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Freeman ML, Madathil PT, Pfeiffer LN, Baldwin KW, Chung YJ, Winkler R, Shayegan M, Engel LW. Origin of Pinning Disorder in Magnetic-Field-Induced Wigner Solids. PHYSICAL REVIEW LETTERS 2024; 132:176301. [PMID: 38728701 DOI: 10.1103/physrevlett.132.176301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2023] [Revised: 02/28/2024] [Accepted: 03/29/2024] [Indexed: 05/12/2024]
Abstract
At low Landau level filling factors (ν), Wigner solid phases of two-dimensional electron systems in GaAs are pinned by disorder and exhibit a pinning mode, whose frequency is a measure of the disorder that pins the Wigner solid. Despite numerous studies spanning the past three decades, the origin of the disorder that causes the pinning and determines the pinning mode frequency remains unknown. Here, we present a study of the pinning mode resonance in the low-ν Wigner solid phases of a series of ultralow-disorder GaAs quantum wells which are similar except for their varying well widths d. The pinning mode frequencies f_{p} decrease strongly as d increases, with the widest well exhibiting f_{p} as low as ≃35 MHz. The amount of reduction of f_{p} with increasing d can be explained remarkably well by tails of the wave function impinging into the alloy-disordered Al_{x}Ga_{1-x}As barriers that contain the electrons. However, it is imperative that the model for the confinement and wave function includes the Coulomb repulsion in the growth direction between the electrons as they occupy the quantum well.
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Affiliation(s)
- Matthew L Freeman
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
| | - P T Madathil
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R Winkler
- Northern Illinois University, DeKalb, Illinois 60115, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L W Engel
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
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Freeman ML, Lu TM, Engel LW. Resistively loaded coplanar waveguide for microwave measurements of induced carriers. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2022; 93:043901. [PMID: 35489888 DOI: 10.1063/5.0085112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 02/28/2022] [Indexed: 06/14/2023]
Abstract
We describe the use of a coplanar waveguide (CPW) whose slots are filled with a resistive film, a resistively loaded CPW (RLCPW), to measure two-dimensional electron systems (2DESs). The RLCPW applied to the sample hosting the 2DES provides a uniform metallic surface serving as a gate to control the areal charge density of the 2DES. As a demonstration of this technique, we present measurements on a Si metal-oxide-semiconductor field-effect transistor and a model that successfully converts microwave transmission coefficients into conductivity of a nearby 2DES capacitively coupled to the RLCPW. We also describe the process of fabricating the highly resistive metal film required for fabrication of the RLCPW.
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Affiliation(s)
- M L Freeman
- Physics Department, Florida State University, Tallahassee, Florida 32306, USA
| | - Tzu-Ming Lu
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - L W Engel
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
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3
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Villegas Rosales KA, Madathil PT, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Fractional Quantum Hall Effect Energy Gaps: Role of Electron Layer Thickness. PHYSICAL REVIEW LETTERS 2021; 127:056801. [PMID: 34397247 DOI: 10.1103/physrevlett.127.056801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Accepted: 06/24/2021] [Indexed: 06/13/2023]
Abstract
The fractional quantum Hall effect stands as a quintessential manifestation of an interacting two-dimensional electron system. One of the fractional quantum Hall effect's most fundamental characteristics is the energy gap separating the incompressible ground state from its excitations. Yet, despite nearly four decades of investigations, a quantitative agreement between the theoretically calculated and experimentally measured energy gaps is lacking. Here we report a systematic experimental study that incorporates very high-quality two-dimensional electron systems confined to GaAs quantum wells with fixed density and varying well widths. The results demonstrate a clear decrease of the energy gap as the electron layer is made thicker and the short-range component of the Coulomb interaction is weakened. We also provide a quantitative comparison between the measured energy gaps and the available theoretical calculations that takes into account the role of finite layer thickness and Landau level mixing. All the measured energy gaps fall below the calculations, but as the electron layer thickness increases, the results of experiments and calculations come closer. Accounting for the role of disorder in a phenomenological manner, we find better overall agreement between the measured and calculated energy gaps, although some puzzling discrepancies remain.
