Optical evidence for a Weyl semimetal state in pyrochlore Eu 2 Ir 2 O 7

Sushkov, A. B.; Hofmann, J. B.; Jenkins, G. S.; Ishikawa, J.; Nakatsuji, S.; Das Sarma, S.; Drew, H. D.

doi:10.1103/PhysRevB.92.241108

Title: Optical evidence for a Weyl semimetal state in pyrochlore ${Eu}_{2} {Ir}_{2} O_{7}$

Authors:: Sushkov, A. B.; Hofmann, J. B.; Jenkins, G. S.; Ishikawa, J.; Nakatsuji, S.; Das Sarma, S.; Drew, H. D.

Publication Date:: 2015-12-14

Sponsoring Org.:: USDOE

OSTI Identifier:: 1546130

Grant/Contract Number:: ER 46741-SC0005436

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Name: Physical Review B Journal Volume: 92 Journal Issue: 24; Journal ID: ISSN 1098-0121

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Citation Formats


                    Sushkov, A. B., Hofmann, J. B., Jenkins, G. S., Ishikawa, J., Nakatsuji, S., Das Sarma, S., and Drew, H. D. Optical evidence for a Weyl semimetal state in pyrochlore Eu 2 Ir 2 O 7.  United States: N. p., 2015. 
        Web.  doi:10.1103/PhysRevB.92.241108.

Copy to clipboard


                    Sushkov, A. B., Hofmann, J. B., Jenkins, G. S., Ishikawa, J., Nakatsuji, S., Das Sarma, S., & Drew, H. D. Optical evidence for a Weyl semimetal state in pyrochlore Eu 2 Ir 2 O 7.  United States.  doi:https://doi.org/10.1103/PhysRevB.92.241108

Copy to clipboard


                    Sushkov, A. B., Hofmann, J. B., Jenkins, G. S., Ishikawa, J., Nakatsuji, S., Das Sarma, S., and Drew, H. D. Mon .  
        "Optical evidence for a Weyl semimetal state in pyrochlore Eu 2 Ir 2 O 7".  United States.  doi:https://doi.org/10.1103/PhysRevB.92.241108.

Copy to clipboard


                    
@article{osti_1546130,

  title        = {Optical evidence for a Weyl semimetal state in pyrochlore Eu 2 Ir 2 O 7},

  author       = {Sushkov, A. B. and Hofmann, J. B. and Jenkins, G. S. and Ishikawa, J. and Nakatsuji, S. and Das Sarma, S. and Drew, H. D.},

  abstractNote = {},

  doi          = {10.1103/PhysRevB.92.241108},

  journal      = {Physical Review B},

  number       = 24,

  volume       = 92,

  place        = {United States},

  year         = {2015},

  month        = {12}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Publisher's Version of Record
DOI: https://doi.org/10.1103/PhysRevB.92.241108

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 87 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Comparative study of low-temperature x-ray diffraction experiments on $R_{2} {Ir}_{2} O_{7}$ ( $R = Nd$ , Eu, and Pr)
journal, December 2014

Takatsu, Hiroshi; Watanabe, Kunihiko; Goto, Kazuki
Physical Review B, Vol. 90, Issue 23
DOI: 10.1103/PhysRevB.90.235110

Infrared Lattice Spectra of Rare-Earth Stannate and Titanate Pyrochlores
journal, January 1971

McCaffrey, John F.; McDevitt, Neil T.; Phillippi, Conrad M.
Journal of the Optical Society of America, Vol. 61, Issue 2
DOI: 10.1364/JOSA.61.000209

Topological insulators and superconductors
journal, October 2011

Qi, Xiao-Liang; Zhang, Shou-Cheng
Reviews of Modern Physics, Vol. 83, Issue 4
DOI: 10.1103/RevModPhys.83.1057

Variation of Charge Dynamics in the Course of Metal-Insulator Transition for Pyrochlore-Type ${Nd}_{2} {Ir}_{2} O_{7}$
journal, September 2012

