DOI: 10.1038/srep32446. Universal optical conductivity of a disordered Weyl semimetal

Universal optical conductivity of a disordered Weyl semimetal

10.1038/srep32446

Crossref journal-article

Springer Science and Business Media LLC

Scientific Reports (297)

Abstract

AbstractTopological Weyl semimetals, besides manifesting chiral anomaly, can also accommodate a disorder-driven unconventional quantum phase transition into a metallic phase. A fundamentally and practically important question in this regard concerns an experimentally measurable quantity that can clearly distinguish these two phases. We show that the optical conductivity while serving this purpose can also play the role of a bonafide order parameter across such disorder-driven semimetal-metal quantum phase transition by virtue of displaying distinct scaling behavior in the semimetallic and metallic phases, as well as inside the quantum critical fan supporting a non-Fermi liquid. We demonstrate that the correction to the dielectric constant and optical conductivity in a dirty Weyl semimetal due to weak disorder is independent of the actual nature of point-like impurity scatterers. Therefore, optical conductivity can be used as an experimentally measurable quantity to study the critical properties and to pin the universality class of the disorder-driven quantum phase transition in Weyl semimetals.

Bibliography

Roy, B., JuriÄiÄ, V., & Das Sarma, S. (2016). Universal optical conductivity of a disordered Weyl semimetal. Scientific Reports, 6(1).

Authors 3

Bitan Roy (first)
Vladimir Juričić (additional)
Sankar Das Sarma (additional)

