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Sitek A, Urbaneja Torres M, Manolescu A. Corner and side localization of electrons in irregular hexagonal semiconductor shells. NANOTECHNOLOGY 2019; 30:454001. [PMID: 31370045 DOI: 10.1088/1361-6528/ab37a1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We discuss the low energy electronic states in hexagonal rings. These states correspond to the transverse modes in core-shell nanowires built of III-V semiconductors which typically have a hexagonal cross section. In the case of symmetric structures the 12 lowest states (including the spin) are localized in the corners, while the next following 12 states are localized mostly on the sides. Depending on the material parameters, in particular the effective mass, the ring diameter and width, the corner and side states may be separated by a considerable energy gap, ranging from few to tens of meV. In a realistic fabrication process geometric asymmetries are unavoidable, and therefore the particles are not symmetrically distributed between all corner and side areas. Possibly, even small deformations may shift the localization of the ground state to one of the sides. The transverse states or the transitions between them may be important in transport or optical experiments. Still, up to date, there are only very few experimental investigations of the localization-dependent properties of core-shell nanowires.
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Affiliation(s)
- Anna Sitek
- School of Science and Engineering, Reykjavik University, Menntavegur 1, IS-101 Reykjavik, Iceland. Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland
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Sitek A, Ţolea M, Niţă M, Serra L, Gudmundsson V, Manolescu A. In-gap corner states in core-shell polygonal quantum rings. Sci Rep 2017; 7:40197. [PMID: 28071750 PMCID: PMC5223208 DOI: 10.1038/srep40197] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2016] [Accepted: 12/02/2016] [Indexed: 11/20/2022] Open
Abstract
We study Coulomb interacting electrons confined in polygonal quantum rings. We focus on the interplay of localization at the polygon corners and Coulomb repulsion. Remarkably, the Coulomb repulsion allows the formation of in-gap states, i.e., corner-localized states of electron pairs or clusters shifted to energies that were forbidden for non-interacting electrons, but below the energies of corner-side-localized states. We specify conditions allowing optical excitation to those states.
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Affiliation(s)
- Anna Sitek
- Science Institute, University of Iceland, Reykjavik, IS-107, Iceland.,School of Science and Engineering, Reykjavik University, Reykjavik, IS-101, Iceland.,Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wroclaw University of Science and Technology, Wroclaw, 50-370, Poland
| | - Mugurel Ţolea
- National Institute of Materials Physics, Bucharest-Magurele, P.O. Box MG-7, Romania
| | - Marian Niţă
- National Institute of Materials Physics, Bucharest-Magurele, P.O. Box MG-7, Romania
| | - Llorenç Serra
- Institute of Interdisciplinary Physics and Complex Systems IFISC (CSIC-UIB), Palma de Mallorca, E-07122, Spain.,Department of Physics, University of the Balearic Islands, Palma de Mallorca, E-07122, Spain
| | - Vidar Gudmundsson
- Science Institute, University of Iceland, Reykjavik, IS-107, Iceland
| | - Andrei Manolescu
- School of Science and Engineering, Reykjavik University, Reykjavik, IS-101, Iceland
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O'Callaghan M, Miller BN. Path integral Monte Carlo on a lattice. II. Bound states. Phys Rev E 2016; 94:012120. [PMID: 27575090 DOI: 10.1103/physreve.94.012120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2015] [Indexed: 11/07/2022]
Abstract
The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and the atoms are restricted to sites on a one-dimensional lattice. A path integral formalism developed within the context of the canonical ensemble is utilized, where the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp in the context of a square well potential, forcing the qp to occupy bound states. We consider a one-dimensional square well potential where all atoms on the lattice are occupied with one atom with an on-site potential except for a contiguous set of sites of various lengths centered at the middle of the lattice. Comparison of the potential energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the numerical calculations.