Ueda, K.; Fujioka, J.; Takahashi, Y.
Physical Review Letters, Vol. 109, Issue 13
DOI: 10.1103/PhysRevLett.109.136402

Correlated Quantum Phenomena in the Strong Spin-Orbit Regime
journal, March 2014

Witczak-Krempa, William; Chen, Gang; Kim, Yong Baek
Annual Review of Condensed Matter Physics, Vol. 5, Issue 1
DOI: 10.1146/annurev-conmatphys-020911-125138

Phase Diagram of Pyrochlore Iridates: All-in–All-out Magnetic Ordering and Non-Fermi-Liquid Properties
journal, October 2015

Shinaoka, Hiroshi; Hoshino, Shintaro; Troyer, Matthias
Physical Review Letters, Vol. 115, Issue 15
DOI: 10.1103/PhysRevLett.115.156401

Mott physics and band topology in materials with strong spin–orbit interaction
journal, March 2010

Pesin, Dmytro; Balents, Leon
Nature Physics, Vol. 6, Issue 5
DOI: 10.1038/nphys1606

Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide
journal, August 2015

Xu, Su-Yang; Alidoust, Nasser; Belopolski, Ilya
Nature Physics, Vol. 11, Issue 9
DOI: 10.1038/nphys3437

Colloquium: Topological insulators
journal, November 2010

Hasan, M. Z.; Kane, C. L.
Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067
DOI: 10.1103/RevModPhys.82.3045

Metallic Spin-Liquid Behavior of the Geometrically Frustrated Kondo Lattice $\Pr_{2} {Ir}_{2} O_{7}$
journal, March 2006

Nakatsuji, S.; Machida, Y.; Maeno, Y.
Physical Review Letters, Vol. 96, Issue 8
DOI: 10.1103/PhysRevLett.96.087204

Time-reversal symmetry breaking and spontaneous Hall effect without magnetic dipole order
journal, December 2009

Machida, Yo; Nakatsuji, Satoru; Onoda, Shigeki
Nature, Vol. 463, Issue 7278
DOI: 10.1038/nature08680

Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity
journal, June 2013

Timusk, T.; Carbotte, J. P.; Homes, C. C.
Physical Review B, Vol. 87, Issue 23
DOI: 10.1103/PhysRevB.87.235121

Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2
journal, May 2014

Neupane, Madhab; Xu, Su-Yang; Sankar, Raman
Nature Communications, Vol. 5, Issue 1
DOI: 10.1038/ncomms4786

Lifshitz transition and Van Hove singularity in a three-dimensional topological Dirac semimetal
journal, August 2015

Xu, Su-Yang; Liu, Chang; Belopolski, I.
Physical Review B, Vol. 92, Issue 7
DOI: 10.1103/PhysRevB.92.075115

Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi
journal, January 2014

Liu, Z. K.; Zhou, B.; Zhang, Y.
Science, Vol. 343, Issue 6173
DOI: 10.1126/science.1245085

Universality of Plasmon Excitations in Dirac Semimetals
journal, December 2015

Kharzeev, Dmitri E.; Pisarski, Robert D.; Yee, Ho-Ung
Physical Review Letters, Vol. 115, Issue 23
DOI: 10.1103/PhysRevLett.115.236402

Discovery of a Weyl fermion semimetal and topological Fermi arcs
journal, July 2015

Xu, S. -Y.; Belopolski, I.; Alidoust, N.
Science, Vol. 349, Issue 6248
DOI: 10.1126/science.aaa9297

First-Principles Study on Cubic Pyrochlore Iridates Y ₂ Ir ₂ O ₇ and Pr ₂ Ir ₂ O ₇
journal, July 2015

Ishii, Fumiyuki; Mizuta, Yo Pierre; Kato, Takehiro
Journal of the Physical Society of Japan, Vol. 84, Issue 7
DOI: 10.7566/JPSJ.84.073703

Longer-range lattice anisotropy strongly competing with spin-orbit interactions in pyrochlore iridates
journal, March 2014

