1
|
Yan J, Wu Y, Yuan S, Liu X, Pfeiffer LN, West KW, Liu Y, Fu H, Xie XC, Lin X. Anomalous quantized plateaus in two-dimensional electron gas with gate confinement. Nat Commun 2023; 14:1758. [PMID: 36997525 PMCID: PMC10064851 DOI: 10.1038/s41467-023-37495-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2022] [Accepted: 03/16/2023] [Indexed: 04/01/2023] Open
Abstract
AbstractQuantum information can be coded by the topologically protected edges of fractional quantum Hall (FQH) states. Investigation on FQH edges in the hope of searching and utilizing non-Abelian statistics has been a focused challenge for years. Manipulating the edges, e.g. to bring edges close to each other or to separate edges spatially, is a common and essential step for such studies. The FQH edge structures in a confined region are typically presupposed to be the same as that in the open region in analysis of experimental results, but whether they remain unchanged with extra confinement is obscure. In this work, we present a series of unexpected plateaus in a confined single-layer two-dimensional electron gas (2DEG), which are quantized at anomalous fractions such as 9/4, 17/11, 16/13 and the reported 3/2. We explain all the plateaus by assuming surprisingly larger filling factors in the confined region. Our findings enrich the understanding of edge states in the confined region and in the applications of gate manipulation, which is crucial for the experiments with quantum point contact and interferometer.
Collapse
|
2
|
Nakamura J, Liang S, Gardner GC, Manfra MJ. Half-Integer Conductance Plateau at the ν=2/3 Fractional Quantum Hall State in a Quantum Point Contact. PHYSICAL REVIEW LETTERS 2023; 130:076205. [PMID: 36867801 DOI: 10.1103/physrevlett.130.076205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2022] [Accepted: 01/17/2023] [Indexed: 06/18/2023]
Abstract
The ν=2/3 fractional quantum Hall state is the hole-conjugate state to the primary Laughlin ν=1/3 state. We investigate transmission of edge states through quantum point contacts fabricated on a GaAs/AlGaAs heterostructure designed to have a sharp confining potential. When a small but finite bias is applied, we observe an intermediate conductance plateau with G=0.5(e^{2}/h). This plateau is observed in multiple QPCs, and persists over a significant range of magnetic field, gate voltage, and source-drain bias, making it a robust feature. Using a simple model that considers scattering and equilibration between counterflowing charged edge modes, we find this half-integer quantized plateau to be consistent with full reflection of an inner counterpropagating -1/3 edge mode while the outer integer mode is fully transmitted. In a QPC fabricated on a different heterostructure which has a softer confining potential, we instead observe an intermediate conductance plateau at G=(1/3)(e^{2}/h). These results provide support for a model at ν=2/3 in which the edge transitions from a structure having an inner upstream -1/3 charge mode and outer downstream integer mode to a structure with two downstream 1/3 charge modes when the confining potential is tuned from sharp to soft and disorder prevails.
Collapse
Affiliation(s)
- J Nakamura
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - S Liang
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - G C Gardner
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- Microsoft Quantum Lab West Lafayette, West Lafayette, Indiana 47907, USA
| | - M J Manfra
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- Microsoft Quantum Lab West Lafayette, West Lafayette, Indiana 47907, USA
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| |
Collapse
|
3
|
Yang B. Fractional Quantum Hall Effect from Frustration-Free Hamiltonians. PHYSICAL REVIEW LETTERS 2020; 125:176402. [PMID: 33156656 DOI: 10.1103/physrevlett.125.176402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Accepted: 09/24/2020] [Indexed: 05/06/2023]
Abstract
We show that there is an emergent lattice description for the continuous fractional quantum Hall (FQH) systems, with a generalized set of few-body coherent states. In particular, model Hamiltonians of the FQH effect (FQHE) are equivalent to the real-space von Neumann lattice of local projection operators imposed on a continuous system in the thermodynamic limit. It can be analytically derived that tuning local one-body potentials in such lattices amounts to the tuning of individual two- or few-body pseudopotentials. For some cases, we can realize pure few-body pseudopotentials important for stabilizing exotic non-Abelian topological phases. Thus, this new approach can potentially lead to the experimental realization of coveted non-Abelian quantum fluids including the Moore-Read state and the Fibonacci state. The reformulation of the FQHE as a sum of local projections opens up new paths for rigorously proving the incompressibility of microscopic Hamiltonians in the thermodynamic limit.
Collapse
Affiliation(s)
- Bo Yang
- Division of Physics and Applied Physics, Nanyang Technological University, Singapore 637371 and Institute of High Performance Computing, A*STAR, Singapore, 138632
| |
Collapse
|
4
|
Wu Y, Liu H, Liu J, Jiang H, Xie XC. Double-frequency Aharonov-Bohm effect and non-Abelian braiding properties of Jackiw-Rebbi zero-mode. Natl Sci Rev 2020; 7:572-578. [PMID: 34692076 PMCID: PMC8288965 DOI: 10.1093/nsr/nwz189] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2019] [Revised: 10/21/2019] [Accepted: 10/21/2019] [Indexed: 11/14/2022] Open
Abstract
Ever since its first proposal in 1976, Jackiw-Rebbi zero-mode has been drawing extensive attention for its charming properties including charge fractionalization, topologically protected zero-energy and possible non-Abelian statistics. We investigate these properties through the Jackiw-Rebbi zero-modes in quantum spin Hall insulators. Though charge fractionalization is not manifested, Jackiw-Rebbi zero-mode's zero-energy nature leads to a double-frequency Aharonov-Bohm effect, implying that it can be viewed as a special case of Majorana zero-mode without particle-hole symmetry. Such relation is strengthened for Jackiw-Rebbi zero-modes also exhibiting non-Abelian properties in the absence of superconductivity. Furthermore, in the condition that the degeneracy of Jackiw-Rebbi zero-modes is lifted, we demonstrate a novel non-Abelian braiding with continuously tunable fusion rule, which is a generalization of Majorana zero-modes' braiding properties.
Collapse
Affiliation(s)
- Yijia Wu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Haiwen Liu
- Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Jie Liu
- Department of Applied Physics, School of Science, Xi'an Jiaotong University, Xi'an 710049, China
| | - Hua Jiang
- School of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - X C Xie
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.,Beijing Academy of Quantum Information Sciences, Beijing 100193, China.,CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| |
Collapse
|