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Liu C, Zhao C, Zhong S, Chen C, Zhang Z, Jia Y, Wang J. Equally Spaced Quantum States in van der Waals Epitaxy-Grown Nanoislands. NANO LETTERS 2021; 21:9285-9292. [PMID: 34677982 DOI: 10.1021/acs.nanolett.1c03423] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Pursuing the confinement of linearly dispersive relativistic Fermions is of interest in both fundamental physics and potential applications. Here, we report strong STM evidence for the equally spaced, strikingly sharp, and densely distributed quantum well states (QWSs) near Fermi energy in Pb(111) nanoislands, van der Waals epitaxially grown on graphitized 6H-SiC(0001). The observations can be explained as the quantized energies of confined linearly dispersive [111] electrons, which essentially "simulate" the out-of-plane relativistic quasiparticles. The equally spaced QWSs with an origin of confined relativistic electrons are supported by phenomenological simulations and Fabry-Pérot fittings based on the relativistic Fermions. First-principles calculations further reveal that the spin-orbit coupling strengthens the relativistic nature of electrons near Fermi energy. Our finding uncovers the unique equally spaced quantum states in electronic systems beyond Landau levels and may inspire future studies on confined relativistic quasiparticles in flourishing topological materials and applications in structurally simpler quantum cascade laser.
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Affiliation(s)
- Chaofei Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Chunxiang Zhao
- International Laboratory for Quantum Functional Materials of Henan, and School of Physics and Microelectronics, Zhengzhou University, Zhengzhou 450001, China
| | - Shan Zhong
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Cheng Chen
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Zhenyu Zhang
- International Center for Quantum Design of Functional Materials (ICQD), Hefei National Laboratory for Physical Sciences at Microscale, and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Yu Jia
- International Laboratory for Quantum Functional Materials of Henan, and School of Physics and Microelectronics, Zhengzhou University, Zhengzhou 450001, China
| | - Jian Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
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Su WB, Lu SM, Jeng HT, Chan WY, Chang HH, Pai WW, Liu HL, Chang CS. Observing quantum trapping on MoS 2 through the lifetimes of resonant electrons: revealing the Pauli exclusion principle. NANOSCALE ADVANCES 2020; 2:5848-5856. [PMID: 36133857 PMCID: PMC9418783 DOI: 10.1039/d0na00682c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/19/2020] [Accepted: 11/11/2020] [Indexed: 06/16/2023]
Abstract
We demonstrate that the linewidth of the field emission resonance (FER) observed on the surface of MoS2 using scanning tunneling microscopy can vary by up to one order of magnitude with an increasing electric field. This phenomenon originates from quantum trapping, in which the electron relaxed from a resonant electron in the FER is momentarily trapped in a potential well on the MoS2 surface due to its wave nature. Because the relaxed electron and the resonant electron have the same spin, through the action of the Pauli exclusion principle, the lifetimes of the resonant electrons can be substantially prolonged when the relaxed electrons engage in resonance trapping. The linewidth of the FER is thus considerably reduced to as narrow as 12 meV. The coexistence of the resonant electron and the relaxed electron requires the emission of two electrons, which can occur through the exchange interaction.
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Affiliation(s)
- Wei-Bin Su
- Institute of Physics, Academia Sinica Nankang Taipei 11529 Taiwan
| | - Shin-Ming Lu
- Institute of Physics, Academia Sinica Nankang Taipei 11529 Taiwan
| | - Horng-Tay Jeng
- Department of Physics, National Tsing Hua University Hsinchu 30013 Taiwan
- Institute of Physics, Academia Sinica Nankang Taipei 11529 Taiwan
- Physics Division, National Center for Theoretical Sciences Hsinchu 30013 Taiwan
| | - Wen-Yuan Chan
- Institute of Physics, Academia Sinica Nankang Taipei 11529 Taiwan
| | - Ho-Hsiang Chang
- Institute of Physics, Academia Sinica Nankang Taipei 11529 Taiwan
| | - Woei Wu Pai
- Center for Condensed Matter Sciences, National Taiwan University Taipei 10617 Taiwan
| | - Hsiang-Lin Liu
- Department of Physics, National Taiwan Normal University Taipei 11677 Taiwan
| | - Chia-Seng Chang
- Institute of Physics, Academia Sinica Nankang Taipei 11529 Taiwan
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Aladyshkin AY. Quantum-well and modified image-potential states in thin Pb(111) films: an estimate for the local work function. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:435001. [PMID: 32640444 DOI: 10.1088/1361-648x/aba3f0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2020] [Accepted: 07/08/2020] [Indexed: 06/11/2023]
Abstract
Quantum-confined electronic states such as quantum-well states (QWS) inside thin Pb(111) films and modified image-potential states (IPS) above the Pb(111) films grown on Si(111) 7 × 7 substrate were studied by means of low-temperature scanning tunnelling microscopy (STM) and spectroscopy (STS) in the regime of constant currentI. By plotting the position of thenth emission resonancesUnversusn2/3and extrapolating the linear fit for the dependenceUn(n2/3) in the high-nlimit towardsn= 0, we estimate the local work function for the Pb(111) film:W≃ 3.8 ± 0.1 eV. We experimentally demonstrate that modifications of the shape of the STM tip can change the number of the emission peaks associated with the resonant tunnelling via quantized IPS levels for the same Pb terrace; however it does not affect the estimate of the local work function for the flat Pb terraces. We observe that the maxima in the spectra of the differential tunnelling conductance dI/dUrelated to both the QWS and the modified IPS resonances are less pronounced if the STM tip becomes more blunt.