Hozoi, L.; Gretarsson, H.; Clancy, J. P.
Physical Review B, Vol. 89, Issue 11
DOI: 10.1103/PhysRevB.89.115111

Kramers–Kronig constrained variational analysis of optical spectra
journal, August 2005

Kuzmenko, A. B.
Review of Scientific Instruments, Vol. 76, Issue 8
DOI: 10.1063/1.1979470

Metal–Insulator Transitions in Pyrochlore Oxides Ln ₂ Ir ₂ O ₇
journal, September 2011

Matsuhira, Kazuyuki; Wakeshima, Makoto; Hinatsu, Yukio
Journal of the Physical Society of Japan, Vol. 80, Issue 9
DOI: 10.1143/JPSJ.80.094701

Plasmon signature in Dirac-Weyl liquids
journal, June 2015

Hofmann, Johannes; Das Sarma, S.
Physical Review B, Vol. 91, Issue 24
DOI: 10.1103/PhysRevB.91.241108

Optical spectroscopy study of the three-dimensional Dirac semimetal ${ZrTe}_{5}$
journal, August 2015

Chen, R. Y.; Zhang, S. J.; Schneeloch, J. A.
Physical Review B, Vol. 92, Issue 7
DOI: 10.1103/PhysRevB.92.075107

Experimental Realization of a Three-Dimensional Dirac Semimetal
journal, July 2014

Borisenko, Sergey; Gibson, Quinn; Evtushinsky, Danil
Physical Review Letters, Vol. 113, Issue 2
DOI: 10.1103/PhysRevLett.113.027603

Infrared study of the electronic structure of the metallic pyrochlore iridate Bi $_{2}$ Ir $_{2}$ O $_{7}$
journal, May 2013

Lee, Y. S.; Moon, S. J.; Riggs, Scott C.
Physical Review B, Vol. 87, Issue 19
DOI: 10.1103/PhysRevB.87.195143

Observation of Weyl nodes in TaAs
journal, August 2015

Lv, B. Q.; Xu, N.; Weng, H. M.
Nature Physics, Vol. 11, Issue 9
DOI: 10.1038/nphys3426

Pyrochlore electrons under pressure, heat, and field: Shedding light on the iridates
journal, April 2013

Witczak-Krempa, William; Go, Ara; Kim, Yong Baek
Physical Review B, Vol. 87, Issue 15
DOI: 10.1103/PhysRevB.87.155101

Observation of three-dimensional massless Kane fermions in a zinc-blende crystal
journal, January 2014

Orlita, M.; Basko, D. M.; Zholudev, M. S.
Nature Physics, Vol. 10, Issue 3
DOI: 10.1038/nphys2857

Charge transport in gapless electron-hole systems with arbitrary band dispersion
journal, May 2015

Das Sarma, S.; Hwang, E. H.
Physical Review B, Vol. 91, Issue 19
DOI: 10.1103/PhysRevB.91.195104

Three-Dimensional Topological Insulators
journal, March 2011

Hasan, M. Zahid; Moore, Joel E.
Annual Review of Condensed Matter Physics, Vol. 2, Issue 1
DOI: 10.1146/annurev-conmatphys-062910-140432

A stable three-dimensional topological Dirac semimetal Cd3As2
journal, May 2014

Liu, Z. K.; Jiang, J.; Zhou, B.
Nature Materials, Vol. 13, Issue 7
DOI: 10.1038/nmat3990

Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates
journal, May 2011

Wan, Xiangang; Turner, Ari M.; Vishwanath, Ashvin
Physical Review B, Vol. 83, Issue 20
DOI: 10.1103/PhysRevB.83.205101

Continuous transition between antiferromagnetic insulator and paramagnetic metal in the pyrochlore iridate Eu $_{2}$ Ir $_{2}$ O $_{7}$
journal, June 2012

Ishikawa, Jun J.; O'Farrell, Eoin C. T.; Nakatsuji, Satoru
Physical Review B, Vol. 85, Issue 24
DOI: 10.1103/PhysRevB.85.245109

Many-body effects and ultraviolet renormalization in three-dimensional Dirac materials
journal, September 2015