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Affiliation(s)
- Mark O'Callaghan
- Department of Physics and Astronomy, Texas Christian University, Fort Worth, Texas 76129, USA
| | - Bruce N Miller
- Department of Physics and Astronomy, Texas Christian University, Fort Worth, Texas 76129, USA
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Estarellas C, Serra L. Resonant Anderson localization in segmented wires. Phys Rev E 2016; 93:032105. [PMID: 27078290 DOI: 10.1103/physreve.93.032105] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2015] [Indexed: 11/07/2022]
Abstract
We discuss a model of random segmented wire, with linear segments of two-dimensional wires joined by circular bends. The joining vertices act as scatterers on the propagating electron waves. The model leads to resonant Anderson localization when all segments are of similar length. The resonant behavior is present with one and also with several propagating modes. The probability distributions evolve from diffusive to localized regimes when increasing the number of segments in a similar way for long and short localization lengths. As a function of the energy, a finite segmented wire typically evolves from localized to diffusive to ballistic behavior in each conductance plateau.
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Affiliation(s)
- Cristian Estarellas
- Institut de Física Interdisciplinària i de Sistemes Complexos, IFISC (CSIC-UIB), E-07122 Palma de Mallorca, Spain
| | - Llorenç Serra
- Institut de Física Interdisciplinària i de Sistemes Complexos, IFISC (CSIC-UIB), E-07122 Palma de Mallorca, Spain.,Departament de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
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Dick R. A Model System for Dimensional Competition in Nanostructures: A Quantum Wire on a Surface. NANOSCALE RESEARCH LETTERS 2008; 3:140-144. [PMCID: PMC3244799 DOI: 10.1007/s11671-008-9126-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2008] [Accepted: 03/13/2008] [Indexed: 05/30/2023]
Abstract
The retarded Green’s function (E−H + iε)−1is given for a dimensionally hybrid Hamiltonian which interpolates between one and two dimensions. This is used as a model for dimensional competition in propagation effects in the presence of one-dimensional subsystems on a surface. The presence of a quantum wire generates additional exponential terms in the Green’s function. The result shows how the location of the one-dimensional subsystem affects propagation of particles.
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Affiliation(s)
- Rainer Dick
- Physics and Engineering Physics, University of Saskatchewan, 116 Science Place, Saskatoon, SK, Canada, S7N 5E2
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Xu G, Jiang L, Jiang P, Lu D, Xie X. Noninteger conductance steps in a gapped double electron waveguide. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:2287-2290. [PMID: 9978980 DOI: 10.1103/physrevb.51.2287] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wu H, Sprung DW. Inverse-square potential and the quantum vortex. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 49:4305-4311. [PMID: 9910743 DOI: 10.1103/physreva.49.4305] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Kawamura T, Leburton JP. Quantum ballistic transport through a double-bend waveguide structure: Effects of disorder. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:8857-8865. [PMID: 10007103 DOI: 10.1103/physrevb.48.8857] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Palacios JJ, Tejedor C. Mode-matching technique for transmission calculations in electron waveguides at high magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:5386-5394. [PMID: 10009058 DOI: 10.1103/physrevb.48.5386] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Itoh T, Sano N, Yoshii A. Quasi-zero-dimensional states in ballistic quantum wires. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:16601-16604. [PMID: 10006101 DOI: 10.1103/physrevb.47.16601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Xu H. Ballistic transport in quantum channels modulated with double-bend structures. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:9537-9544. [PMID: 10005018 DOI: 10.1103/physrevb.47.9537] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Yuan SQ, Gu BY. Characteristics of quantum conductance in a quasi-one-dimension quantum wire containing cavity structures. ACTA ACUST UNITED AC 1993. [DOI: 10.1007/bf01309166] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Vacek K, Okiji A, Kasai H. Multichannel ballistic magnetotransport through quantum wires with double circular bends. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:3695-3705. [PMID: 10006472 DOI: 10.1103/physrevb.47.3695] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wu H, Sprung DW. Theoretical study of multiple-bend quantum wires. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:1500-1505. [PMID: 10006165 DOI: 10.1103/physrevb.47.1500] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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