Magneto-Excitons in Semiconductor Quantum Rings
|
|
- Cameron Harvey
- 5 years ago
- Views:
Transcription
1 phys. stat. sol. (a) 190, No. 3, (2002) Magneto-Excitons in Semiconductor Quantum Rings I. Galbraith 1 ), F. J. Braid, and R. J. Warburton Department of Physics, Heriot-Watt University, Edinburgh, UK (Received September 4, 2001; accepted September 10, 2001) Subject classification: Ji; b; n; S7.12 In this paper we present calculations of the magneto-excitonic absorption spectrum for two different quantum ring geometries. Calculations are performed using a direct diagonalization of the single particle wavefunctions. Two different behaviours including the novel appearance of a ground state exciton with a finite angular momentum are described and calculations of the conditional correlation function are used to explore the nature of the exciton peaks. Magneto-excitons in semiconductor quantum rings present a fascinating example of how quantum-confined geometry can influence the optical and electrical properties of semiconductors. By interrupting the growth appropriately, rings of diameter approximately 500 A can be formed in the GaAs/InAs material system [1]. Typical exciton binding energies in these rings are 30 mev, which is much larger than the single particle energy spacings. Hence the Coulomb interaction mixes the discrete valence and conduction levels such as to reduce the average electron hole separation. The application of a magnetic field perpendicular to the rings shifts the single particle energy levels dramatically, in particular when exactly one flux quantum passes through the ring, the lowest lying electron energy level is the angular momentum, l e ¼ 1, state. An interesting question then arises as to the nature of the exciton in this case since the magnetic field is driving the electron and hole in opposite senses while the influence of the Coulomb attraction, V eh, is to keep the pair as close as possible. This problem has been tackled in various levels of approximation. Chaplik [2] and Römer et al. [3] considered analytical approximations to the case of infinitely narrow confining rings and found that Aharonov-Bohm-like oscillations should appear in the ground state exciton oscillator strength. Using more realistic, finite confinement potential and a numerical approach Song et al. [4] and Hu et al. [5] showed that such oscillations do not appear when finite thickness ring potentials are used. We present here calculations of the optical and angular momentum characteristics of two different ring geometries, showing distinctly different properties. We need to solve the Schr odinger equation for the electron and hole motion, including the Coulomb interaction and the magnetic field applied perpendicular to the ring ðh e 0 þhh 0 þv ehþ Yðr e ; r h Þ¼EYðr e ; r h Þ ; where H e 0 ¼ 1 2m* e ðp e eaþ 2 þv e ðr e Þ ; 1 ) Corresponding author; Tel.: (+44) ; Fax: (+44) ; I.Galbraith@hw.ac.uk # WILEY-VCH Verlag Berlin GmbH, Berlin, /02/ $ 17.50þ.50/0
2 782 I. Galbraith et al.: Magneto-Excitons in Semiconductor Quantum Rings is the Hamiltonian of a single electron in the ring potential, V e ðr e Þ, and similarly, H h 0, for the hole. Expanding the solution as Yðr e ; r h Þ¼ P n; m A nm w e n ðr eþ w h m ðr hþ ; where w e ðr e Þ and w h ðr h Þ are the wavefunctions of the single electron and hole in the quantum ring and exploiting the orthogonality of the single particle wavefunctions we get ðe e p þ Eh q EÞA pq þ P nm A nm ÐÐ w e p ðr e Þ w h q ðr hþv eh ðr e r h Þ w e n ðr eþ w h m ðr hþ dr e dr h ¼ 0 ; where E e p ; Eh q are the single particle energies. We account for the finite width of the confinement potential in the growth direction using a form factor which multiplies the Coulomb potential in momentum space, reducing the problem to a quasi-two dimensional one. Numerically solving the eigenvalue problem of Eq. (1) [6] gives the transition energies E a and oscillator strengths F a, via F a ¼ P 2 ð A a ij M ij ; M ij ij ¼ d l e rw e i 0 lh j i ðrþ wh j ðrþ dr ; where li e and lj h are the orbital angular momentum quantum numbers of the single particle states. Assuming a Gaussian line shape we can construct the absorption spectrum from the energy positions and oscillator strengths. The novelty in the system is clearly dictated by the confining potentials for the electrons and holes in the ring. As precise parameters, such as the ring size, composition, bandstructure and strain for the rings grown to date are rather poorly known we will explore the influence of different confinement regimes on the optical spectrum. We choose as a first example the ring potential, V e ðr e Þ¼ð1=2Þ m e ðw e=r e Þ 2 ðre 2 R2 e Þ2, and similarly V h ðr h Þ. These consist of an offset potential well having a minimum at a radius R eðhþ ¼ 200 A and having a soft potential turnover in the center. We use hw e ¼ 14 mev and m e ¼ 0:067m 0 for the electron and some low lying electron single particle wave functions are shown as the inset to Fig. 1. The main part of Fig. 1 depicts the energetic positions of these single particle electronic states as a function of magnetic field applied perpendicular to the ring. As can be seen the ring geometry has a profound effect in producing an l e ¼ 1 ground state for 3 T < B < 7.2 T and l e ¼ 2 ground state for B > 7.2 T. This corresponds well with the number of flux quanta passing through the ring [2]. Similar results are found for the hole states, for which we pffiffiffiffiffiffiffiffiffiffiffiffiffiffi choose hw h ¼ hw e m e =m h, with m h ¼ 0:2m 0 to reflect the reduced in-plane heavy-hole mass due to the confinement in the growth direction. As the strength of the confinement decreases the minima of the non-zero angular momentum curves become less pronounced so this novel nature requires the electron to be confined away from the ring center. The absorption strength for this ring as a function of magnetic field is depicted in Fig. 2. The energy zero corresponds to the bottom of the confining potential wells and the ground state exciton is bound by 18 mev in this structure. The lowest exciton energy shows a parabolic field dependence (/ 19B 2 mev) but there is no reflection of the ð1þ
3 phys. stat. sol. (a) 190, No. 3 (2002) 783 Fig. 1. Electron energy levels in a quantum ring as a function of magnetic field. The insert shows the lowest lying wavefunctions which are offset vertically by their confinement energy underlying non-zero angular momentum electron ground state for any magnetic field. The total angular momentum operator, L, commutes with the Hamiltonian because of the cylindrical symmetry of the problem and is therefore quantized. However the electron and hole components of that total are not quantized and in fact, calculated from the eigenvectors of Eq. (1) increase monotonically with increasing field, remaining equal and opposite for the optically active states. So with finite width rings there is sufficient Coulomb inter-mixing to eliminate the strong field dependence of the single particle states. Our calculations also compute the states with finite total angular momentum and we find that the L ¼ 0 state always has the lowest energy. Fig. 2. Quantum ring absorption spectrum as a function of magnetic field
4 784 I. Galbraith et al.: Magneto-Excitons in Semiconductor Quantum Rings We can further explore the nature of each absorption resonance by computing the conditional correlation function, P c ðr Þ¼ j Yðr ; r þ Þj Ð 2 j Yðr; rþ Þj 2 dr ; i.e. given a hole at r þ what is the probability of observing an electron at r.infig.3 this is shown for the B ¼ 0 exciton ground state with r þ directly below the peak. As can be seen the electron is clearly localized around the hole, this localization being achieved by mixing equal measures of states with l ¼1; 2; 3 :::. This picture does not alter much as the magnetic field is increased. The higher energy states in Fig. 2 exhibit a complex interplay between the magnetic