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Melnikov MY, Shakirov AA, Shashkin AA, Huang SH, Liu CW, Kravchenko SV. Spin independence of the strongly enhanced effective mass in ultra-clean SiGe/Si/SiGe two-dimensional electron system. Sci Rep 2023; 13:17364. [PMID: 37833499 PMCID: PMC10575913 DOI: 10.1038/s41598-023-44580-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2023] [Accepted: 10/10/2023] [Indexed: 10/15/2023] Open
Abstract
The effective mass at the Fermi level is measured in the strongly interacting two-dimensional (2D) electron system in ultra-clean SiGe/Si/SiGe quantum wells in the low-temperature limit in tilted magnetic fields. At low electron densities, the effective mass is found to be strongly enhanced and independent of the degree of spin polarization, which indicates that the mass enhancement is not related to the electrons' spins. The observed effect turns out to be universal for silicon-based 2D electron systems, regardless of random potential, and cannot be explained by existing theories.
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Affiliation(s)
- M Yu Melnikov
- Institute of Solid State Physics, Chernogolovka, Moscow District, 142432, Russia
| | - A A Shakirov
- Institute of Solid State Physics, Chernogolovka, Moscow District, 142432, Russia
| | - A A Shashkin
- Institute of Solid State Physics, Chernogolovka, Moscow District, 142432, Russia
| | - S H Huang
- Department of Electrical Engineering and Graduate Institute of Electronics Engineering, National Taiwan University, Taipei, 106, Taiwan
| | - C W Liu
- Department of Electrical Engineering and Graduate Institute of Electronics Engineering, National Taiwan University, Taipei, 106, Taiwan
| | - S V Kravchenko
- Department of Physics, Northeastern University, Boston, MA, 02115, USA.
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2
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Sankar S, Sela E, Han C. Measuring Topological Entanglement Entropy Using Maxwell Relations. PHYSICAL REVIEW LETTERS 2023; 131:016601. [PMID: 37478453 DOI: 10.1103/physrevlett.131.016601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/31/2022] [Accepted: 06/08/2023] [Indexed: 07/23/2023]
Abstract
Topological entanglement entropy (TEE) is a key diagnostic of topological order, allowing one to detect the presence of Abelian or non-Abelian anyons. However, there are currently no experimentally feasible protocols to measure TEE in condensed matter systems. Here, we propose a scheme to measure the TEE of chiral topological phases, carrying protected edge states, based on a nontrivial connection with the thermodynamic entropy change occurring in a quantum point contact (QPC) as it pinches off the topological liquid into two. We show how this entropy change can be extracted using Maxwell relations from charge detection of a nearby quantum dot. We demonstrate this explicitly for the Abelian Laughlin states, using an exact solution of the sine-Gordon model describing the universal crossover in the QPC. Our approach might open a new thermodynamic detection scheme of topological states also with non-Abelian statistics.
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Affiliation(s)
- Sarath Sankar
- School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Eran Sela
- School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Cheolhee Han
- School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
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3
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Spin effect on the low-temperature resistivity maximum in a strongly interacting 2D electron system. Sci Rep 2022; 12:5080. [PMID: 35332223 PMCID: PMC8948273 DOI: 10.1038/s41598-022-09034-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2022] [Accepted: 03/16/2022] [Indexed: 11/08/2022] Open
Abstract
The increase in the resistivity with decreasing temperature followed by a drop by more than one order of magnitude is observed on the metallic side near the zero-magnetic-field metal-insulator transition in a strongly interacting two-dimensional electron system in ultra-clean SiGe/Si/SiGe quantum wells. We find that the temperature [Formula: see text], at which the resistivity exhibits a maximum, is close to the renormalized Fermi temperature. However, rather than increasing along with the Fermi temperature, the value [Formula: see text] decreases appreciably for spinless electrons in spin-polarizing (parallel) magnetic fields. The observed behaviour of [Formula: see text] cannot be described by existing theories. The results indicate the spin-related origin of the effect.
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4
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Rozen A, Park JM, Zondiner U, Cao Y, Rodan-Legrain D, Taniguchi T, Watanabe K, Oreg Y, Stern A, Berg E, Jarillo-Herrero P, Ilani S. Entropic evidence for a Pomeranchuk effect in magic-angle graphene. Nature 2021; 592:214-219. [PMID: 33828314 DOI: 10.1038/s41586-021-03319-3] [Citation(s) in RCA: 37] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Accepted: 01/29/2021] [Indexed: 11/09/2022]
Abstract
In the 1950s, Pomeranchuk1 predicted that, counterintuitively, liquid 3He may solidify on heating. This effect arises owing to high excess nuclear spin entropy in the solid phase, where the atoms are spatially localized. Here we find that an analogous effect occurs in magic-angle twisted bilayer graphene2-6. Using both local and global electronic entropy measurements, we show that near a filling of one electron per moiré unit cell, there is a marked increase in the electronic entropy to about 1kB per unit cell (kB is the Boltzmann constant). This large excess entropy is quenched by an in-plane magnetic field, pointing to its magnetic origin. A sharp drop in the compressibility as a function of the electron density, associated with a reset of the Fermi level back to the vicinity of the Dirac point, marks a clear boundary between two phases. We map this jump as a function of electron density, temperature and magnetic field. This reveals a phase diagram that is consistent with a Pomeranchuk-like temperature- and field-driven transition from a low-entropy electronic liquid to a high-entropy correlated state with nearly free magnetic moments. The correlated state features an unusual combination of seemingly contradictory properties, some associated with itinerant electrons-such as the absence of a thermodynamic gap, metallicity and a Dirac-like compressibility-and others associated with localized moments, such as a large entropy and its disappearance under a magnetic field. Moreover, the energy scales characterizing these two sets of properties are very different: whereas the compressibility jump has an onset at a temperature of about 30 kelvin, the bandwidth of magnetic excitations is about 3 kelvin or smaller. The hybrid nature of the present correlated state and the large separation of energy scales have implications for the thermodynamic and transport properties of the correlated states in twisted bilayer graphene.