References 53 Referenced 65

Sachdev, S. Quantum Phase Transitions (Cambridge University Press, 2nd ed., 2007). (10.1002/9780470022184.hmm108)
Herbut, I. F. A Modern Approach to Critical Phenomena (Cambridge University Press, Cambridge, 2007). (10.1017/CBO9780511755521)
Hassan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045 (2010). (10.1103/RevModPhys.82.3045) / Rev. Mod. Phys. by MZ Hassan (2010)
Qi, X. L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (2011). (10.1103/RevModPhys.83.1057) / Rev. Mod. Phys. by XL Qi (2011)
Zhang, C. et al. Tantalum Monoarsenide: an Exotic Compensated Semimetal. arXiv:1502.00251.
Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613 (2015). (10.1126/science.aaa9297) / Science by S-Y Xu (2015)
Lv, B. Q. et al. Experimental Discovery of Weyl Semimetal TaAs. Phys. Rev. X 5, 031013 (2015). / Phys. Rev. X by BQ Lv (2015)
Xu, S.-Y. et al. Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide. Nature Physics 11, 748 (2015). (10.1038/nphys3437) / Nature Physics by S-Y Xu (2015)
Xu, N. et al. Observation of Weyl nodes and Fermi arcs in tantalum phosphide. Nature Communications 7, 11006 (2016). (10.1038/ncomms11006) / Nature Communications by N Xu (2016)
Shekhar, C. et al. Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP. Nature Physics 11, 645 (2015). (10.1038/nphys3372) / Nature Physics by C Shekhar (2015)
Wang, Z. et al. Helicity-protected ultrahigh mobility Weyl fermions in NbP. Phys. Rev. B 93, 121112(R) (2016). (10.1103/PhysRevB.93.121112) / Phys. Rev. B by Z Wang (2016)
Chang, G. et al. A strongly robust Weyl fermion semimetal state in Ta3S2. arXiv:1512.08781. (10.1126/sciadv.1600295)
Borisenko, S. et al. Time-Reversal Symmetry Breaking Type-II Weyl State in YbMnBi2. arXiv:1507.04847.
Liu, J. Y. et al. Discovery of a topological semimetal phase coexisting with ferromagnetic behavior in Sr1−yMnSb2 (y ~ 0.08). arXiv:1507.07978.
Burkov, A. A. Chiral anomaly and transport in Weyl metals. J. Phys.: Condens. Matter 27, 113201 (2015). / J. Phys.: Condens. Matter by AA Burkov (2015)
Bansil, A., Lin, H. & Das, T. Colloquium: Topological band theory. Rev. Mod. Phys. 88, 021004 (2016). (10.1103/RevModPhys.88.021004) / Rev. Mod. Phys. by A Bansil (2016)
Fradkin, E. Critical behavior of disordered degenerate semiconductors. II. Spectrum and transport properties in mean-field theory. Phys. Rev. B 33, 3263 (1986). (10.1103/PhysRevB.33.3263) / Phys. Rev. B by E Fradkin (1986)
Shindou, R. & Murakami, S. Effects of disorder in three-dimensional Z2 quantum spin Hall systems. Phys. Rev. B 79, 045321 (2009). (10.1103/PhysRevB.79.045321) / Phys. Rev. B by R Shindou (2009)
Ominato, Y. & Koshino, M. Quantum transport in a three-dimensional Weyl electron system. Phys. Rev. B 89, 054202 (2014). (10.1103/PhysRevB.89.054202) / Phys. Rev. B by Y Ominato (2014)
Goswami, P. & Chakravarty, S. Quantum Criticality between Topological and Band Insulators in 3 + 1 Dimensions. Phys. Rev. Lett. 107, 196803 (2011). (10.1103/PhysRevLett.107.196803) / Phys. Rev. Lett. by P Goswami (2011)
Roy, B. & Das Sarma, S. Diffusive quantum criticality in three-dimensional disordered Dirac semimetals. Phys. Rev. B 90, 241112(R) (2014). (10.1103/PhysRevB.90.241112) / Phys. Rev. B by B Roy (2014)
Syzranov, S. V., Radzihovsky, L. & Gurarie, V. Critical Transport in Weakly Disordered Semiconductors and Semimetals. Phys. Rev. Lett. 114, 166601 (2015). (10.1103/PhysRevLett.114.166601) / Phys. Rev. Lett. by SV Syzranov (2015)
Altland, A. & Bagrets, D. Effective Field Theory of the Disordered Weyl Semimetal. Phys. Rev. Lett. 114, 257201 (2015). (10.1103/PhysRevLett.114.257201) / Phys. Rev. Lett. by A Altland (2015)
Kobayashi, K., Ohtsuki, T. & Imura, K.-I. Disordered Weak and Strong Topological Insulators. Phys. Rev. Lett. 110, 236803 (2013). (10.1103/PhysRevLett.110.236803) / Phys. Rev. Lett. by K Kobayashi (2013)
Kobayashi, K., Ohtsuki, T., Imura, K.-I. & Herbut, I. F. Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators. Phys. Rev. Lett. 112, 016402 (2014). (10.1103/PhysRevLett.112.016402) / Phys. Rev. Lett. by K Kobayashi (2014)
Sbierski, B., Pohl, G., Bergholtz, E. J. & Brouwer, P. W. Quantum Transport of Disordered Weyl Semimetals at the Nodal Point. Phys. Rev. Lett. 113, 026602 (2014). (10.1103/PhysRevLett.113.026602) / Phys. Rev. Lett. by B Sbierski (2014)
Pixley, J. H., Goswami, P. & Das Sarma, S. Anderson Localization and the Quantum Phase Diagram of Three Dimensional Disordered Dirac Semimetals. Phys. Rev. Lett. 115, 076601 (2015). (10.1103/PhysRevLett.115.076601) / Phys. Rev. Lett. by JH Pixley (2015)
Sbierski, B., Bergholtz, E. J. & Brouwer, P. W. Quantum critical exponents for a disordered three-dimensional Weyl node. Phys. Rev. B 92, 115145 (2015). (10.1103/PhysRevB.92.115145) / Phys. Rev. B by B Sbierski (2015)
Pixley, J. H., Goswami, P. & Das Sarma, S. Disorder-driven itinerant quantum criticality of three-dimensional massless Dirac fermions. Phys. Rev. B 93, 085103 (2016). (10.1103/PhysRevB.93.085103) / Phys. Rev. B by JH Pixley (2016)
Liu, S., Ohtsuki, T. & Shindou, R. Effect of Disorder in a Three-Dimensional Layered Chern Insulator. Phys. Rev. Lett. 116, 066401 (2016). (10.1103/PhysRevLett.116.066401) / Phys. Rev. Lett. by S Liu (2016)