field and Coulomb interaction which lead to a variety on energy shifts and anti-crossings. Looking at the correlation function we can identify those peaks in the transmission for which the electrons and holes are tightly correlated and those whose motion is essentially determined by the single particle properties. A quite different behaviour emerges when the confinement for electrons and holes is different. In particular when the inner potential for the hole is weak and the hole is essentially confined in a dot-like potential, whilst the electron is confined in a finite radius ring. To model this case we take exactly the same parameters as above, except that we use a simple parabolic confining potential for the holes. The exciton energies and their total angular momenta for B ¼ 7 T are plotted in Fig. 4. As can be seen, these states form a discrete parabolic band with the lowest energy states for each L being set apart from the rest. This picture is exactly analogous to the normal exciton dispersion curves for the center of mass motion. Interestingly here the lowest state is for L ¼ 1 i.e. an optically dark state with a finite center of mass angular momentum. This is shown most clearly in the insert. The optical spectra for this case show again nothing dramatic as a function of the magnetic field as the absorption only probes the optically active states and is insensitive to the existence of a dark ground state. In this paper we have presented calculations for two different quantum ring geometries demonstrating two different behaviours including the novel appearance of a Fig. 3. Conditional correlation function for the ground state exciton in the ring at B ¼ 0. The limit of the plot region is at a radius of 50 nm
5 phys. stat. sol. (a) 190, No. 3 (2002) 785 Fig. 4. Excitonic state energies versus total angular momentum for B ¼ 7:0 T when the hole is confined in a dot-like potential ground state exciton with a finite angular momentum. Progress in growth techniques and nano-optics will allow more detailed experimental studies of such effects in single quantum rings. References [1] A. Lorke, R. J. Luyken, A. O. Govorov, J. P. Kotthaus, J. M. Garcia, and P. M. Petroff, Phys. Rev. Lett. 84, 2223 (2000). [2] A. Chaplik, Sov. Phys. JETP Lett. 62, 900 (1995). [3] R. A. Römer and M. E. Raikh, Phys. Rev. B 62, 7045 (2001). [4] J. Song and S. E. Ulloa, Phys. Rev. B 63, 5302 (2001). [5] H. Hu, J.-L. Zhu, D.-J. Li, and J.-J. Xiong, Phys. Rev. B 63, 5307 (2001). [6] T. Chakraborty and P. Pietiläinen, Phys. Rev. B 50, 8460 (1994).
6
Linear dynamic polarizability and absorption spectrum of an exciton in a quantum ring in a magnetic field
Linear dynamic polarizability and absorption spectrum of an exciton in a quantum ring in a magnetic field A V Ghazaryan 1, A P Djotyan 1, K Moulopoulos, A A Kirakosyan 1 1 Department of Physics, Yerevan
More informationDependence of energy gap on magnetic field in semiconductor nano-scale quantum rings
Surface Science 532 535 (2003) 8 85 www.elsevier.com/locate/susc Dependence of energy gap on magnetic field in semiconductor nano-scale quantum rings Yiming Li a,b, *, Hsiao-Mei Lu c, O. Voskoboynikov
More informationarxiv:cond-mat/ v1 [cond-mat.mes-hall] 13 Oct 2000
Low energy exciton states in a nanoscopic semiconducting ring arxiv:cond-mat/0010186v1 [cond-mat.mes-hall] 13 Oct 000 Hui Hu a, Guang-Ming Zhang a,b, Jia-Lin Zhu a,b, Jia-Jiong Xiong a a Department of
More informationSpectroscopy of self-assembled quantum rings
Spectroscopy of self-assembled quantum rings RJWarburton 1, B Urbaszek 1,EJMcGhee 1,CSchulhauser 2, A Högele 2, K Karrai 2, A O Govorov 3,JABarker 4, B D Gerardot 5,PMPetroff 5,and JMGarcia 6 1 Department
More informationAharonov-Bohm effect for pedestrian
Aharonov-Bohm effect for pedestrian J. Planelles, J.I.Climente and J.L. Movilla Departament de Ciències Experimentals, Universitat Jaume I, 080 Castelló, Spain planelle@exp.uji.es Abstract. When a magnetic