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Affiliation(s)
- A Yu Aladyshkin
- Institute for Physics of Microstructures RAS, 603950, Nizhny Novgorod, GSP-105, Russia
- Lobachevsky State University of Nizhny Novgorod, 603950, Nizhny Novgorod, 23 Gagarin Avenue, Russia
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Chan WY, Lu SM, Su WB, Liao CC, Hoffmann G, Tsai TR, Chang CS. Sharpness-induced energy shifts of quantum well states in Pb islands on Cu(111). NANOTECHNOLOGY 2017; 28:095706. [PMID: 28135205 DOI: 10.1088/1361-6528/aa583a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We elucidate that the tip sharpness in scanning tunneling microscopy (STM) can be characterized through the number of field-emission (FE) resonances. A higher number of FE resonances indicates higher sharpness. We observe empty quantum well (QW) states in Pb islands on Cu(111) under different tip sharpness levels. We found that QW states observed by sharper tips always had lower energies, revealing negative energy shifts. This sharpness-induced energy shift originates from an inhomogeneous electric field in the STM gap. An increase in sharpness increases the electric field inhomogeneity, that is, enhances the electric field near the tip apex, but weakens the electric field near the sample. As a result, higher sharpness can increase the electronic phase in vacuum, causing the lowering of QW state energies. Moreover, the behaviors of negative energy shift as a function of state energy are entirely different for Pb islands with a thickness of two and nine atomic layers. This thickness-dependent behavior results from the electrostatic force in the STM gap decreasing with increasing tip sharpness. The variation of the phase contributed from the expansion deformation induced by the electrostatic force in a nine-layer Pb island is significantly greater, sufficient to effectively negate the increase of electronic phase in vacuum.
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Affiliation(s)
- Wen-Yuan Chan
- Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan, Republic of China
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5
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Cao RX, Sun L, Miao BF, Li QL, Zheng C, Wu D, You B, Zhang W, Han P, Bader SD, Zhang WY, Ding HF. Spectroscopic study of Gd nanostructures quantum confined in Fe corrals. Sci Rep 2015; 5:12092. [PMID: 26160318 PMCID: PMC4498218 DOI: 10.1038/srep12092] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2015] [Accepted: 06/12/2015] [Indexed: 12/05/2022] Open
Abstract
Low dimensional nanostructures have attracted attention due to their rich physical properties and potential applications. The essential factor for their functionality is their electronic properties, which can be modified by quantum confinement. Here the electronic states of Gd atom trapped in open Fe corrals on Ag(111) were studied via scanning tunneling spectroscopy. A single spectroscopic peak above the Fermi level is observed after Gd adatoms are trapped inside Fe corrals, while two peaks appear in empty corrals. The single peak position is close to the higher energy peak of the empty corrals. These findings, attributed to quantum confinement of the corrals and Gd structures trapped inside, are supported by tight-binding calculations. This demonstrates and provides insights into atom trapping in open corrals of various diameters, giving an alternative approach to modify the properties of nano-objects.
