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Kumar P, Singh G, Guan X, Roy S, Lee J, Kim IY, Li X, Bu F, Bahadur R, Iyengar SA, Yi J, Zhao D, Ajayan PM, Vinu A. The Rise of Xene Hybrids. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024; 36:e2403881. [PMID: 38899836 DOI: 10.1002/adma.202403881] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2024] [Revised: 05/22/2024] [Indexed: 06/21/2024]
Abstract
Xenes, mono-elemental atomic sheets, exhibit Dirac/Dirac-like quantum behavior. When interfaced with other 2D materials such as boron nitride, transition metal dichalcogenides, and metal carbides/nitrides/carbonitrides, it enables them with unique physicochemical properties, including structural stability, desirable bandgap, efficient charge carrier injection, flexibility/breaking stress, thermal conductivity, chemical reactivity, catalytic efficiency, molecular adsorption, and wettability. For example, BN acts as an anti-oxidative shield, MoS2 injects electrons upon laser excitation, and MXene provides mechanical flexibility. Beyond precise compositional modulations, stacking sequences, and inter-layer coupling controlled by parameters, achieving scalability and reproducibility in hybridization is crucial for implementing these quantum materials in consumer applications. However, realizing the full potential of these hybrid materials faces challenges such as air gaps, uneven interfaces, and the formation of defects and functional groups. Advanced synthesis techniques, a deep understanding of quantum behaviors, precise control over interfacial interactions, and awareness of cross-correlations among these factors are essential. Xene-based hybrids show immense promise for groundbreaking applications in quantum computing, flexible electronics, energy storage, and catalysis. In this timely perspective, recent discoveries of novel Xenes and their hybrids are highlighted, emphasizing correlations among synthetic parameters, structure, properties, and applications. It is anticipated that these insights will revolutionize diverse industries and technologies.
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Affiliation(s)
- Prashant Kumar
- Global Innovative Centre for Advanced Nanomaterials (GICAN), College of Engineering, Science and Environment (CESE), University of Newcastle, University Drive, Callaghan, New South Wales, 2308, Australia
| | - Gurwinder Singh
- Global Innovative Centre for Advanced Nanomaterials (GICAN), College of Engineering, Science and Environment (CESE), University of Newcastle, University Drive, Callaghan, New South Wales, 2308, Australia
| | - Xinwei Guan
- Global Innovative Centre for Advanced Nanomaterials (GICAN), College of Engineering, Science and Environment (CESE), University of Newcastle, University Drive, Callaghan, New South Wales, 2308, Australia
| | - Soumyabrata Roy
- Department of Materials Science and Nano Engineering, Rice University, 6100 Main St, Houston, TX, 77005, USA
- Department of Sustainable Energy Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, 208016, India
| | - Jangmee Lee
- Global Innovative Centre for Advanced Nanomaterials (GICAN), College of Engineering, Science and Environment (CESE), University of Newcastle, University Drive, Callaghan, New South Wales, 2308, Australia
| | - In Young Kim
- Global Innovative Centre for Advanced Nanomaterials (GICAN), College of Engineering, Science and Environment (CESE), University of Newcastle, University Drive, Callaghan, New South Wales, 2308, Australia
| | - Xiaomin Li
- Department of Chemistry, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Laboratory of Advanced Materials, State Key Laboratory of Molecular Engineering of Polymers, iChEM (Collaborative Innovation Center of Chemistry for Energy Materials), Fudan University, Shanghai, 200433, P. R. China
| | - Fanxing Bu
- Department of Chemistry, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Laboratory of Advanced Materials, State Key Laboratory of Molecular Engineering of Polymers, iChEM (Collaborative Innovation Center of Chemistry for Energy Materials), Fudan University, Shanghai, 200433, P. R. China
| | - Rohan Bahadur