More informationImpurity effects on the Aharonov-Bohm optical signatures of neutral quantum-ring magnetoexcitons
PHYSICAL REVIEW B 70, 155318 (2004) Impurity effects on the Aharonov-Bohm optical signatures of neutral quantum-ring magnetoexcitons L. G. G. V. Dias da Silva, 1,2 S. E. Ulloa, 2 and A. O. Govorov 2 1
More informationElectronic structure and magneto-optics of self-assembled quantum dots
PHYSICAL REVIEW B VOLUME 54, NUMBER 8 15 AUGUST 1996-II Electronic structure and magneto-optics of self-assembled quantum dots Arkadiusz Wojs Institute for Microstructural Sciences, National Research Council
More informationAharonov-Bohm interference in neutral excitons: effects of built-in electric fields
Universidade de São Paulo Biblioteca Digital da Produção Intelectual - BDPI Departamento de Física e Ciências Materiais - IFSC/FCM Artigos e Materiais de Revistas Científicas - IFSC/FCM 2010-02 Aharonov-Bohm
More informationFractional oscillations of electronic states in a quantum ring
EUROPHYSICS LETTERS 1 December 1996 Europhys Lett, 36 (7), pp 533-538 (1996) Fractional oscillations of electronic states in a quantum ring K Niemelä 1, P Pietiläinen 1,PHyvönen 1 and T Chakraborty 2 (
More informationThe octagon method for finding exceptional points, and application to hydrogen-like systems in parallel electric and magnetic fields
Institute of Theoretical Physics, University of Stuttgart, in collaboration with M. Feldmaier, F. Schweiner, J. Main, and H. Cartarius The octagon method for finding exceptional points, and application
More informationPHYSICS OF SEMICONDUCTORS AND THEIR HETEROSTRUCTURES
PHYSICS OF SEMICONDUCTORS AND THEIR HETEROSTRUCTURES Jasprit Singh University of Michigan McGraw-Hill, Inc. New York St. Louis San Francisco Auckland Bogota Caracas Lisbon London Madrid Mexico Milan Montreal
More informationOptical Anisotropy of Quantum Disks in the External Static Magnetic Field
Vol. 114 (2008) ACTA PHYSICA POLONICA A No. 5 Proc. XXXVII International School of Semiconducting Compounds, Jaszowiec 2008 Optical Anisotropy of Quantum Disks in the External Static Magnetic Field P.
More informationELECTRIC FIELD EFFECTS ON THE EXCITON BOUND TO AN IONIZED DONOR IN PARABOLIC QUANTUM WELLS
Journal of Optoelectronics and Advanced Materials Vol. 7, No. 5, October 005, p. 775-78 ELECTRIC FIELD EFFECTS ON THE EXCITON BOUND TO AN IONIZED DONOR IN PARABOLIC QUANTUM WELLS E. C. Niculescu *, L.
More informationElectronic Structure of a Hydrogenic Acceptor Impurity in Semiconductor Nano-structures
Nanoscale Res Lett (7) 2:4 6 DOI.7/s67-7-998-9 NANO EXPRESS Electronic Structure of a Hydrogenic Acceptor Impurity in Semiconductor Nano-structures Shu-Shen Li Æ Jian-Bai Xia Received: 7 September 7 /
More informationChapter 3 Properties of Nanostructures
Chapter 3 Properties of Nanostructures In Chapter 2, the reduction of the extent of a solid in one or more dimensions was shown to lead to a dramatic alteration of the overall behavior of the solids. Generally,
More informationarxiv:cond-mat/ v1 [cond-mat.mes-hall] 17 Sep 1997
Multiband theory of quantum-dot quantum wells: Dark excitons, bright excitons, and charge separation in heteronanostructures arxiv:cond-mat/9709193v1 [cond-mat.mes-hall] 17 Sep 1997 W. Jaskólski and Garnett
More informationCMT. Excitons in self-assembled type- II quantum dots and coupled dots. Karen Janssens Milan Tadic Bart Partoens François Peeters
Excitons in self-assembled type- II quantum dots and coupled dots CMT Condensed Matter Theory Karen Janssens Milan Tadic Bart Partoens François Peeters Universiteit Antwerpen Self-assembled quantum dots
More informationNANOSCIENCE AND NANOTECHNOLOGIES Layered Nanostructures. Eduard Kazaryan, Havk Sarkisyan
LAYERED NANOSTRUCTURES Eduard Kazaryan Faculty of Physics and Technology, Russian Armenian University, Armenia Hayk Sarkisyan Faculty of Physics and Technology, Russian Armenian University, Armenia Faculty
More informationinterband transitions in semiconductors M. Fox, Optical Properties of Solids, Oxford Master Series in Condensed Matter Physics
