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Sharma A, Pu S, Balram AC, Jain JK. Fractional Quantum Hall Effect with Unconventional Pairing in Monolayer Graphene. PHYSICAL REVIEW LETTERS 2023; 130:126201. [PMID: 37027884 DOI: 10.1103/physrevlett.130.126201] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2022] [Accepted: 02/24/2023] [Indexed: 06/19/2023]
Abstract
Motivated by the observation of even denominator fractional quantum Hall effect in the n=3 Landau level of monolayer graphene [Kim et al., Nat. Phys. 15, 154 (2019)NPAHAX1745-247310.1038/s41567-018-0355-x], we consider a Bardeen-Cooper-Schrieffer variational state for composite fermions and find that the composite-fermion Fermi sea in this Landau level is unstable to an f-wave pairing. Analogous calculation suggests the possibility of a p-wave pairing of composite fermions at half filling in the n=2 graphene Landau level, whereas no pairing instability is found at half filling in the n=0 and n=1 graphene Landau levels. The relevance of these results to experiments is discussed.
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Affiliation(s)
- Anirban Sharma
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Songyang Pu
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Ajit C Balram
- Institute of Mathematical Sciences, CIT Campus, Chennai, 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai, 400094, India
| | - J K Jain
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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2
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Jacak JE. Limits of Applicability of the Composite Fermion Model. MATERIALS (BASEL, SWITZERLAND) 2021; 14:4267. [PMID: 34361462 PMCID: PMC8348463 DOI: 10.3390/ma14154267] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/30/2021] [Revised: 07/18/2021] [Accepted: 07/24/2021] [Indexed: 11/16/2022]
Abstract
The popular model of composite fermions, proposed in order to rationalize FQHE, were insufficient in view of recent experimental observations in graphene monolayer and bilayer, in higher Landau levels in GaAs and in so-called enigmatic FQHE states in the lowest Landau level of GaAs. The specific FQHE hierarchy in double Hall systems of GaAs 2DES and graphene also cannot be explained in the framework of composite fermions. We identify the limits of the usability of the composite fermion model by means of topological methods, which elucidate the phenomenological assumptions in composite fermion structure and admit further development of FQHE understanding. We demonstrate how to generalize these ideas in order to explain experimentally observed FQHE phenomena, going beyond the explanation ability of the conventional composite fermion model.
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Affiliation(s)
- Janusz E Jacak
- Department of Quantum Technologies, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
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Jacak JE. Topological Classification of Correlations in 2D Electron Systems in Magnetic or Berry Fields. MATERIALS (BASEL, SWITZERLAND) 2021; 14:1650. [PMID: 33801698 PMCID: PMC8037989 DOI: 10.3390/ma14071650] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/30/2021] [Revised: 03/15/2021] [Accepted: 03/24/2021] [Indexed: 11/16/2022]
Abstract
Recent topology classification of 2D electron states induced by different homotopy classes of mappings of the planar Brillouin zone into Bloch space can be supplemented by a homotopy classification of various phases of multi-electron homotopy patterns induced by Coulomb interaction between electrons. The general classification of such type is presented. It explains the topologically protected correlations responsible for integer and fractional Hall effects in 2D multi-electron systems in the presence of perpendicular quantizing magnetic field or Berry field, the latter in topological Chern insulators. The long-range quantum entanglement is essential for homotopy correlated phases in contrast to local binary entanglement for conventional phases with local order parameters. The classification of homotopy long-range correlated phases induced by the Coulomb interaction of electrons has been derived in terms of homotopy invariants and illustrated by experimental observations in GaAs 2DES, graphene monolayer, and bilayer and in Chern topological insulators. The homotopy phases are demonstrated to be topologically protected and immune to the local crystal field, local disorder, and variation of the electron interaction strength. The nonzero interaction between electrons is shown, however, to be essential for the definition of the homotopy invariants, which disappear in gaseous systems.
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Affiliation(s)
- Janusz E Jacak
- Department of Quantum Technologies, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
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Jacak JE. Homotopy Phases of FQHE with Long-Range Quantum Entanglement in Monolayer and Bilayer Hall Systems. NANOMATERIALS (BASEL, SWITZERLAND) 2020; 10:E1286. [PMID: 32629942 PMCID: PMC7408279 DOI: 10.3390/nano10071286] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/09/2020] [Revised: 06/08/2020] [Accepted: 06/19/2020] [Indexed: 06/11/2023]
Abstract
Correlated phases in Hall systems have topological character. Multilayer configurations of planar electron systems create the opportunity to change topological phases on demand using macroscopic factors, such as vertical voltage. We present an analysis of such phenomena in close relation to recent experiments with multilayer Hall setups including GaAs and graphene multi-layers. The consequences of the blocking or not of the inter-layer electron tunneling in stacked Hall configurations are analyzed and presented in detail. Multilayer Hall systems are thus tunable topological composite nanomaterials, in the case of graphene-stacked systems by both intra- and inter-layer voltage.
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Affiliation(s)
- Janusz Edward Jacak
- Department of Quantum Technologies, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
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Polshyn H, Zhou H, Spanton EM, Taniguchi T, Watanabe K, Young AF. Quantitative Transport Measurements of Fractional Quantum Hall Energy Gaps in Edgeless Graphene Devices. PHYSICAL REVIEW LETTERS 2018; 121:226801. [PMID: 30547606 DOI: 10.1103/physrevlett.121.226801] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2018] [Revised: 10/19/2018] [Indexed: 06/09/2023]
Abstract
Owing to their wide tunability, multiple internal degrees of freedom, and low disorder, graphene heterostructures are emerging as a promising experimental platform for fractional quantum Hall (FQH) studies. Here, we report FQH thermal activation gap measurements in dual graphite-gated monolayer graphene devices fabricated in an edgeless Corbino geometry. In devices with substrate-induced sublattice splitting, we find a tunable crossover between single- and multicomponent FQH states in the zero energy Landau level. Activation gaps in the single-component regime show excellent agreement with numerical calculations using a single broadening parameter Γ≈7.2 K. In the first excited Landau level, in contrast, FQH gaps are strongly influenced by Landau level mixing, and we observe an unexpected valley-ordered state at integer filling ν=-4.