- Global Innovative Centre for Advanced Nanomaterials (GICAN), College of Engineering, Science and Environment (CESE), University of Newcastle, University Drive, Callaghan, New South Wales, 2308, Australia
| | - Sathvik Ajay Iyengar
- Department of Materials Science and Nano Engineering, Rice University, 6100 Main St, Houston, TX, 77005, USA
| | - Jiabao Yi
- Global Innovative Centre for Advanced Nanomaterials (GICAN), College of Engineering, Science and Environment (CESE), University of Newcastle, University Drive, Callaghan, New South Wales, 2308, Australia
| | - Dongyuan Zhao
- Department of Chemistry, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Laboratory of Advanced Materials, State Key Laboratory of Molecular Engineering of Polymers, iChEM (Collaborative Innovation Center of Chemistry for Energy Materials), Fudan University, Shanghai, 200433, P. R. China
| | - Pulickel M Ajayan
- Department of Materials Science and Nano Engineering, Rice University, 6100 Main St, Houston, TX, 77005, USA
| | - Ajayan Vinu
- Global Innovative Centre for Advanced Nanomaterials (GICAN), College of Engineering, Science and Environment (CESE), University of Newcastle, University Drive, Callaghan, New South Wales, 2308, Australia
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Huang SM, Wang PC, Hung KY, Cheng FE, Li CY, Chou M. On the Paramagnetic-Like Susceptibility Peaks at Zero Magnetic Field in [Formula: see text] Single Crystals. NANOSCALE RESEARCH LETTERS 2022; 17:107. [PMID: 36355312 PMCID: PMC9649580 DOI: 10.1186/s11671-022-03743-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Accepted: 11/01/2022] [Indexed: 06/16/2023]
Abstract
A weakly temperature-dependent paramagnetic-like susceptibility peak at zero magnetic field is observed in [Formula: see text] with only marginal amount of ferromagnetic impurities. The ferromagnetic hysteresis loop and the magnetic moment splitting between zero-field-cooled and field-cooled processes indicate ferromagnetism in the samples. The paramagnetic-like susceptibility peak height is proportional to the remanent magnetic moment of hysteresis loops. High-resolution transmission electron microscope image supports that the observed ferromagnetic feature originates from lattice distortion. These results imply that the weakly temperature-dependent paramagnetic-like susceptibility peak originates from weak lattice distortion and/or superparamagnetism.
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Affiliation(s)
- Shiu-Ming Huang
- Department of Physics, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
- Center of Crystal Research, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
| | - Pin-Cing Wang
- Department of Physics, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
| | - Kuo-Yi Hung
- Department of Physics, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
| | - Fu-En Cheng
- Department of Physics, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
| | - Chang-Yu Li
- Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
| | - Mitch Chou
- Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
- Center of Crystal Research, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
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Huang SM, Wang PC, Chen PC, Hong JL, Cheng CM, Jian HL, Yan YJ, Yu SH, Chou MMC. The Singularity Paramagnetic Peak of Bi 0.3Sb 1.7Te 3 with p-type Surface State. NANOSCALE RESEARCH LETTERS 2022; 17:12. [PMID: 35032238 PMCID: PMC8761187 DOI: 10.1186/s11671-021-03650-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 12/30/2021] [Indexed: 06/14/2023]
Abstract
The magnetization measurement was performed in the Bi0.3Sb1.7Te3 single crystal. The magnetic susceptibility revealed a paramagnetic peak independent of the experimental temperature variation. It is speculated to be originated from the free-aligned spin texture at the Dirac point. The ARPES reveals that the Fermi level lies below the Dirac point. The Fermi wavevector extracted from the de Haas-van Alphen oscillation is consistent with the energy dispersion in the ARPES. Our experimental results support that the observed paramagnetic peak in the susceptibility curve does not originate from the free-aligned spin texture at the Dirac point.