interband transitions in semiconductors M. Fox, Optical Properties of Solids, Oxford Master Series in Condensed Matter Physics interband transitions in quantum wells Atomic wavefunction of carriers in
More informationMagnetostatic modulation of nonlinear refractive index and absorption in quantum wires
Superlattices and Microstructures, Vol. 23, No. 6, 998 Article No. sm96258 Magnetostatic modulation of nonlinear refractive index and absorption in quantum wires A. BALANDIN, S.BANDYOPADHYAY Department
More informationWe are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists. International authors and editors
We are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists 3,800 116,000 120M Open access books available International authors and editors Downloads Our
More informationMagneto-Optical Properties of Quantum Nanostructures
Magneto-optics of nanostructures Magneto-Optical Properties of Quantum Nanostructures Milan Orlita Institute of Physics, Charles University Institute of Physics, Academy of Sciences of the Czech Republic
More informationOptical properties of wurtzite and zinc-blende GaNÕAlN quantum dots
Optical properties of wurtzite and zinc-blende GaNÕAlN quantum dots Vladimir A. Fonoberov a) and Alexander A. Balandin b) Nano-Device Laboratory, Department of Electrical Engineering, University of California
More informationQuantum Monte Carlo Simulations of Exciton Condensates
Quantum Monte Carlo Simulations of Exciton Condensates J. Shumway a and D. M. Ceperley b a Dept. of Physics and Astronomy, Arizona State University, Tempe, AZ 8583 b Dept. of Physics, University of Illinois,
More informationPhysics of Low-Dimensional Semiconductor Structures
Physics of Low-Dimensional Semiconductor Structures Edited by Paul Butcher University of Warwick Coventry, England Norman H. March University of Oxford Oxford, England and Mario P. Tosi Scuola Normale
More information14. Structure of Nuclei
14. Structure of Nuclei Particle and Nuclear Physics Dr. Tina Potter Dr. Tina Potter 14. Structure of Nuclei 1 In this section... Magic Numbers The Nuclear Shell Model Excited States Dr. Tina Potter 14.
More informationLevel Repulsion of Localised Excitons Observed in Near-Field Photoluminescence Spectra
phys. stat. sol. (a) 190, No. 3, 631 635 (2002) Level Repulsion of Localised Excitons Observed in Near-Field Photoluminescence Spectra A. Crottini (a), R. Idrissi Kaitouni (a), JL. Staehli 1 ) (a), B.
More informationSpin Transport in III-V Semiconductor Structures
Spin Transport in III-V Semiconductor Structures Ki Wook Kim, A. A. Kiselev, and P. H. Song Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27695-7911 We
More informationSingly ionized double-donor complex in vertically coupled quantum dots
Manjarres-García et al. Nanoscale Research Letters 1, 7:89 http://www.nanoscalereslett.com/content/7/1/89 NANO EXPRESS Open Access Singly ionized double-donor complex in vertically coupled quantum dots
More informationECE440 Nanoelectronics. Lecture 07 Atomic Orbitals
ECE44 Nanoelectronics Lecture 7 Atomic Orbitals Atoms and atomic orbitals It is instructive to compare the simple model of a spherically symmetrical potential for r R V ( r) for r R and the simplest hydrogen
More informationLecture contents. Burstein shift Excitons Interband transitions in quantum wells Quantum confined Stark effect. NNSE 618 Lecture #15
1 Lecture contents Burstein shift Excitons Interband transitions in quantum wells Quantum confined Stark effect Absorption edges in semiconductors Offset corresponds to bandgap Abs. coefficient is orders
More informationShallow Donor Impurity Ground State in a GaAs/AlAs Spherical Quantum Dot within an Electric Field
Commun. Theor. Phys. (Beijing, China) 52 (2009) pp. 710 714 c Chinese Physical Society and IOP Publishing Ltd Vol. 52, No. 4, October 15, 2009 Shallow Donor Impurity Ground State in a GaAs/AlAs Spherical
More informationQUANTUM INTERFERENCE IN SEMICONDUCTOR RINGS
