of spatially modulated phase transition, Phys. Rev. D 82, 126001 (2010).
- A. Donos and J. P. Gauntlett, Black holes dual to helical current phases, Phys. Rev. D 86, 064010 (2012).
- A. Donos and S. A. Hartnoll, Interaction-driven localization in holography, Nat. Phys. 9, 649 (2013).
- A. Donos, B. Goutéraux, and E. Kiritsis, Holographic metals and insulators with helical symmetry, J. High Energy Phys. 09 (2014) 038.
- A. Donos, J. P. Gauntlett, T. Griffin, N. Lohitsiri, and L. Melgar, Holographic DC conductivity and Onsager relations, J. High Energy Phys. 07 (2017) 006.
- A. Donos, J. P. Gauntlett, T. Griffin, and L. Melgar, DC conductivity of magnetised holographic matter, J. High Energy Phys. 01 (2016) 113.
- E. Banks, A. Donos, and J. P. Gauntlett, Thermoelectric DC conductivities and Stokes flows on black hole horizons, J. High Energy Phys. 10 (2015) 103.
- A. Donos and J. P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, J. High Energy Phys. 11 (2014) 081.
- N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79, 025023 (2009).
- A. Romero-Bermúdez, A. Krikun, K. Schalm, and J. Zaanen, Anomalous attenuation of plasmons in strange metals and holography, Phys. Rev. B 99, 235149 (2019).
- F. Balm, A. Krikun, A. Romero-Bermúdez, K. Schalm, and J. Zaanen, Isolated zeros destroy Fermi surface in holographic models with a lattice, J. High Energy Phys. 01 (2020) 151.
- 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, 165149 (2019).
- S. Smit, E. Mauri, L. Bawden, F. Heringa, F. Gerritsen, E. van Heumen, Y. Huang, T. Kondo, T. Takeuchi, N. Hussey et al., Momentum-dependent scaling exponents of nodal self-energies measured in strange metal cuprates and modelled using semi-holography, arXiv:2112.06576.