Abstract
We consider the magneto-transports of quantum matters doped with magnetic impurities near the quantum critical points (QCP). For this, we first find new black hole solution with hyper-scaling violation which is dual to such system. By considering the fluctuation near this exact solution, we calculated all transport coefficients using the holographic method. We applied our result to the surface state of the topological insulator with magnetic doping and found two QCP’s, one bosonic and the other fermionic. It turns out that doped Bi2Se3 and Bi2Te3 correspond to different QCP’s. We also investigated transports of QCP’s as functions of physical parameters and found that there are phase transitions as well as crossovers from weak localization to weak anti-localization.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
J. Zaanen, Y.-W. Sun, Y. Liu and K. Schalm, Holographic Duality in Condensed Matter Physics, Cambridge University Press, Cambridge U.K. (2015).
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis and R. Meyer, Effective Holographic Theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].
B. Gouteraux and E. Kiritsis, Generalized Holographic Quantum Criticality at Finite Density, JHEP 12 (2011) 036 [arXiv:1107.2116] [INSPIRE].
L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev. B 85 (2012) 035121 [arXiv:1112.0573] [INSPIRE].
N. Iizuka et al., Extremal Horizons with Reduced Symmetry: Hyperscaling Violation, Stripes and a Classification for the Homogeneous Case, JHEP 03 (2013) 126 [arXiv:1212.1948] [INSPIRE].
X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP 06 (2012) 041 [arXiv:1201.1905] [INSPIRE].
K. Narayan, On Lifshitz scaling and hyperscaling violation in string theory, Phys. Rev. D 85 (2012) 106006 [arXiv:1202.5935] [INSPIRE].
E. Perlmutter, Hyperscaling violation from supergravity, JHEP 06 (2012) 165 [arXiv:1205.0242] [INSPIRE].
M. Cadoni and S. Mignemi, Phase transition and hyperscaling violation for scalar Black Branes, JHEP 06 (2012) 056 [arXiv:1205.0412] [INSPIRE].
M. Alishahiha and H. Yavartanoo, On Holography with Hyperscaling Violation, JHEP 11 (2012) 034 [arXiv:1208.6197] [INSPIRE].
P. Dey and S. Roy, Lifshitz metric with hyperscaling violation from NS5-Dp states in string theory, Phys. Lett. B 720 (2013) 419 [arXiv:1209.1049] [INSPIRE].
M. Cadoni and M. Serra, Hyperscaling violation for scalar black branes in arbitrary dimensions, JHEP 11 (2012) 136 [arXiv:1209.4484] [INSPIRE].
B.S. Kim, Hyperscaling violation: a unified frame for effective holographic theories, JHEP 11 (2012) 061 [arXiv:1210.0540] [INSPIRE].
S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].
S.-J. Sin, S.-S. Xu and Y. Zhou, Holographic Superconductor for a Lifshitz fixed point, Int. J. Mod. Phys. A 26 (2011) 4617 [arXiv:0909.4857] [INSPIRE].
S.A. Hartnoll and D.M. Hofman, Generalized Lifshitz-Kosevich scaling at quantum criticality from the holographic correspondence, Phys. Rev. B 81 (2010) 155125 [arXiv:0912.0008] [INSPIRE].
K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of Charged Dilaton Black Holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [INSPIRE].
K. Goldstein, N. Iizuka, S. Kachru, S. Prakash, S.P. Trivedi and A. Westphal, Holography of Dyonic Dilaton Black Branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [INSPIRE].
V. Keranen and L. Thorlacius, Thermal Correlators in Holographic Models with Lifshitz scaling, Class. Quant. Grav. 29 (2012) 194009 [arXiv:1204.0360] [INSPIRE].
Z. Zhao, Q. Pan and J. Jing, Notes on analytical study of holographic superconductors with Lifshitz scaling in external magnetic field, Phys. Lett. B 735 (2014) 438 [arXiv:1311.6260] [INSPIRE].
J.-W. Lu, Y.-B. Wu, P. Qian, Y.-Y. Zhao and X. Zhang, Lifshitz Scaling Effects on Holographic Superconductors, Nucl. Phys. B 887 (2014) 112 [arXiv:1311.2699] [INSPIRE].
Y. Bu, Holographic superconductors with z = 2 Lifshitz scaling, Phys. Rev. D 86 (2012) 046007 [arXiv:1211.0037] [INSPIRE].
E.J. Brynjolfsson, U.H. Danielsson, L. Thorlacius and T. Zingg, Holographic Superconductors with Lifshitz Scaling, J. Phys. A 43 (2010) 065401 [arXiv:0908.2611] [INSPIRE].
S. Harrison, S. Kachru and H. Wang, Resolving Lifshitz Horizons, JHEP 02 (2014) 085 [arXiv:1202.6635] [INSPIRE].
A. Donos and J.P. Gauntlett, Novel metals and insulators from holography, JHEP 06 (2014) 007 [arXiv:1401.5077] [INSPIRE].
M. Blake, A. Donos and N. Lohitsiri, Magnetothermoelectric Response from Holography, JHEP 08 (2015) 124 [arXiv:1502.03789] [INSPIRE].
R.A. Davison and B. Goutéraux, Momentum dissipation and effective theories of coherent and incoherent transport, JHEP 01 (2015) 039 [arXiv:1411.1062] [INSPIRE].
B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP 04 (2014) 181 [arXiv:1401.5436] [INSPIRE].