QUANTUM INTERFERENCE IN SEMICONDUCTOR RINGS PhD theses Orsolya Kálmán Supervisors: Dr. Mihály Benedict Dr. Péter Földi University of Szeged Faculty of Science and Informatics Doctoral School in Physics
More informationThe Aharanov Bohm Effect
Supplement 6-A The Aharanov Bohm Effect Let us return to the description of an electron of charge e and mass m e, in a timeindependent magnetic field. The system is described by the Hamiltonian and the
More informationPseudopotential Theory of Semiconductor Quantum Dots
phys. stat. sol. (b) 224, No. 3, 727 734 (2001) Pseudopotential Theory of Semiconductor Quantum Dots Alex Zunger National Renewable Energy Laboratory, Golden, CO 80401, USA (Received July 31, 2000; accepted
More informationTunneling Spectroscopy of Disordered Two-Dimensional Electron Gas in the Quantum Hall Regime
Tunneling Spectroscopy of Disordered Two-Dimensional Electron Gas in the Quantum Hall Regime The Harvard community has made this article openly available. Please share how this access benefits you. Your
More informationQUANTUM WELLS, WIRES AND DOTS
QUANTUM WELLS, WIRES AND DOTS Theoretical and Computational Physics of Semiconductor Nanostructures Second Edition Paul Harrison The University of Leeds, UK /Cf}\WILEY~ ^INTERSCIENCE JOHN WILEY & SONS,
More informationSUPPLEMENTARY INFORMATION
A Dirac point insulator with topologically non-trivial surface states D. Hsieh, D. Qian, L. Wray, Y. Xia, Y.S. Hor, R.J. Cava, and M.Z. Hasan Topics: 1. Confirming the bulk nature of electronic bands by
More informationPDF hosted at the Radboud Repository of the Radboud University Nijmegen
PDF hosted at the Radboud Repository of the Radboud University Nijmegen The following full text is a preprint version which may differ from the publisher's version. For additional information about this
More informationCHAPTER 6 Quantum Mechanics II
CHAPTER 6 Quantum Mechanics II 6.1 6.2 6.3 6.4 6.5 6.6 6.7 The Schrödinger Wave Equation Expectation Values Infinite Square-Well Potential Finite Square-Well Potential Three-Dimensional Infinite-Potential
More information3: Many electrons. Orbital symmetries. l =2 1. m l
3: Many electrons Orbital symmetries Atomic orbitals are labelled according to the principal quantum number, n, and the orbital angular momentum quantum number, l. Electrons in a diatomic molecule experience
More informationPhysics of Semiconductors (Problems for report)
Physics of Semiconductors (Problems for report) Shingo Katsumoto Institute for Solid State Physics, University of Tokyo July, 0 Choose two from the following eight problems and solve them. I. Fundamentals
More informationIntensity / a.u. 2 theta / deg. MAPbI 3. 1:1 MaPbI 3-x. Cl x 3:1. Supplementary figures
Intensity / a.u. Supplementary figures 110 MAPbI 3 1:1 MaPbI 3-x Cl x 3:1 220 330 0 10 15 20 25 30 35 40 45 2 theta / deg Supplementary Fig. 1 X-ray Diffraction (XRD) patterns of MAPbI3 and MAPbI 3-x Cl
More informationSupplementary Figure S1 Definition of the wave vector components: Parallel and perpendicular wave vector of the exciton and of the emitted photons.
Supplementary Figure S1 Definition of the wave vector components: Parallel and perpendicular wave vector of the exciton and of the emitted photons. Supplementary Figure S2 The calculated temperature dependence
More informationVariation of Electronic State of CUBOID Quantum Dot with Size
Nano Vision, Vol.1 (1), 25-33 (211) Variation of Electronic State of CUBOID Quantum Dot with Size RAMA SHANKER YADAV and B. S. BHADORIA* Department of Physics, Bundelkhand University, Jhansi-284128 U.P.
More informationChapter 2 Energy Transfer Review
Chapter 2 Energy Transfer Review In this chapter, we discuss the basic concepts of excitation energy transfer, making the distinction between radiative and nonradiative, and giving a brief overview on
More informationNo reason one cannot have double-well structures: With MBE growth, can control well thicknesses and spacings at atomic scale.