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Affiliation(s)
- H Polshyn
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - H Zhou
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - E M Spanton
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - T Taniguchi
- Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan
| | - K Watanabe
- Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan
| | - A F Young
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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Li J, Tupikov Y, Watanabe K, Taniguchi T, Zhu J. Effective Landau Level Diagram of Bilayer Graphene. PHYSICAL REVIEW LETTERS 2018; 120:047701. [PMID: 29437431 DOI: 10.1103/physrevlett.120.047701] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2017] [Revised: 11/18/2017] [Indexed: 06/08/2023]
Abstract
The E=0 octet of bilayer graphene in the filling factor range of -4<ν<4 is a fertile playground for many-body phenomena, yet a Landau level diagram is missing due to strong interactions and competing quantum degrees of freedom. We combine measurements and modeling to construct an empirical and quantitative spectrum. The single-particlelike diagram incorporates interaction effects effectively and provides a unified framework to understand the occupation sequence, gap energies, and phase transitions observed in the octet. It serves as a new starting point for more sophisticated calculations and experiments.
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Affiliation(s)
- Jing Li
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Yevhen Tupikov
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Kenji Watanabe
- National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Jun Zhu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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Jacak JE. Unconventional fractional quantum Hall effect in bilayer graphene. Sci Rep 2017; 7:8720. [PMID: 28821795 PMCID: PMC5562899 DOI: 10.1038/s41598-017-09166-5] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2017] [Accepted: 07/24/2017] [Indexed: 12/05/2022] Open
Abstract
Recent experimental progress in Hall measurements in bilayer graphene in the so-called open-face configuration of boron nitride encapsulated samples, together with the earlier technique of suspended samples, allows for precise observation of the fractional quantum Hall effect (FQHE) in all 4 subbands of the Lowest Landau level (with n = 0 and n = 1) and in the next LL subbands (with n = 2) in the bilayer system. Many newly observed FQHE features do not agree with a conventional model of composite fermions and reveal a different hierarchy in comparison to monolayer graphene or GaAs 2DEG. We explain the peculiarity of the FQHE hierarchy in the bilayer system in the framework of a topological approach, which includes the composite fermion model as its special case. Inclusion of a topological effect caused by the hopping of electrons between the two sheets in the bilayer system allowed for an explanation of the FQHE hierarchy in the graphene bilayer in satisfactory accordance with the experimental observations.
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Affiliation(s)
- Janusz Edward Jacak
- Department of Quantum Technologies, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wyb. Wyspianskiego 27, 50-370, Wrocław, Poland.
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Chuang C, Yang Y, Pookpanratana S, Hacker CA, Liang CT, Elmquist RE. Chemical-doping-driven crossover from graphene to "ordinary metal" in epitaxial graphene grown on SiC. NANOSCALE 2017; 9:11537-11544. [PMID: 28767112 DOI: 10.1039/c7nr04155a] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Atmospheric chemical doping can be used to modify the electronic properties of graphene. Here we report that the chemical atmospheric doping (derived from air, oxygen and water vapor) of low-carrier-density monolayer epitaxial graphene on SiC can be readily tuned by a simple low-temperature (T ≤ 450 K), in situ vacuum gentle heating method. Interestingly, such an approach allows, for the first time, the observation of a crossover from graphene (μt/μq ≈ 2) to an "ordinary metal" (μt/μq ≈ 1) with decreasing carrier density, where μt and μq are transport mobility and quantum mobility, respectively. In the low carrier density limit, our results are consistent with the theoretical prediction that μt is inversely proportional to charged impurity density. Our data also suggest that atmospheric chemical doping can be used to vary intervalley scattering in graphene which plays a crucial role in backward scattering events.
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Affiliation(s)
- Chiashain Chuang
- National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, USA.
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Huang LI, Yang Y, Liu CW, Elmquist RE, Lo ST, Liu FH, Liang CT. Unusual renormalization group (RG) flow and temperature-dependent phase transition in strongly-insulating monolayer epitaxial graphene. RSC Adv 2017. [DOI: 10.1039/c7ra05463g] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
By changing the measurement temperature (T), one can vary the effective sample size so as to study the renormalization group (RG) (or T-driven) flow of a semiconductor, a topological insulator, or a graphene device in the complex conductivity plane.
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Affiliation(s)
- Lung-I. Huang
- National Institute of Standards and Technology (NIST)
- Gaithersburg
- USA
- Department of Physics
- National Taiwan University
| | - Yanfei Yang
- National Institute of Standards and Technology (NIST)
- Gaithersburg
- USA
- Joint Quantum Institute
- University of Maryland
| | - Chieh-Wen Liu
- National Institute of Standards and Technology (NIST)
- Gaithersburg
- USA
- Graduate Institute of Applied Physics
- National Taiwan University
| | | | - Shun-Tsung Lo
- Graduate Institute of Applied Physics
- National Taiwan University
- Taipei 106
- Taiwan
| | - Fan-Hung Liu
- Graduate Institute of Applied Physics
- National Taiwan University
- Taipei 106
- Taiwan
| | - Chi-Te Liang
- Department of Physics
- National Taiwan University
- Taipei 106
- Taiwan
- Graduate Institute of Applied Physics
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