1
|
Hayrapetyan DB, Kazaryan EM, Mkrtchyan MA, Sarkisyan HA. Long-wave Absorption of Few-Hole Gas in Prolate Ellipsoidal Ge/Si Quantum Dot: Implementation of Analytically Solvable Moshinsky Model. NANOMATERIALS (BASEL, SWITZERLAND) 2020; 10:E1896. [PMID: 32977448 PMCID: PMC7598227 DOI: 10.3390/nano10101896] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/14/2020] [Revised: 09/12/2020] [Accepted: 09/15/2020] [Indexed: 11/16/2022]
Abstract
In this paper, the behavior of a heavy hole gas in a strongly prolate ellipsoidal Ge/Si quantum dot has been investigated. Due to the specific geometry of the quantum dot, the interaction between holes is considered one-dimensional. Based on the adiabatic approximation, it is shown that in the z-direction, hole gas is localized in a one-dimensional parabolic well. By modeling the potential of pair interaction between holes in the framework of oscillatory law, the problem is reduced to a one-dimensional, analytically solvable Moshinsky model. The exact energy spectrum of the few-hole gas has been calculated. A detailed analysis of the energy spectrum is presented. The character of long-wave transitions between the center-of-mass levels of the system has been obtained when Kohn theorem is realized.
Collapse
Affiliation(s)
- David B. Hayrapetyan
- Institute of Engineering and Physics, Russian-Armenian University, 123 Hovsep Emin Str., Yerevan 0051, Armenia; (D.B.H.); (E.M.K.); (M.A.M.)
| | - Eduard M. Kazaryan
- Institute of Engineering and Physics, Russian-Armenian University, 123 Hovsep Emin Str., Yerevan 0051, Armenia; (D.B.H.); (E.M.K.); (M.A.M.)
- Institute of Physics, Nanotechnology and Telecommunications, Peter the Great St. Petersburg Polytechnic University, 195251 Saint Petersburg, Russia
| | - Mher A. Mkrtchyan
- Institute of Engineering and Physics, Russian-Armenian University, 123 Hovsep Emin Str., Yerevan 0051, Armenia; (D.B.H.); (E.M.K.); (M.A.M.)
| | - Hayk A. Sarkisyan
- Institute of Engineering and Physics, Russian-Armenian University, 123 Hovsep Emin Str., Yerevan 0051, Armenia; (D.B.H.); (E.M.K.); (M.A.M.)
- Institute of Physics, Nanotechnology and Telecommunications, Peter the Great St. Petersburg Polytechnic University, 195251 Saint Petersburg, Russia
| |
Collapse
|
2
|
Sarkisyan HA, Hayrapetyan DB, Petrosyan LS, Kazaryan EM, Sofronov AN, Balagula RM, Firsov DA, Vorobjev LE, Tonkikh AA. Realization of the Kohn's Theorem in Ge/Si Quantum Dots with Hole Gas: Theory and Experiment. NANOMATERIALS (BASEL, SWITZERLAND) 2019; 9:E56. [PMID: 30609851 PMCID: PMC6359628 DOI: 10.3390/nano9010056] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/15/2018] [Revised: 12/20/2018] [Accepted: 12/25/2018] [Indexed: 11/16/2022]
Abstract
This article discusses specific quantum transitions in a few-particle hole gas, localized in a strongly oblate lens-shaped quantum dot. Based on the adiabatic method, the possibility of realizing the generalized Kohn theorem in such a system is shown. The criteria for the implementation of this theorem in a lens-shaped quantum dot, fulfilled in the experiment, is presented. An analytical expression is obtained for the frequencies of resonant absorption of far-infrared radiation by a gas of heavy holes, which depends on the geometric parameters of the quantum dot. The results of experiments on far-infrared absorption in the arrays of p-doped Ge/Si quantum dots grown by molecular beam epitaxy (MBE) with gradually increasing average number of holes in dot are presented. Experimental results show that the Coulomb interaction between the holes does not affect the resonant frequency of the transitions. A good agreement between the theoretical and experimental results is shown.
Collapse
Affiliation(s)
- Hayk A Sarkisyan
- Institute of Engineering and Physics, Russian-Armenian University, Yerevan 0051, Armenia.
- Institute of Physics, Nanotechnology and Telecommunications, Peter the Great St. Petersburg Polytechnic University, Saint Petersburg 195251, Russia.
- Department of Physics, Yerevan State University, Yerevan 0025, Armenia.
| | - David B Hayrapetyan
- Institute of Engineering and Physics, Russian-Armenian University, Yerevan 0051, Armenia.
- Institute of Physics, Nanotechnology and Telecommunications, Peter the Great St. Petersburg Polytechnic University, Saint Petersburg 195251, Russia.
| | | | - Eduard M Kazaryan
- Institute of Engineering and Physics, Russian-Armenian University, Yerevan 0051, Armenia.