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Affiliation(s)
- R X Cao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 22 Hankou Road, Nanjing 210093, People's Republic of China
| | - L Sun
- 1] National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 22 Hankou Road, Nanjing 210093, People's Republic of China [2] Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 22 Hankou Road, Nanjing 210093, P. R. China
| | - B F Miao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 22 Hankou Road, Nanjing 210093, People's Republic of China
| | - Q L Li
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 22 Hankou Road, Nanjing 210093, People's Republic of China
| | - C Zheng
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 22 Hankou Road, Nanjing 210093, People's Republic of China
| | - D Wu
- 1] National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 22 Hankou Road, Nanjing 210093, People's Republic of China [2] Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 22 Hankou Road, Nanjing 210093, P. R. China
| | - B You
- 1] National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 22 Hankou Road, Nanjing 210093, People's Republic of China [2] Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 22 Hankou Road, Nanjing 210093, P. R. China
| | - W Zhang
- 1] National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 22 Hankou Road, Nanjing 210093, People's Republic of China [2] Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 22 Hankou Road, Nanjing 210093, P. R. China
| | - P Han
- 1] Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 22 Hankou Road, Nanjing 210093, P. R. China [2] School of Electronic Science and Engineering, Nanjing University, 22 Hankou Road, Nanjing 210093, People's Republic of China
| | - S D Bader
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - W Y Zhang
- 1] National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 22 Hankou Road, Nanjing 210093, People's Republic of China [2] Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 22 Hankou Road, Nanjing 210093, P. R. China
| | - H F Ding
- 1] National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 22 Hankou Road, Nanjing 210093, People's Republic of China [2] Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 22 Hankou Road, Nanjing 210093, P. R. China
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6
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Stępniak A, Leon Vanegas A, Caminale M, Oka H, Sander D, Kirschner J. Atomic layer superconductivity. SURF INTERFACE ANAL 2014. [DOI: 10.1002/sia.5516] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Agnieszka Stępniak
- Max‐Planck‐Institute für Mikrostrukturphysik Weinberg 2 D‐06120 Halle (Saale) Germany
| | - Augusto Leon Vanegas
- Max‐Planck‐Institute für Mikrostrukturphysik Weinberg 2 D‐06120 Halle (Saale) Germany
- Martin Luther Universität Institute of Physics Halle (Saale) Germany
| | - Michael Caminale
- Max‐Planck‐Institute für Mikrostrukturphysik Weinberg 2 D‐06120 Halle (Saale) Germany
| | - Hirofumi Oka
- Max‐Planck‐Institute für Mikrostrukturphysik Weinberg 2 D‐06120 Halle (Saale) Germany
| | - Dirk Sander
- Max‐Planck‐Institute für Mikrostrukturphysik Weinberg 2 D‐06120 Halle (Saale) Germany
| | - Jürgen Kirschner
- Max‐Planck‐Institute für Mikrostrukturphysik Weinberg 2 D‐06120 Halle (Saale) Germany
- Martin Luther Universität Institute of Physics Halle (Saale) Germany
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7
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Chan WY, Huang HS, Su WB, Lin WH, Jeng HT, Wu MK, Chang CS. Field-induced expansion deformation in Pb islands on Cu(111): evidence from energy shift of empty quantum-well states. PHYSICAL REVIEW LETTERS 2012; 108:146102. [PMID: 22540808 DOI: 10.1103/physrevlett.108.146102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2011] [Indexed: 05/31/2023]
Abstract
We use scanning tunneling microscopy and spectroscopy to measure the energy shift of empty quantum-well (QW) states in Pb islands on the Cu(111) surface. It is found that, with an increase of the electric field, the behavior of the energy shift can be grouped into two different modes for most QW states. In the first mode, the state energy moves toward high energy monotonically. In the second mode, the state energy shifts to a lower energy initially and then turns around to a higher energy. Moreover, we have observed that the QW states of higher energy behave in preference to the first mode, but they gradually change to the second mode as the Pb island becomes thicker. This thickness-dependent behavior reflects the existence of local expansion in the Pb islands, due to the electric field, and that the expansion is larger for a thicker island. QW states can thus be used for studying the localized lattice deformation in the nanometer scale.
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Affiliation(s)
- W Y Chan
- Institute of Physics, Academia Sinica, Nankang, Taipei 115, Taiwan
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8
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Pan S, Liu Q, Ming F, Wang K, Xiao X. Interface effects on the quantum well states of Pb thin films. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:485001. [PMID: 22034437 DOI: 10.1088/0953-8984/23/48/485001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Using scanning tunneling spectroscopy, we have studied the interface effect on quantum well states of Pb thin films grown on various metal-terminated (Pb, Ag, and Au) n-type Si(111) surfaces and on two different p-type Si(111) surfaces. The dispersion relation E(k) of the electrons of the Pb film and the phase shift at the substrate interface were determined by applying the quantization rule to the measured energy positions of the quantum well states. Characteristic features in the phase shift versus energy curves were identified and were correlated to the directional conduction band of the silicon substrate and to the Schottky barrier formed between the metal film and the semiconductor. A model involving the band structure of the substrate, the Schottky barrier, and the effective thickness of the interface was introduced to qualitatively but comprehensively explain all the observed features of the phase shift at the substrate interface. Our physical understanding of the phase shift is critically important for using interface modification to control the quantum well states.
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Affiliation(s)
- Shuan Pan
- Department of Physics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
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9
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Zugarramurdi A, Zabala N, Borisov AG, Chulkov EV. Comment on "Phase contribution of image potential on empty quantum well states in Pb islands on the Cu(111) surface". PHYSICAL REVIEW LETTERS 2011; 106:249601-249602. [PMID: 21770611 DOI: 10.1103/physrevlett.106.249601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2011] [Indexed: 05/31/2023]
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