Throckmorton, Robert E.; Hofmann, Johannes; Barnes, Edwin
Physical Review B, Vol. 92, Issue 11
DOI: 10.1103/PhysRevB.92.115101

Similar Records in DOE PAGES and OSTI.GOV collections:

Magnetic Excitations across the Metal-Insulator Transition in the Pyrochlore Iridate ${Eu}_{2} {Ir}_{2} O_{7}$ [Evolution of Magnetic Excitations across the Metal-Insulator Transition in the Pyrochlore Iridate ${Eu}_{2} {Ir}_{2} O_{7}$ ]

Journal Article Chun, Sae Hwan ; Yuan, Bo ; Casa, Diego ; ... - Physical Review Letters

Here, we report a resonant inelastic x-ray scattering study of the magnetic excitation spectrum in a highly insulating Eu₂Ir₂O₇ single crystal that exhibits a metal-insulator transition at T_MI = 111(7) K. A propagating magnon mode with a 20 meV bandwidth and a 28 meV magnon gap is found in the excitation spectrum at 7 K, which is expected in the all-in-all-out magnetically ordered state. This magnetic excitation exhibits substantial softening as the temperature is raised towards T_MI and turns into a highly damped excitation in the paramagnetic phase. Remarkably, the softening occurs throughout the whole Brillouin zone including the zonemore »« less
Cited by 3
DOI: https://doi.org/10.1103/PhysRevLett.120.177203

Full Text Available
Evolution of structure and magnetism across the metal-insulator transition in the pyrochlore iridate ${({Nd}_{1 - x} {Ca}_{x})}_{2} {Ir}_{2} O_{7}$

Journal Article Porter, Zach ; Zoghlin, Eli ; Britner, Samuel ; ... - Physical Review B

We report on the evolution of the thermal metal-insulator transition in polycrystalline samples of Nd₂Ir₂O₇ upon hole doping via substitution of Ca²⁺ for Nd³⁺. Ca substitution mediates a filling-controlled Mott-like transition with minimal resolvable structural changes and without altering site symmetry. Local structure confirms that Ca substitution does not result in local chemical phase separation, and absorption spectroscopy establishes that Ir cations maintain a spin-orbit entangled electronic configuration. The metal-insulator transition coincides with antiferromagnetic ordering on the Ir sublattice for all measured samples, and both decrease in onset temperature with Ca content. As a result, weak low-temperature upturns in susceptibilitymore »« less
Cited by 1
DOI: https://doi.org/10.1103/PhysRevB.100.054409

Full Text Available
Noncollinear Magnetic Structure and Multipolar Order in ${Eu}_{2} {Ir}_{2} O_{7}$

Journal Article Wang, Yilin ; Weng, Hongming ; Fu, Liang ; ... - Physical Review Letters

The magnetic properties of the pyrochlore iridate material Eu₂Ir₂O₇ (5d⁵) have been studied based on first principles calculations, where the crystal field splitting Δ , spin-orbit coupling (SOC) λ, and Coulomb interaction U within Ir 5 d orbitals all play significant roles. The ground state phase diagram has been obtained with respect to the strength of SOC and Coulomb interaction U , where a stable antiferromagnetic ground state with all-in–all-out (AIAO) spin structure has been found. In addition, another antiferromagnetic state with energy close to AIAO has also been found to be stable. The calculated nonlinear magnetization of the twomore »« less
Cited by 2
DOI: https://doi.org/10.1103/physrevlett.119.187203

Full Text Available
Fragile singlet ground-state magnetism in the pyrochlore osmates $R_{2} {Os}_{2} O_{7}$ ( $R = Y$ and Ho)

Journal Article Zhao, Z. Y. ; Calder, S. ; Aczel, A. A. ; ... - Physical Review B