Bera, S., Sau, J. D. & Roy, B. Dirty Weyl semimetals: stability, phase transition and quantum criticality. Phys. Rev. B 93, 201302 (2016). (10.1103/PhysRevB.93.201302) / Phys. Rev. B by S Bera (2016)
Shapourian, H. & Hughes, T. L. Phase diagrams of disordered Weyl semimetals. Phys. Rev. B 93, 075108 (2016). (10.1103/PhysRevB.93.075108) / Phys. Rev. B by H Shapourian (2016)
Adam, S., Hwang, E. H., Galitski, V. M. & Das Sarma, S. A self-consistent theory for graphene transport. Proc. Natl. Acad. Sci. USA 104, 18392 (2007). (10.1073/pnas.0704772104) / Proc. Natl. Acad. Sci. USA by S Adam (2007)
Das Sarma, S., Adam, S., Hwang, E. H. & Rossi, E. Electronic transport in two-dimensional graphene. Rev. Mod. Phys. 83, 407 (2011). (10.1103/RevModPhys.83.407) / Rev. Mod. Phys. by S Das Sarma (2011)
Nandkishore, R., Huse, D. A. & Sondhi, S. L. Rare region effects dominate weakly disordered three-dimensional Dirac points. Phys. Rev. B 89, 245110 (2014). (10.1103/PhysRevB.89.245110) / Phys. Rev. B by R Nandkishore (2014)
Pixley, J. H., Huse, D. A. & Das Sarma, S. Rare region induced avoided quantum criticality in disordered three-dimensional Dirac and Weyl semimetals. Phys. Rev. X 6, 021042 (2012). / Phys. Rev. X by JH Pixley (2012)
Ueda, K. et al. Variation of Charge Dynamics in the Course of Metal-Insulator Transition for Pyrochlore-Type Nd2Ir2O7 . Phys. Rev. Lett. 109, 136402 (2012). (10.1103/PhysRevLett.109.136402) / Phys. Rev. Lett. by K Ueda (2012)
Timusk, T., Carbotte, J. P., Homes, C. C., Basov, D. N. & Sharapov, S. G. Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity. Phys. Rev. B 87, 235121 (2013). (10.1103/PhysRevB.87.235121) / Phys. Rev. B by T Timusk (2013)
Sushkov, A. B. et al. Optical evidence for a Weyl semimetal state in pyrochlore Eu2Ir2O7 . Phys. Rev. B 92, 241108(R) (2015). (10.1103/PhysRevB.92.241108) / Phys. Rev. B by AB Sushkov (2015)
Roy, B. & Sau, J. D. Magnetic catalysis and axionic charge-density-wave in Weyl semimetals. Phys. Rev. B 92, 125141 (2015). (10.1103/PhysRevB.92.125141) / Phys. Rev. B by B Roy (2015)
Huang, Z., Das, T., Balatsky, A. V. & Arovas, D. P. Stability of Weyl metals under impurity scattering. Phys. Rev. B 87, 155123 (2013). (10.1103/PhysRevB.87.155123) / Phys. Rev. B by Z Huang (2013)
Juričić, V., Vafek, O. & Herbut, I. F. Conductivity of interacting massless Dirac particles in graphene: Collisionless regime. Phys. Rev. B 82, 235402 (2010). (10.1103/PhysRevB.82.235402) / Phys. Rev. B by V Juričić (2010)
Herbut, I. F., Juričić, V. & Vafek, O. Coulomb interaction, ripples and the minimal conductivity of graphene. Phys. Rev. Lett. 100, 046403 (2008). (10.1103/PhysRevLett.100.046403) / Phys. Rev. Lett. by IF Herbut (2008)
Hosur, P., Parameswaran, S. A. & Vishwanath, A. Charge Transport in Weyl Semimetals. Phys. Rev. Lett. 108, 046602 (2012). (10.1103/PhysRevLett.108.046602) / Phys. Rev. Lett. by P Hosur (2012)
Rosenstein, B. & Lewkowicz, M. Dynamics of electric transport in interacting Weyl semimetals. Phys. Rev. B 88, 045108 (2013). (10.1103/PhysRevB.88.045108) / Phys. Rev. B by B Rosenstein (2013)
Mastropietro, V., Interacting Weyl semimetals on a lattice. J. Phys. A: Math. Theor. 47, 465003 (2014). (10.1088/1751-8113/47/46/465003) / J. Phys. A: Math. Theor. by V Mastropietro (2014)
Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011). (10.1103/PhysRevB.83.205101) / Phys. Rev. B by X Wan (2011)
Roy, B. & Das Sarma, S. Quantum phases of interacting electrons in three-dimensional dirty Dirac semimetals. arXiv:1511.06367.
Wegner, F. Electrons in disordered systems. Scaling near the mobility edge. Z. Phys. B 25, 327 (1976). (10.1007/BF01315248) / Z. Phys. B by F Wegner (1976)
Das Sarma, S. & Hwang, E. H. Charge transport in gapless electron-hole systems with arbitrary band dispersion. Phys. Rev. B 91, 195104 (2015). (10.1103/PhysRevB.91.195104) / Phys. Rev. B by S Das Sarma (2015)
Das Sarma, S., Hwang, E. H. & Min, H. Carrier screening, transport and relaxation in three-dimensional Dirac semimetals. Phys. Rev. B 91, 035201 (2015). (10.1103/PhysRevB.91.035201) / Phys. Rev. B by S Das Sarma (2015)
Borisenko, S. et al. Experimental Realization of a Three-Dimensional Dirac Semimetal. Phys. Rev. Lett. 113, 027603 (2014). (10.1103/PhysRevLett.113.027603) / Phys. Rev. Lett. by S Borisenko (2014)
Liu, Z. K. et al. Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi. Science 343, 864 (2014). (10.1126/science.1245085) / Science by ZK Liu (2014)

Dates

Type	When
Created	8 years, 11 months ago (Aug. 30, 2016, 5:19 a.m.)
Deposited	2 years, 7 months ago (Jan. 4, 2023, 5:28 p.m.)
Indexed	2 weeks, 5 days ago (Aug. 6, 2025, 8:16 a.m.)
Issued	8 years, 11 months ago (Aug. 30, 2016)
Published	8 years, 11 months ago (Aug. 30, 2016)
Published Online	8 years, 11 months ago (Aug. 30, 2016)

Funders 0

None

BibTeX

@article{Roy_2016, title={Universal optical conductivity of a disordered Weyl semimetal}, volume={6}, ISSN={2045-2322}, url={http://dx.doi.org/10.1038/srep32446}, DOI={10.1038/srep32446}, number={1}, journal={Scientific Reports}, publisher={Springer Science and Business Media LLC}, author={Roy, Bitan and Juričić, Vladimir and Das Sarma, Sankar}, year={2016}, month=aug }

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