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Affiliation(s)
- Shiu-Ming Huang
- Department of Physics, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
- Taiwan Consortium of Emergent Crystalline Materials, TCECM, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
- Center of Crystal Research, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
| | - Pin-Cing Wang
- Department of Physics, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
| | - Pin-Cyuan Chen
- Department of Physics, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
| | - Jai-Long Hong
- Department of Physics, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
| | - Cheng-Maw Cheng
- National Synchrotron Radiation Research Center, Hsin-Chiu, 80076 Taiwan
| | - Hao-Lun Jian
- Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
| | - You-Jhih Yan
- Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
| | - Shih-Hsun Yu
- Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
| | - Mitch M. C. Chou
- Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
- Taiwan Consortium of Emergent Crystalline Materials, TCECM, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
- Center of Crystal Research, National Sun Yat-Sen University, Kaohsiung, 80424 Taiwan
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Huang SM, Wang PC, Jian HL, Chou MMC. The Magnetic Susceptibility Bifurcation in the Ni-Doped Sb 2Te 3 Topological Insulator with Antiferromagnetic Order Accompanied by Weak Ferromagnetic Alignment. NANOSCALE RESEARCH LETTERS 2021; 16:180. [PMID: 34928440 PMCID: PMC8688649 DOI: 10.1186/s11671-021-03637-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/13/2021] [Accepted: 12/07/2021] [Indexed: 06/14/2023]
Abstract
The magnetic susceptibility reveals a discontinuity at Néel temperature and a hysteresis loop with low coercive field was observed below Néel temperature. The magnetic susceptibility of zero field cool and field cool processes coincide at a temperature above the discontinuity, and they split at temperature blow the discontinuity. The magnetic susceptibility splitting is larger at lower external magnetic fields. No more magnetic susceptibility splitting was observed at a magnetic field above 7000 Oe which is consistent with the magnetic anisotropy energy. Our study supports that these magnetic susceptibility characteristics originate from an antiferromagnetic order accompanied by weak ferromagnetism.
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Affiliation(s)
- Shiu-Ming Huang
- Department of Physics, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
- Center of Crystal Research, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
| | - Pin-Cing Wang
- Department of Physics, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
| | - Hao-Lun Jian
- Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
| | - Mitch M. C. Chou
- Center of Crystal Research, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
- Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
- Taiwan Consortium of Emergent Crystalline Materials, TCECM, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
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Faílde D, Baldomir D. Emergent topological fields and relativistic phonons within the thermoelectricity in topological insulators. Sci Rep 2021; 11:14335. [PMID: 34253786 PMCID: PMC8275584 DOI: 10.1038/s41598-021-93667-x] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2021] [Accepted: 06/22/2021] [Indexed: 02/06/2023] Open
Abstract
Topological edge states are predicted to be responsible for the high efficient thermoelectric response of topological insulators, currently the best thermoelectric materials. However, to explain their figure of merit the coexistence of topological electrons, entropy and phonons can not be considered independently. In a background that puts together electrodynamics and topology, through an expression for the topological intrinsic field, we treat relativistic phonons within the topological surface showing their ability to modulate the Berry curvature of the bands and then playing a fundamental role in the thermoelectric effect. Finally, we show how the topological insulators under such relativistic thermal excitations keep time reversal symmetry allowing the observation of high figures of merit at high temperatures. The emergence of this new intrinsic topological field and other constraints are suitable to have experimental consequences opening new possibilities of improving the efficiency of this topological effect for their based technology.
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Affiliation(s)
- Daniel Faílde
- Departamento de Física Aplicada, Instituto de Investigacións Tecnolóxicas, Universidade de Santiago de Compostela, Campus Vida s/n, 15782, Santiago de Compostela, Spain.
| | - Daniel Baldomir
- Departamento de Física Aplicada, Instituto de Investigacións Tecnolóxicas, Universidade de Santiago de Compostela, Campus Vida s/n, 15782, Santiago de Compostela, Spain.
