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Patlatiuk T, Scheller CP, Hill D, Tserkovnyak Y, Egues JC, Barak G, Yacoby A, Pfeiffer LN, West KW, Zumbühl DM. Edge-State Wave Functions from Momentum-Conserving Tunneling Spectroscopy. PHYSICAL REVIEW LETTERS 2020; 125:087701. [PMID: 32909808 DOI: 10.1103/physrevlett.125.087701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2020] [Accepted: 07/21/2020] [Indexed: 06/11/2023]
Abstract
We perform momentum-conserving tunneling spectroscopy using a GaAs cleaved-edge overgrowth quantum wire to investigate adjacent quantum Hall edge states. We use the lowest five wire modes with their distinct wave functions to probe each edge state and apply magnetic fields to modify the wave functions and their overlap. This reveals an intricate and rich tunneling conductance fan structure which is succinctly different for each of the wire modes. We self-consistently solve the Poisson-Schrödinger equations to simulate the spectroscopy, reproducing the striking fans in great detail, thus, confirming the calculations. Further, the model predicts hybridization between wire states and Landau levels, which is also confirmed experimentally. This establishes momentum-conserving tunneling spectroscopy as a powerful technique to probe edge state wave functions.
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Affiliation(s)
- T Patlatiuk
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - C P Scheller
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - D Hill
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
| | - Y Tserkovnyak
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
| | - J C Egues
- Instituto de Física de São Carlos, Universidade de São Paulo, 13560-970 São Carlos, São Paulo, Brazil
| | - G Barak
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - A Yacoby
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, 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
| | - D M Zumbühl
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
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Patlatiuk T, Scheller CP, Hill D, Tserkovnyak Y, Barak G, Yacoby A, Pfeiffer LN, West KW, Zumbühl DM. Evolution of the quantum Hall bulk spectrum into chiral edge states. Nat Commun 2018; 9:3692. [PMID: 30209251 PMCID: PMC6135798 DOI: 10.1038/s41467-018-06025-3] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2018] [Accepted: 08/13/2018] [Indexed: 11/30/2022] Open
Abstract
One of the most intriguing and fundamental properties of topological systems is the correspondence between the conducting edge states and the gapped bulk spectrum. Here, we use a GaAs cleaved edge quantum wire to perform momentum-resolved spectroscopy of the quantum Hall edge states in a tunnel-coupled 2D electron gas. This reveals the momentum and position of the edge states with unprecedented precision and shows the evolution from very low magnetic fields all the way to high fields where depopulation occurs. We present consistent analytical and numerical models, inferring the edge states from the well-known bulk spectrum, finding excellent agreement with the experiment-thus providing direct evidence for the bulk to edge correspondence. In addition, we observe various features beyond the single-particle picture, such as Fermi level pinning, exchange-enhanced spin splitting and signatures of edge-state reconstruction.
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Affiliation(s)
- T Patlatiuk
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
| | - C P Scheller
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland
| | - D Hill
- Department of Physics and Astronomy, University of California, Los Angeles, CA, 90095, USA
| | - Y Tserkovnyak
- Department of Physics and Astronomy, University of California, Los Angeles, CA, 90095, USA
| | - G Barak
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - A Yacoby
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
| | - D M Zumbühl
- Departement Physik, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland.
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Papa E, Stroh T. Metal-insulator transition tuned by external gates in Hall systems with constrictions. PHYSICAL REVIEW LETTERS 2006; 97:046801. [PMID: 16907604 DOI: 10.1103/physrevlett.97.046801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2005] [Indexed: 05/11/2023]
Abstract
The nature of a metal-insulator transition tuned by external gates in quantum Hall systems with point constrictions, as reported in recent experiments [S. Roddaro, Phys. Rev. Lett. 95, 156804 (2005)10.1103/PhysRevLett.95.156804], is examined. We attribute this phenomenon to a splitting of the integer edge into conducting and insulating stripes, the latter wide enough to allow for the stability of the edge structure. Interchannel impurity scattering and interchannel Coulomb interactions do not destabilize this picture.
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Affiliation(s)
- Emiliano Papa
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904-4714, USA
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