- Institute of Physics, Nanotechnology and Telecommunications, Peter the Great St. Petersburg Polytechnic University, Saint Petersburg 195251, Russia.
| | - Anton N Sofronov
- Institute of Physics, Nanotechnology and Telecommunications, Peter the Great St. Petersburg Polytechnic University, Saint Petersburg 195251, Russia.
| | - Roman M Balagula
- Institute of Physics, Nanotechnology and Telecommunications, Peter the Great St. Petersburg Polytechnic University, Saint Petersburg 195251, Russia.
| | - Dmitry A Firsov
- Institute of Physics, Nanotechnology and Telecommunications, Peter the Great St. Petersburg Polytechnic University, Saint Petersburg 195251, Russia.
| | - Leonid E Vorobjev
- Institute of Physics, Nanotechnology and Telecommunications, Peter the Great St. Petersburg Polytechnic University, Saint Petersburg 195251, Russia.
| | | |
Collapse
|
3
|
McDonald CR, Orlando G, Abraham JW, Hochstuhl D, Bonitz M, Brabec T. Theory of the quantum breathing mode in harmonic traps and its use as a diagnostic tool. PHYSICAL REVIEW LETTERS 2013; 111:256801. [PMID: 24483751 DOI: 10.1103/physrevlett.111.256801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2012] [Indexed: 06/03/2023]
Abstract
An analytical expression for the quantum breathing frequency ωb of harmonically trapped quantum particles with inverse power-law repulsion is derived. It is verified by ab initio numerical calculations for electrons confined in a lateral (2D) quantum dot. We show how this relation can be used to express the ground state properties of harmonically trapped quantum particles as functions of the breathing frequency by presenting analytical results for the kinetic, trap, and repulsive energy and for the linear entropy. Measurement of ωb together with these analytical relations represents a tool to characterize the state of harmonically trapped interacting particles--from the Fermi gas to the Wigner crystal regime.
Collapse
Affiliation(s)
- C R McDonald
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N6N5, Canada
| | - G Orlando
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N6N5, Canada
| | - J W Abraham
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - D Hochstuhl
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - M Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - T Brabec
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N6N5, Canada
| |
Collapse
|
4
|
Foulon S, Brosens F, Devreese JT, Lemmens LF. Density of a gas of spin-polarized fermions in a magnetic field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:016111. [PMID: 11304318 DOI: 10.1103/physreve.63.016111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2000] [Indexed: 05/23/2023]
Abstract
For a fermion gas with equally spaced energy levels that is subjected to a magnetic field, the particle density is calculated. The derivation is based on the path integral approach for identical particles, in combination with the inversion techniques for the generating function of the static response functions. Explicit results are presented for the ground state density as a function of the magnetic field with a number of particles ranging from 1 to 45.
Collapse
Affiliation(s)
- S Foulon
- Departement Natuurkunde, Universiteit Antwerpen (UIA), Universiteitsplein 1, B-2610 Antwerpen, Belgium
| | | | | | | |
Collapse
|
5
|
Lemmens LF, Brosens F, Devreese JT. Partition function of a spinor gas. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:3358-65. [PMID: 11088109 DOI: 10.1103/physreve.61.3358] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/1999] [Indexed: 11/07/2022]
Abstract
For a spinor gas, i.e., a mixture of identical particles with several internal degrees of freedom, we derive the partition function in terms of the Feynman-Kac functionals of polarized components. As an example we study a spin-1 Bose gas with the spins subjected to an external magnetic field and confined by a parabolic potential. From the analysis of the free energy for a finite number of particles, we find that the specific heat of this ideal spinor gas as a function of temperature has two maxima: one is related to a Schottky anomaly, due to the lifting of the spin degeneracy by the external field, the other maximum is the signature of Bose-Einstein condensation.