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Imaging current distribution in a topological insulator Bi 2Se 3 in the presence of competing surface and bulk contributions to conductivity. Sci Rep 2021; 11:7445. [PMID: 33811220 PMCID: PMC8018954 DOI: 10.1038/s41598-021-86706-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2020] [Accepted: 03/15/2021] [Indexed: 11/10/2022] Open
Abstract
Two-dimensional (2D) topological surface states in a three-dimensional topological insulator (TI) should produce uniform 2D surface current distribution. However, our transport current imaging studies on Bi2Se3 thin film reveal non-uniform current sheet flow at 15 K with strong edge current flow. This is consistent with other imaging studies on thin films of Bi2Se3. In contrast to strong edge current flow in thin films, in single crystal of Bi2Se3 at 15 K our current imaging studies show the presence of 3.6 nm thick uniform 2D sheet current flow. Above 70 K, this uniform 2D sheet current sheet begins to disintegrate into a spatially non-uniform flow. The flow becomes patchy with regions having high and low current density. The area fraction of the patches with high current density rapidly decreases at temperatures above 70 K, with a temperature dependence of the form \documentclass[12pt]{minimal}
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\begin{document}$$1/\left| {T - 70} \right|^{0.35}$$\end{document}1/T-700.35. The temperature scale of 70 K coincides with the onset of bulk conductivity in the crystal due to electron doping by selenium vacancy clusters in Bi2Se3. Thus our results show a temperature dependent competition between surface and bulk conductivity produces a temperature dependent variation in uniformity of current flow in the topological insulator.
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Singha R, Satpati B, Mandal P. Fermi surface topology and signature of surface Dirac nodes in LaBi. Sci Rep 2017; 7:6321. [PMID: 28740199 PMCID: PMC5524763 DOI: 10.1038/s41598-017-06697-9] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2017] [Accepted: 06/14/2017] [Indexed: 11/09/2022] Open
Abstract
Novel topological state of matter is one of the rapidly growing fields in condensed matter physics research in recent times. While these materials are fascinating from the aspect of fundamental physics of relativistic particles, their exotic transport properties are equally compelling due to the potential technological applications. Extreme magnetoresistance and ultrahigh carrier mobility are two such major hallmarks of topological materials and often used as primary criteria for identifying new compounds belonging to this class. Recently, LaBi has emerged as a new system, which exhibits the above mentioned properties. However, the topological nature of its band structure remains unresolved. Here, using the magnetotransport and magnetization measurements, we have probed the bulk and surface states of LaBi. Similar to earlier reports, extremely large magnetoresistance and high carrier mobility have been observed with compensated electron and hole density. The Fermi surface properties have been analyzed from both Shubnikov-de Haas and de Haas-van Alphen oscillation techniques. In the magnetization measurement, a prominent paramagnetic singularity has been observed, which demonstrates the non-trivial nature of the surface states in LaBi. Our study unambiguously confirms that LaBi is a three-dimensional topological insulator with possible linear dispersion in the gapped bulk band structure.
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Affiliation(s)
- Ratnadwip Singha
- Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Calcutta, 700 064, India
| | - Biswarup Satpati
- Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Calcutta, 700 064, India
| | - Prabhat Mandal
- Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Calcutta, 700 064, India.
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Prominent metallic surface conduction and the singular magnetic response of topological Dirac fermion in three-dimensional topological insulator Bi 1.5Sb 0.5Te 1.7Se 1.3. Sci Rep 2017; 7:4883. [PMID: 28687771 PMCID: PMC5501823 DOI: 10.1038/s41598-017-05164-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2016] [Accepted: 04/11/2017] [Indexed: 11/08/2022] Open
Abstract
We report semiconductor to metal-like crossover in the temperature dependence of resistivity (ρ) due to the switching of charge transport from bulk to surface channel in three-dimensional topological insulator Bi1.5Sb0.5Te1.7Se1.3. Unlike earlier studies, a much sharper drop in ρ(T) is observed below the crossover temperature due to the dominant surface conduction. Remarkably, the resistivity of the conducting surface channel follows a rarely observable T 2 dependence at low temperature, as predicted theoretically for a two-dimensional Fermi liquid system. The field dependence of magnetization shows a cusp-like paramagnetic peak in the susceptibility (χ) at zero field over the diamagnetic background. The peak is found to be robust against temperature and χ decays linearly with the field from its zero-field value. This unique behavior of the χ is associated with the spin-momentum locked topological surface state in Bi1.5Sb0.5Te1.7Se1.3. The reconstruction of the surface state with time is clearly reflected through the reduction of the peak height with the age of the sample.