The story so far: Can use semiconductor structures to confine free carriers electrons and holes. Can get away with writing Schroedinger-like equation for Bloch envelope function to understand, e.g., -confinement
More informationCharging and Kondo Effects in an Antidot in the Quantum Hall Regime
Semiconductor Physics Group Cavendish Laboratory University of Cambridge Charging and Kondo Effects in an Antidot in the Quantum Hall Regime M. Kataoka C. J. B. Ford M. Y. Simmons D. A. Ritchie University
More informationStrain-Induced Band Profile of Stacked InAs/GaAs Quantum Dots
Engineering and Physical Sciences * Department of Physics, Faculty of Science, Ubon Ratchathani University, Warinchamrab, Ubon Ratchathani 490, Thailand ( * Corresponding author s e-mail: w.sukkabot@gmail.com)
More informationQuantum Confinement in Graphene
Quantum Confinement in Graphene from quasi-localization to chaotic billards MMM dominikus kölbl 13.10.08 1 / 27 Outline some facts about graphene quasibound states in graphene numerical calculation of
More informationP. W. Atkins and R. S. Friedman. Molecular Quantum Mechanics THIRD EDITION
P. W. Atkins and R. S. Friedman Molecular Quantum Mechanics THIRD EDITION Oxford New York Tokyo OXFORD UNIVERSITY PRESS 1997 Introduction and orientation 1 Black-body radiation 1 Heat capacities 2 The
More informationSupporting Information for: Heavy-Metal-Free Fluorescent ZnTe/ZnSe Nanodumbbells
Supporting Information for: Heavy-Metal-Free Fluorescent ZnTe/ZnSe Nanodumbbells Botao Ji, Yossef E. Panfil and Uri Banin * The Institute of Chemistry and Center for Nanoscience and Nanotechnology, The
More informationPII: S (98)
Pergamon Solid State Communications, Vol. 18, No. 4, pp. 199 24, 1998 1998 Published by Elsevier Science Ltd 38 198/98 $ - see front matter PII: S38 198(98)35- THERMODYNAMIC EQUILIBRIUM OF SCREENED EXCITON
More informationThe Λ(1405) is an anti-kaon nucleon molecule. Jonathan Hall, Waseem Kamleh, Derek Leinweber, Ben Menadue, Ben Owen, Tony Thomas, Ross Young
The Λ(1405) is an anti-kaon nucleon molecule Jonathan Hall, Waseem Kamleh, Derek Leinweber, Ben Menadue, Ben Owen, Tony Thomas, Ross Young The Λ(1405) The Λ(1405) is the lowest-lying odd-parity state of
More informationSUPPLEMENTARY INFORMATION
doi:10.1038/nature12036 We provide in the following additional experimental data and details on our demonstration of an electrically pumped exciton-polariton laser by supplementing optical and electrical
More informationCharged mobile complexes in magnetic fields: a novel selection rule for magnetooptical transitions
JETP LETTERS VOLUE 70, NUBER 8 25 OCT. 1999 Charged mobile complexes in magnetic fields: a novel selection rule for magnetooptical transitions A. B. Dyubenko Institut für Theoretische Physik, J. W. Goethe-Universität,
More informationExcitonic effects on the second-order nonlinear optical properties of semi-spherical quantum dots
NANO EXPRESS Open Access Excitonic effects on the second-order nonlinear optical properties of semi-spherical quantum dots Jefferson Flórez * and Ángela Camacho Abstract We study the excitonic effects
More informationProblem 1: Step Potential (10 points)
Problem 1: Step Potential (10 points) 1 Consider the potential V (x). V (x) = { 0, x 0 V, x > 0 A particle of mass m and kinetic energy E approaches the step from x < 0. a) Write the solution to Schrodinger
More informationElectron correlations in charge coupled vertically stacked quantum rings
PHYSICAL REVIEW B 75, 3533 7 Electron correlations in charge coupled vertically stacked quantum rings B. Szafran, S. Bednarek, and M. Dudziak Faculty of Physics and Applied Computer Science, AGH University
More informationTime part of the equation can be separated by substituting independent equation
Lecture 9 Schrödinger Equation in 3D and Angular Momentum Operator In this section we will construct 3D Schrödinger equation and we give some simple examples. In this course we will consider problems where