The singlet ground state magnetism in pyrochlore osmates Y₂Os₂O₇ and Ho₂Os₂O₇ is studied by DC and AC susceptibility, specific heat, and neutron powder diffraction measurements. Despite the expected non-magnetic singlet in the strong spin-orbit coupling (SOC) limit for Os⁴⁺ (5d⁴), Y₂Os₂O₇ exhibits a spin-glass (SG) ground state below 4 K with weak magnetism, suggesting possible proximity to a quantum phase transition between the non-magnetic state in the strong SOC limit and the magnetic state in the strong superexchange limit. Ho₂Os₂O₇ has the same structural distortion as occurs in Y₂Os₂O₇. However, the Os sublattice in Ho₂Os₂O₇ shows long- range magnetic orderingmore »« less
Cited by 5
DOI: https://doi.org/10.1103/PhysRevB.93.134426

Full Text Available
XY antiferromagnetic ground state in the effective $S = \frac{1}{2}$ pyrochlore ${Yb}_{2} {Ge}_{2} O_{7}$

Journal Article Hallas, Alannah M. ; Gaudet, J. ; Wilson, Murray N. ; ... - Physical Review B

We report neutron scattering and muon spin relaxation measurements (μSR) on the pyrochlore antiferromagnet Yb₂Ge₂O₇. Inelastic neutron scattering was used to probe the transitions between crystal electric field levels, allowing us to determine the eigenvalues and eigenvectors appropriate to the J=more »« less
Cited by 8
DOI: https://doi.org/10.1103/PhysRevB.93.104405

Full Text Available

Similar Records

Title: Optical evidence for a Weyl semimetal state in pyrochlore Eu 2 Ir 2 O 7

Citation Formats

Comparative study of low-temperature x-ray diffraction experiments on R 2 Ir 2 O 7 ( R = Nd , Eu, and Pr) journal, December 2014

Infrared Lattice Spectra of Rare-Earth Stannate and Titanate Pyrochlores journal, January 1971

Topological insulators and superconductors journal, October 2011

Variation of Charge Dynamics in the Course of Metal-Insulator Transition for Pyrochlore-Type Nd 2 Ir 2 O 7 journal, September 2012

Correlated Quantum Phenomena in the Strong Spin-Orbit Regime journal, March 2014

Phase Diagram of Pyrochlore Iridates: All-in–All-out Magnetic Ordering and Non-Fermi-Liquid Properties journal, October 2015

Mott physics and band topology in materials with strong spin–orbit interaction journal, March 2010

Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide journal, August 2015

Colloquium: Topological insulators journal, November 2010

Metallic Spin-Liquid Behavior of the Geometrically Frustrated Kondo Lattice Pr 2 Ir 2 O 7 journal, March 2006

Time-reversal symmetry breaking and spontaneous Hall effect without magnetic dipole order journal, December 2009

Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity journal, June 2013

Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2 journal, May 2014

Lifshitz transition and Van Hove singularity in a three-dimensional topological Dirac semimetal journal, August 2015

Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi journal, January 2014

Universality of Plasmon Excitations in Dirac Semimetals journal, December 2015

Discovery of a Weyl fermion semimetal and topological Fermi arcs journal, July 2015

First-Principles Study on Cubic Pyrochlore Iridates Y 2 Ir 2 O 7 and Pr 2 Ir 2 O 7 journal, July 2015

Longer-range lattice anisotropy strongly competing with spin-orbit interactions in pyrochlore iridates journal, March 2014

Kramers–Kronig constrained variational analysis of optical spectra journal, August 2005

Metal–Insulator Transitions in Pyrochlore Oxides Ln 2 Ir 2 O 7 journal, September 2011

Plasmon signature in Dirac-Weyl liquids journal, June 2015

Optical spectroscopy study of the three-dimensional Dirac semimetal ZrTe 5 journal, August 2015

Experimental Realization of a Three-Dimensional Dirac Semimetal journal, July 2014

Infrared study of the electronic structure of the metallic pyrochlore iridate Bi 2 Ir 2 O 7 journal, May 2013

Observation of Weyl nodes in TaAs journal, August 2015

Pyrochlore electrons under pressure, heat, and field: Shedding light on the iridates journal, April 2013

Observation of three-dimensional massless Kane fermions in a zinc-blende crystal journal, January 2014