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Affiliation(s)
- K A Villegas Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - P T Madathil
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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Jin D, Xia Y, Christensen T, Freeman M, Wang S, Fong KY, Gardner GC, Fallahi S, Hu Q, Wang Y, Engel L, Xiao ZL, Manfra MJ, Fang NX, Zhang X. Topological kink plasmons on magnetic-domain boundaries. Nat Commun 2019; 10:4565. [PMID: 31594922 PMCID: PMC6783483 DOI: 10.1038/s41467-019-12092-x] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Accepted: 07/31/2019] [Indexed: 11/09/2022] Open
Abstract
Two-dimensional topological materials bearing time reversal-breaking magnetic fields support protected one-way edge modes. Normally, these edge modes adhere to physical edges where material properties change abruptly. However, even in homogeneous materials, topology still permits a unique form of edge modes – kink modes – residing at the domain boundaries of magnetic fields within the materials. This scenario, despite being predicted in theory, has rarely been demonstrated experimentally. Here, we report our observation of topologically-protected high-frequency kink modes – kink magnetoplasmons (KMPs) – in a GaAs/AlGaAs two-dimensional electron gas (2DEG) system. These KMPs arise at a domain boundary projected from an externally-patterned magnetic field onto a uniform 2DEG. They propagate unidirectionally along the boundary, protected by a difference of gap Chern numbers (\documentclass[12pt]{minimal}
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\begin{document}$$\pm1$$\end{document}±1) in the two domains. They exhibit large tunability under an applied magnetic field or gate voltage, and clear signatures of nonreciprocity even under weak-coupling to evanescent photons. Topological kink modes are peculiar edge excitations that take place at domain boundaries of magnetic fields inside homogeneous materials. Here, the authors experimentally observe kink magnetoplasmons in a 2D electron gas using custom-shaped strong permanent magnets on top of a GaAs/AlGaAs heterojunction.
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Affiliation(s)
- Dafei Jin
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, 94706, USA.,Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL, 60439, USA
| | - Yang Xia
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, 94706, USA
| | - Thomas Christensen
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Matthew Freeman
- National High Magnetic Field Laboratory, Tallahassee, FL, 32310, USA
| | - Siqi Wang
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, 94706, USA
| | - King Yan Fong
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, 94706, USA
| | - Geoffrey C Gardner
- Microsoft Quantum Purdue and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA
| | - Saeed Fallahi
- Department of Physics and Astronomy and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA
| | - Qing Hu
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Yuan Wang
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, 94706, USA
| | - Lloyd Engel
- National High Magnetic Field Laboratory, Tallahassee, FL, 32310, USA
| | - Zhi-Li Xiao
- Material Science Division, Argonne National Laboratory, Argonne, IL, 60439, USA
| | - Michael J Manfra
- Microsoft Quantum Purdue, Department of Physics and Astronomy, Birck Nanotechnology Center, Schools of Electrical and Computer Engineering and Materials Engineering, Purdue University, West Lafayette, IN, 47907, USA
| | - Nicholas X Fang
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Xiang Zhang
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, 94706, USA. .,Faculties of Sciences and Engineering University of Hong Kong, Hong Kong SAR, PR, China.
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Mueed MA, Kamburov D, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Geometric Resonance of Composite Fermions near Bilayer Quantum Hall States. PHYSICAL REVIEW LETTERS 2016; 117:246801. [PMID: 28009213 DOI: 10.1103/physrevlett.117.246801] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Indexed: 06/06/2023]
Abstract
Via the application of a parallel magnetic field, we induce a single-layer to bilayer transition in two-dimensional electron systems confined to wide GaAs quantum wells and study the geometric resonance of composite fermions (CFs) with a periodic density modulation in our samples. The measurements reveal that CFs exist close to bilayer quantum Hall states, formed at Landau level filling factors ν=1 and 1/2. Near ν=1, the geometric resonance features are consistent with half the total electron density in the bilayer system, implying that CFs prefer to stay in separate layers and exhibit a two-component behavior. In contrast, close to ν=1/2, CFs appear single-layer-like (single component) as their resonance features correspond to the total density.
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Affiliation(s)
- M A Mueed
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - D Kamburov
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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Liu Y, Hasdemir S, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Observation of an Anisotropic Wigner Crystal. PHYSICAL REVIEW LETTERS 2016; 117:106802. [PMID: 27636486 DOI: 10.1103/physrevlett.117.106802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2016] [Indexed: 06/06/2023]
Abstract
We report a new correlated phase of two-dimensional charged carriers in high magnetic fields, manifested by an anisotropic insulating behavior at low temperatures. It appears in a large range of low Landau level fillings 1/3≲ν≲2/3 in hole systems confined to wide GaAs quantum wells when the sample is tilted in magnetic field to an intermediate angle. The parallel field component (B_{∥}) leads to a crossing of the lowest two Landau levels, and an elongated hole wave function in the direction of B_{∥}. Under these conditions, the in-plane resistance exhibits an insulating behavior, with the resistance along B_{∥} about 10 times smaller than the resistance perpendicular to B_{∥}. We interpret this anisotropic insulating phase as a two-component, striped Wigner crystal.
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Affiliation(s)
- Yang Liu
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - S Hasdemir
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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