Quantum Criticality between Topological and Band Insulators in3+1Dimensions
Open accessAbstract
Four-component massive and massless Dirac fermions in the presence of long range Coulomb interaction and chemical potential disorder exhibit striking fermionic quantum criticality. For an odd number of flavors of Dirac fermions, the sign of the Dirac mass distinguishes the topological and the trivial band insulator phases, and the gapless semimetallic phase corresponds to the quantum critical point that separates the two. Up to a critical strength of disorder, the semimetallic phase remains stable, and the universality class of the direct phase transition between two insulating phases is unchanged. Beyond the critical strength of disorder the semimetallic phase undergoes a phase transition into a disorder controlled diffusive metallic phase, and there is no longer a direct phase transition between the two types of insulating phases.
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Analogous calculations for 3D semimetals show a vanishing density of states persisting up to a finite value of disorder strength (Fradkin, 1986; Goswami and Chakravarty, 2011; Hosur et al., 2012; Pixley et al., 2016a) beyond which a metallic state is expected.
“Analogous calculations for 3D semimetals show a vanishing density of states persisting up to a finite value of disorder strength (Fradkin, 1986; Goswami and Chakravarty, 2011; Hosur et al. , 2012; Pixley et al. , 2016a) beyond which a metallic state is expected.”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Goswami and Chakravarty, 2011
In Dirac systems, due to particle-hole symmetry there can be current carrying states with zero total momentum.
“But in Dirac systems, due to particle-hole symmetry there can be current carrying states with zero total momentum (Fritz et al. , 2008; Goswami and Chakravarty, 2011).”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Goswami and Chakravarty, 2011
Cites
Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator
Xu, S.-Y., Xia, Y., Wray, L. A., Jia, S., Meier, F., Dil, J. H., Osterwalder, J., Slomski, B., Bansil, A., Lin, H., et al. (2011) · Science · doi:10.1126/science.1201607 · Cited by 461 · see citing works
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Weyl and Dirac semimetals in three-dimensional solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.015001 · Cited by 4,528 · see citing works
“But in Dirac systems, due to particle-hole symmetry there can be current carrying states with zero total momentum (Fritz et al., 2008; Goswami and Chakravarty, 2011).”
BackgroundDiscovery of a Three-Dimensional Topological Dirac Semimetal, Na <sub>3</sub> Bi
Liu, Z. K., Zhou, B., Zhang, Y., Wang, Z. J., Weng, H. M., Prabhakaran, D., Mo, S.-K., Shen, Z. X., Fang, Z., Dai, X., et al. (2014) · Science · doi:10.1126/science.1245085 · Cited by 2,328 · see citing works
Classification of stable three-dimensional Dirac semimetals with nontrivial topology
Yang, B.-J., & Nagaosa, N. (2014) · Nature Communications · doi:10.1038/ncomms5898 · Cited by 864 · see citing works
Recent developments in transport phenomena in Weyl semimetals
Hosur, P., & Qi, X. (2013) · Comptes Rendus. Physique · doi:10.1016/j.crhy.2013.10.010 · Cited by 743 · see citing works
Observation of three-dimensional massless Kane fermions in a zinc-blende crystal
Orlita, M., Basko, D. M., Zholudev, M. S., Teppe, F., Knap, W., Gavrilenko, V. I., Mikhailov, N. N., Dvoretskii, S. A., Neugebauer, P., Faugeras, C., et al. (2014) · Nature Physics · doi:10.1038/nphys2857 · Cited by 244 · see citing works
Recent Progress in the Study of Topological Semimetals
Bernevig, A., Weng, H., Fang, Z., & Dai, X. (2018) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.87.041001 · Cited by 176 · see citing works
Weyl and Dirac Semimetals in Three Dimensional Solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2017) · arXiv
“But in Dirac systems, due to particle-hole symmetry there can be current carrying states with zero total momentum (Fritz et al., 2008; Goswami and Chakravarty, 2011).”
Background
- Authors
- Goswami, P., & Chakravarty, S.
- Affiliations
- Rice University (US)
- University of California, Los Angeles (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2011-11-02
- Volume
- 107
- Issue
- 19
- Pages
- 196803-196803
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2021175989
- Cited by
- 233
- References
- 1
- Citations by year
- 2026: 4 · 2025: 7 · 2024: 9 · 2023: 9 · 2022: 10 · 2021: 19 · 2020: 15 · 2019: 18 · 2018: 28 · 2017: 34 · 2016: 30 · 2015: 24 · 2014: 15 · 2013: 7 · 2012: 4
- FWCI
- 4.51
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (acceptedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- quantum criticality, topological insulators, band insulator, Dirac fermions, long-range Coulomb interaction, quantum critical point, semimetallic phase, critical exponents, universality class, four-dimensional spacetime
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