D. Giataganas and K. Sfetsos, Non-integrability in non-relativistic theories, JHEP 06 (2014) 018 [arXiv:1403.2703] [INSPIRE].
P. Fonda, L. Franti, V. Keränen, E. Keski-Vakkuri, L. Thorlacius and E. Tonni, Holographic thermalization with Lifshitz scaling and hyperscaling violation, JHEP 08 (2014) 051 [arXiv:1401.6088] [INSPIRE].
I. Papadimitriou, Hyperscaling violating Lifshitz holography, Nucl. Part. Phys. Proc. 273-275 (2016) 1487 [arXiv:1411.0312] [INSPIRE].
M.H. Dehghani, A. Sheykhi and S.E. Sadati, Thermodynamics of nonlinear charged Lifshitz black branes with hyperscaling violation, Phys. Rev. D 91 (2015) 124073 [arXiv:1505.01134] [INSPIRE].
H.-S. Liu, H. Lü and C.N. Pope, Magnetically-Charged Black Branes and Viscosity/Entropy Ratios, JHEP 12 (2016) 097 [arXiv:1602.07712] [INSPIRE].
X.-H. Ge, Y. Tian, S.-Y. Wu and S.-F. Wu, Hyperscaling violating black hole solutions and Magneto-thermoelectric DC conductivities in holography, Phys. Rev. D 96 (2017) 046015 [Erratum ibid. D 97 (2018) 089901] [arXiv:1606.05959] [INSPIRE].
X.-H. Ge, S.-J. Sin, Y. Tian, S.-F. Wu and S.-Y. Wu, Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation, JHEP 01 (2018) 068 [arXiv:1712.00705] [INSPIRE].
Z.-N. Chen, X.-H. Ge, S.-Y. Wu, G.-H. Yang and H.-S. Zhang, Magnetothermoelectric DC conductivities from holography models with hyperscaling factor in Lifshitz spacetime, Nucl. Phys. B 924 (2017) 387 [arXiv:1709.08428] [INSPIRE].
S. Cremonini, M. Cvetič and I. Papadimitriou, Thermoelectric DC conductivities in hyperscaling violating Lifshitz theories, JHEP 04 (2018) 099 [arXiv:1801.04284] [INSPIRE].
S. Mukhopadhyay and C. Paul, Hyperscaling violating geometry with magnetic field and DC conductivity, Nucl. Phys. B 938 (2019) 571 [arXiv:1906.02348] [INSPIRE].
Y. Ahn, H.-S. Jeong, D. Ahn and K.-Y. Kim, Linear-T resistivity from low to high temperature: axion-dilaton theories, JHEP 04 (2020) 153 [arXiv:1907.12168] [INSPIRE].
Y. Seo, G. Song, C. Park and S.-J. Sin, Small Fermi Surfaces and Strong Correlation Effects in Dirac Materials with Holography, JHEP 10 (2017) 204 [arXiv:1708.02257] [INSPIRE].
Y. Seo, G. Song and S.-J. Sin, Strong Correlation Effects on Surfaces of Topological Insulators via Holography, Phys. Rev. B 96 (2017) 041104 [arXiv:1703.07361] [INSPIRE].
M. Liu et al., Crossover between weak antilocalization and weak localization in a magnetically doped topological insulator, Phys. Rev. Lett. 108 (2012) 036805 [arXiv:1103.3353].
D. Zhang et al., Interplay between ferromagnetism, surface states, and quantum corrections in a magnetically doped topological insulator, Phys. Rev. B 86 (2012) 205127 [arXiv:1206.2908].
L. Bao et al., Quantum corrections crossover and ferromagnetism in magnetic topological insulators, Sci. Rep. 3 (2013) 2391.
J. Crossno et al., Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene, Science 351 (2016) 1058 [arXiv:1509.04713].
A. Lucas, J. Crossno, K.C. Fong, P. Kim and S. Sachdev, Transport in inhomogeneous quantum critical fluids and in the Dirac fluid in graphene, Phys. Rev. B 93 (2016) 075426 [arXiv:1510.01738] [INSPIRE].
Y. Seo, G. Song, P. Kim, S. Sachdev and S.-J. Sin, Holography of the Dirac Fluid in Graphene with two currents, Phys. Rev. Lett. 118 (2017) 036601 [arXiv:1609.03582] [INSPIRE].
Y. Seo, K.-Y. Kim, K.K. Kim and S.-J. Sin, Character of matter in holography: Spin-orbit interaction, Phys. Lett. B 759 (2016) 104 [arXiv:1512.08916] [INSPIRE].
E.D.L. Rienks et al., Large magnetic gap at the Dirac point in Bi2 Te3 /MnBi2 Te4 heterostructures, Nature 576 (2019) 423.
H. Min, R. Bistritzer, J.-J. Su and A.H. MacDonald, Room-temperature superfluidity in graphene bilayers, Phys. Rev. B 78 (2008) 121401 [arXiv:0802.3462].
A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].
R. Bousso, Z. Fisher, J. Koeller, S. Leichenauer and A.C. Wall, Proof of the Quantum Null Energy Condition, Phys. Rev. D 93 (2016) 024017 [arXiv:1509.02542] [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
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 1912.12603
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Ge, XH., Seo, Y., Sin, SJ. et al. New black holes with hyperscaling violation for the transports of quantum critical points with magnetic impurity. J. High Energ. Phys. 2020, 128 (2020). https://doi.org/10.1007/JHEP06(2020)128
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2020)128