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Pariari A, Mandal P. Coexistence of topological Dirac fermions on the surface and three-dimensional Dirac cone state in the bulk of ZrTe 5 single crystal. Sci Rep 2017; 7:40327. [PMID: 28067306 PMCID: PMC5220326 DOI: 10.1038/srep40327] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2016] [Accepted: 12/02/2016] [Indexed: 11/08/2022] Open
Abstract
Although, the long-standing debate on the resistivity anomaly in ZrTe5 somewhat comes to an end, the exact topological nature of the electronic band structure remains elusive till today. Theoretical calculations predicted that bulk ZrTe5 to be either a weak or a strong three-dimensional (3D) topological insulator. However, the angle resolved photoemission spectroscopy and transport measurements clearly demonstrate 3D Dirac cone state with a small mass gap between the valence band and conduction band in the bulk. From the magnetization and magneto-transport measurements on ZrTe5 single crystal, we have detected both the signature of helical spin texture from topological surface state and chiral anomaly associated with the 3D Dirac cone state in the bulk. This implies that ZrTe5 hosts a novel electronic phase of material, having massless Dirac fermionic excitation in its bulk gap state, unlike earlier reported 3D topological insulators. Apart from the band topology, it is also apparent from the resistivity and Hall measurements that the anomalous peak in the resistivity can be shifted to a much lower temperature (T < 2 K) by controlling impurity and defects.
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Affiliation(s)
- Arnab Pariari
- Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Calcutta 700 064, India
| | - Prabhat Mandal
- Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Calcutta 700 064, India
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Emergent surface superconductivity in the topological insulator Sb2Te3. Nat Commun 2015; 6:8279. [PMID: 26359207 DOI: 10.1038/ncomms9279] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2014] [Accepted: 08/06/2015] [Indexed: 11/09/2022] Open
Abstract
Surfaces of three-dimensional topological insulators have emerged as one of the most remarkable states of condensed quantum matter where exotic electronic phases of Dirac particles should arise. Here we report on superconductivity in the topological insulator Sb2Te3 with transition to zero resistance induced through a minor tuning of growth chemistry that depletes bulk conduction channels. The depletion shifts Fermi energy towards the Dirac point as witnessed by a factor of 300 reduction of bulk carrier density and by the largest carrier mobility (≳25,000 cm(2) V(-1) s(-1)) found in any topological material. Direct evidence from transport, the unprecedentedly large diamagnetic screening, and the presence of ∼25 meV gaps detected by scanning tunnelling spectroscopy reveal the superconducting condensate to emerge first in surface puddles, with the onset of global phase coherence at ∼9 K. The rich structure of this state lends itself to manipulation via growth conditions and the material parameters such as Fermi velocity and mean free path.
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Lundgren R, Maciejko J. Landau Theory of Helical Fermi Liquids. PHYSICAL REVIEW LETTERS 2015; 115:066401. [PMID: 26296123 DOI: 10.1103/physrevlett.115.066401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2015] [Indexed: 06/04/2023]
Abstract
We construct a phenomenological Landau theory for the two-dimensional helical Fermi liquid found on the surface of a three-dimensional time-reversal invariant topological insulator. In the presence of rotation symmetry, interactions between quasiparticles are described by ten independent Landau parameters per angular momentum channel, by contrast with the two (symmetric and antisymmetric) Landau parameters for a conventional spin-degenerate Fermi liquid. We project quasiparticle states onto the Fermi surface and obtain an effectively spinless, projected Landau theory with a single projected Landau parameter per angular momentum channel that captures the spin-momentum locking or nontrivial Berry phase of the Fermi surface. As a result of this nontrivial Berry phase, projection to the Fermi surface can increase or lower the angular momentum of the quasiparticle interactions. We derive equilibrium properties, criteria for Fermi surface instabilities, and collective mode dispersions in terms of the projected Landau parameters. We briefly discuss experimental means of measuring projected Landau parameters.
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Affiliation(s)
- Rex Lundgren
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Joseph Maciejko
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
- Theoretical Physics Institute, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
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