Collapse
Affiliation(s)
- LF Lemmens
- Departement Natuurkunde, Universiteit Antwerpen RUCA, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
| | | | | |
Collapse
|
6
|
Fujito M, Natori A, Yasunaga H. Many-electron ground states in anisotropic parabolic quantum dots. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:9952-9958. [PMID: 9982559 DOI: 10.1103/physrevb.53.9952] [Citation(s) in RCA: 52] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
7
|
Ugajin R. Magneto-optics in a square-well quantum dot. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:6963-6966. [PMID: 9982133 DOI: 10.1103/physrevb.53.6963] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
8
|
Pedersen FB, Chang YC. Energy levels of one and two holes in parabolic quantum dots. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:1507-1516. [PMID: 9983613 DOI: 10.1103/physrevb.53.1507] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
9
|
Ahn KH, Oh JH, Chang KJ. Correlation effects in a quantum dot at high magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:13757-13760. [PMID: 9980582 DOI: 10.1103/physrevb.52.13757] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
10
|
Oh JH, Chang KJ, Ihm G, Lee SJ. Electronic structure of three-dimensional quantum dots in tilted magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:15397-15400. [PMID: 9975894 DOI: 10.1103/physrevb.50.15397] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
11
|
Belkhir L. Quantum and many-body effects on the capacitance of a spherical-shell quantum dot. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:8885-8888. [PMID: 9974918 DOI: 10.1103/physrevb.50.8885] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
12
|
Boero M, Inkson JC. I-V characteristics of 1D-0D-1D double-barrier structures and persistence of fine structure at high temperatures. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:2479-2484. [PMID: 9976468 DOI: 10.1103/physrevb.50.2479] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
13
|
Zeng YH, Serota RA. Scaling in quantum chaos: A study of quantum dots. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:2492-2501. [PMID: 9976470 DOI: 10.1103/physrevb.50.2492] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
14
|
Bolton F. Optimum Jastrow function for few-electron ground states in a quantum dot: Reduction to a three-particle problem. PHYSICAL REVIEW LETTERS 1994; 73:158-161. [PMID: 10056744 DOI: 10.1103/physrevlett.73.158] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
15
|
Haase RW, Johnson NF. Optical absorption and addition spectra of an N-electron quantum dot: An algebraic Hamiltonian approach. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:14409-14417. [PMID: 10010523 DOI: 10.1103/physrevb.49.14409] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
16
|
Johnson BL, Langer SA. Magnetic-field-confinement effects in a classical two-dimensional interacting electron gas. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:7511-7514. [PMID: 10009490 DOI: 10.1103/physrevb.49.7511] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
17
|
Marsili M. Pair description of the fractional quantum Hall effect with application to edge waves. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:18051-18059. [PMID: 10008444 DOI: 10.1103/physrevb.48.18051] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
18
|
Yang S, MacDonald AH, Johnson MD. Addition spectra of quantum dots in strong magnetic fields. PHYSICAL REVIEW LETTERS 1993; 71:3194-3197. [PMID: 10054881 DOI: 10.1103/physrevlett.71.3194] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
19
|
Xie XC, He S. Magneto-optical spectra of strongly correlated electrons in nonparabolic quantum dots. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:8454-8457. [PMID: 10007047 DOI: 10.1103/physrevb.48.8454] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
20
|
Haase RW, Johnson NF. Classification of N-electron states in a quantum dot. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:1583-1594. [PMID: 10008518 DOI: 10.1103/physrevb.48.1583] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
21
|
Zeng YH, Goodman B, Serota RA. Orbital magnetic response of quantum dots: A signature of electron-electron interactions. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:15660-15668. [PMID: 10005958 DOI: 10.1103/physrevb.47.15660] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
22
|
Johnson BL, Kirczenow G. Electrons in quantum dots: A comparison of interaction energies. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:10563-10566. [PMID: 10005169 DOI: 10.1103/physrevb.47.10563] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
23
|
Pfannkuche D, Gudmundsson V, Maksym PA. Comparison of a Hartree, a Hartree-Fock, and an exact treatment of quantum-dot helium. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:2244-2250. [PMID: 10006264 DOI: 10.1103/physrevb.47.2244] [Citation(s) in RCA: 184] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
24
|
|
25
|
Su B, Goldman VJ, Cunningham JE. Single-electron tunneling in nanometer-scale double-barrier heterostructure devices. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:7644-7655. [PMID: 10002505 DOI: 10.1103/physrevb.46.7644] [Citation(s) in RCA: 78] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
26
|
Tewordt M, Martín-Moreno L, Law VJ, Kelly MJ, Newbury R, Pepper M, Ritchie DA, Frost JE, Jones GA. Resonant tunneling in an AlxGa1-xAs/GaAs quantum dot as a function of magnetic field. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:3948-3952. [PMID: 10004123 DOI: 10.1103/physrevb.46.3948] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
27
|
Johnson NF. Quantum-dot excitation spectrum: Laughlin-like states. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:2636-2639. [PMID: 10003948 DOI: 10.1103/physrevb.46.2636] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
28
|
McEuen PL, Foxman EB, Kinaret J, Meirav U, Kastner MA, Wingreen NS, Wind SJ. Self-consistent addition spectrum of a Coulomb island in the quantum Hall regime. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:11419-11422. [PMID: 10001085 DOI: 10.1103/physrevb.45.11419] [Citation(s) in RCA: 181] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
29
|
Johnson NF, Payne MC. Many-body effects in resonant tunneling through quantum dots. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:3819-3821. [PMID: 10001972 DOI: 10.1103/physrevb.45.3819] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|