Charge transport in gapless electron-hole systems with arbitrary band dispersion journal, May 2015

Three-Dimensional Topological Insulators journal, March 2011

A stable three-dimensional topological Dirac semimetal Cd3As2 journal, May 2014

Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates journal, May 2011

Continuous transition between antiferromagnetic insulator and paramagnetic metal in the pyrochlore iridate Eu 2 Ir 2 O 7 journal, June 2012

Many-body effects and ultraviolet renormalization in three-dimensional Dirac materials journal, September 2015

Title: Optical evidence for a Weyl semimetal state in pyrochlore ${Eu}_{2} {Ir}_{2} O_{7}$

Comparative study of low-temperature x-ray diffraction experiments on $R_{2} {Ir}_{2} O_{7}$ ( $R = Nd$ , Eu, and Pr)
journal, December 2014

Infrared Lattice Spectra of Rare-Earth Stannate and Titanate Pyrochlores
journal, January 1971

Topological insulators and superconductors
journal, October 2011

Variation of Charge Dynamics in the Course of Metal-Insulator Transition for Pyrochlore-Type ${Nd}_{2} {Ir}_{2} O_{7}$
journal, September 2012

Correlated Quantum Phenomena in the Strong Spin-Orbit Regime
journal, March 2014

Phase Diagram of Pyrochlore Iridates: All-in–All-out Magnetic Ordering and Non-Fermi-Liquid Properties
journal, October 2015

Mott physics and band topology in materials with strong spin–orbit interaction
journal, March 2010

Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide
journal, August 2015

Colloquium: Topological insulators
journal, November 2010

Metallic Spin-Liquid Behavior of the Geometrically Frustrated Kondo Lattice $\Pr_{2} {Ir}_{2} O_{7}$
journal, March 2006

Time-reversal symmetry breaking and spontaneous Hall effect without magnetic dipole order
journal, December 2009

Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity
journal, June 2013

Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2
journal, May 2014

Lifshitz transition and Van Hove singularity in a three-dimensional topological Dirac semimetal
journal, August 2015

Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi
journal, January 2014

Universality of Plasmon Excitations in Dirac Semimetals
journal, December 2015

Discovery of a Weyl fermion semimetal and topological Fermi arcs
journal, July 2015

First-Principles Study on Cubic Pyrochlore Iridates Y ₂ Ir ₂ O ₇ and Pr ₂ Ir ₂ O ₇
journal, July 2015

Longer-range lattice anisotropy strongly competing with spin-orbit interactions in pyrochlore iridates
journal, March 2014

Kramers–Kronig constrained variational analysis of optical spectra
journal, August 2005

Metal–Insulator Transitions in Pyrochlore Oxides Ln ₂ Ir ₂ O ₇
journal, September 2011

Plasmon signature in Dirac-Weyl liquids
journal, June 2015

Optical spectroscopy study of the three-dimensional Dirac semimetal ${ZrTe}_{5}$
journal, August 2015

Experimental Realization of a Three-Dimensional Dirac Semimetal
journal, July 2014

Infrared study of the electronic structure of the metallic pyrochlore iridate Bi $_{2}$ Ir $_{2}$ O $_{7}$
journal, May 2013

Observation of Weyl nodes in TaAs
journal, August 2015

Pyrochlore electrons under pressure, heat, and field: Shedding light on the iridates
journal, April 2013

Observation of three-dimensional massless Kane fermions in a zinc-blende crystal
journal, January 2014

Charge transport in gapless electron-hole systems with arbitrary band dispersion
journal, May 2015

Three-Dimensional Topological Insulators
journal, March 2011

A stable three-dimensional topological Dirac semimetal Cd3As2
journal, May 2014

Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates
journal, May 2011

Continuous transition between antiferromagnetic insulator and paramagnetic metal in the pyrochlore iridate Eu $_{2}$ Ir $_{2}$ O $_{7}$
journal, June 2012

Many-body effects and ultraviolet renormalization in three-dimensional Dirac materials
journal, September 2015