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Affiliation(s)
- Asaf Rozen
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Jeong Min Park
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Uri Zondiner
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Yuan Cao
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Daniel Rodan-Legrain
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | | | - Kenji Watanabe
- National Institute for Materials Science, Tsukuba, Japan
| | - Yuval Oreg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Ady Stern
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Erez Berg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel.
| | | | - Shahal Ilani
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel.
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5
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Kavokin AV, Altshuler BL, Sharapov SG, Grigoryev PS, Varlamov AA. The Nernst effect in Corbino geometry. Proc Natl Acad Sci U S A 2020; 117:2846-2851. [PMID: 31992642 PMCID: PMC7022160 DOI: 10.1073/pnas.1916567117] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We study the manifestation of the Nernst effect in the Corbino disk subjected to the normal external magnetic field and to the radial temperature gradient. The Corbino geometry offers a precious opportunity for the direct measurement of the magnetization currents that are masked by kinetic contributions to the Nernst current in the conventional geometry. The magnetization currents, also referred to as the edge currents, are independent on the conductivity of the sample which is why they can be conveniently described within the thermodynamic approach. They can be related to the Landau thermodynamic potential for an infinite system. We demonstrate that the observable manifestation of this, purely thermodynamic, Nernst effect consists in the strong oscillations of the magnetic field measured in the center of the disk as a function of the external field. The oscillations depend on the temperature difference at the edges of the disk. Dirac fermions and 2D electrons with a parabolic spectrum are characterized by oscillations of different phase and frequency. We predict qualitatively different power dependencies of the magnitude of the Nernst signal on the chemical potential for normal and Dirac carriers.
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Affiliation(s)
- A V Kavokin
- Westlake University, Hangzhou 310024, Zhejiang Province, China;
| | - B L Altshuler
- Westlake University, Hangzhou 310024, Zhejiang Province, China;
- Department of Physics, Columbia University, New York, NY 10027
| | - S G Sharapov
- Bogolyubov Institute for Theoretical Physics, National Academy of Science of Ukraine, Kyiv 03680, Ukraine
| | - P S Grigoryev
- Spin Optics Laboratory, St. Petersburg State University, 198504 St. Petersburg, Russia
| | - A A Varlamov
- Consiglio Nazionale delle Ricerche-Superconducting and Other Innovative Materials and Devices Institute (CNR-SPIN), DICII-Universitá di Roma Tor Vergata, I-00133 Roma, Italy
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6
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Sela E, Oreg Y, Plugge S, Hartman N, Lüscher S, Folk J. Detecting the Universal Fractional Entropy of Majorana Zero Modes. PHYSICAL REVIEW LETTERS 2019; 123:147702. [PMID: 31702171 DOI: 10.1103/physrevlett.123.147702] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2019] [Indexed: 06/10/2023]
Abstract
A pair of Majorana zero modes (MZMs) constitutes a nonlocal qubit whose entropy is log2. Upon strongly coupling one of the constituent MZMs to a reservoir with a continuous density of states, a universal entropy change of 1/2log2 is expected to be observed across an intermediate temperature plateau. We adapt the entropy-measurement scheme that was the basis of a recent experiment by Hartman et al. [Nat. Phys. 14, 1083 (2018)10.1038/s41567-018-0250-5] to the case of a proximitized topological system hosting MZMs and propose a method to measure this 1/2log2 entropy change-an unambiguous signature of the nonlocal nature of the topological state. This approach offers an experimental strategy to distinguish MZMs from non topological states.
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Affiliation(s)
- Eran Sela
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, IL-69978 Tel Aviv, Israel
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T1Z1, Canada
| | - Yuval Oreg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Stephan Plugge
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T1Z1, Canada
| | - Nikolaus Hartman
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T1Z1, Canada
| | - Silvia Lüscher
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T1Z1, Canada
| | - Joshua Folk
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T1Z1, Canada
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7
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Entropy spikes as a signature of Lifshitz transitions in the Dirac materials. Sci Rep 2017; 7:10271. [PMID: 28860524 PMCID: PMC5578978 DOI: 10.1038/s41598-017-10643-0] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2017] [Accepted: 08/11/2017] [Indexed: 11/16/2022] Open
Abstract
We demonstrate theoretically that the characteristic feature of a 2D system undergoing N consequent Lifshitz topological transitions is the occurrence of spikes of entropy per particle s of a magnitude ±ln2/(J − 1/2) with 2 ≤ J ≤ N at low temperatures. We derive a general expression for s as a function of chemical potential, temperature and gap magnitude for the gapped Dirac materials. Inside the smallest gap, the dependence of s on the chemical potential exhibits a dip-and-peak structure in the temperature vicinity of the Dirac point. The spikes of the entropy per particles can be considered as a signature of the Dirac materials. These distinctive characteristics of gapped Dirac materials can be detected in transport experiments where the temperature is modulated in gated structures.
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