More information1 Supplementary Figure
Supplementary Figure Tunneling conductance ns.5..5..5 a n =... B = T B = T. - -5 - -5 5 Sample bias mv E n mev 5-5 - -5 5-5 - -5 4 n 8 4 8 nb / T / b T T 9T 8T 7T 6T 5T 4T Figure S: Landau-level spectra
More information1 Reduced Mass Coordinates
Coulomb Potential Radial Wavefunctions R. M. Suter April 4, 205 Reduced Mass Coordinates In classical mechanics (and quantum) problems involving several particles, it is convenient to separate the motion
More informationUpper-barrier excitons: first magnetooptical study
Upper-barrier excitons: first magnetooptical study M. R. Vladimirova, A. V. Kavokin 2, S. I. Kokhanovskii, M. E. Sasin, R. P. Seisyan and V. M. Ustinov 3 Laboratory of Microelectronics 2 Sector of Quantum
More informationThe 4th Windsor Summer School on Condensed Matter Theory Quantum Transport and Dynamics in Nanostructures Great Park, Windsor, UK, August 6-18, 2007
The 4th Windsor Summer School on Condensed Matter Theory Quantum Transport and Dynamics in Nanostructures Great Park, Windsor, UK, August 6-18, 2007 Kondo Effect in Metals and Quantum Dots Jan von Delft
More informationLecture 3: Optical Properties of Insulators, Semiconductors, and Metals. 5 nm
Metals Lecture 3: Optical Properties of Insulators, Semiconductors, and Metals 5 nm Course Info Next Week (Sept. 5 and 7) no classes First H/W is due Sept. 1 The Previous Lecture Origin frequency dependence
More informationSupplementary Figures
Supplementary Figures Supplementary Figure S1: Calculated band structure for slabs of (a) 14 blocks EuRh2Si2/Eu, (b) 10 blocks SrRh2Si2/Sr, (c) 8 blocks YbRh2Si2/Si, and (d) 14 blocks EuRh2Si2/Si slab;
More informationEnhanced Rashba effect for hole states in a quantum dot
epl draft Enhanced Rashba effect for hole states in a quantum dot Aram Manaselyan and Tapash Chakraborty arxiv:0909.3318v2 [cond-mat.mes-hall] 21 Sep 2009 Department of Physics and Astronomy, University
More informationEnergy spectra and oscillatory magnetization of twoelectron self-assembled Inx Ga1-x As quantum rings in GaAs
Energy spectra and oscillatory magnetization of twoelectron self-assembled Inx Ga1-x As quantum rings in GaAs Citation for published version (APA): Fomin, V. M., Gladilin, V. N., Devreese, J. T., Kleemans,
More information3.15. Some symmetry properties of the Berry curvature and the Chern number.
50 Phys620.nb z M 3 at the K point z M 3 3 t ' sin 3 t ' sin (3.36) (3.362) Therefore, as long as M 3 3 t ' sin, the system is an topological insulator ( z flips sign). If M 3 3 t ' sin, z is always positive
More informationVariational wave function for a two-electron quantum dot
Physica B 255 (1998) 145 149 Variational wave function for a two-electron quantum dot A. Harju *, V.A. Sverdlov, B. Barbiellini, R.M. Nieminen Laboratory of Physics, Helsinki University of Technology,
More informationThe Λ(1405) is an anti-kaon nucleon molecule. Jonathan Hall, Waseem Kamleh, Derek Leinweber, Ben Menadue, Ben Owen, Tony Thomas, Ross Young
The Λ(1405) is an anti-kaon nucleon molecule Jonathan Hall, Waseem Kamleh, Derek Leinweber, Ben Menadue, Ben Owen, Tony Thomas, Ross Young The Λ(1405) The Λ(1405) is the lowest-lying odd-parity state of
More informationEnergy dispersion relations for holes inn silicon quantum wells and quantum wires
Purdue University Purdue e-pubs Other Nanotechnology Publications Birck Nanotechnology Center 6--7 Energy dispersion relations for holes inn silicon quantum wells and quantum wires Vladimir Mitin Nizami
More informationarxiv:quant-ph/ v1 13 Mar 2007
The Energy Eigenvalues of the Two Dimensional Hydrogen Atom in a Magnetic Field A. Soylu 1,2, O. Bayrak 1,3, and I. Boztosun 1 1 Department of Physics, Faculty of Arts and Sciences, Erciyes University,
More informationDefense Technical Information Center Compilation Part Notice
UNCLASSIFIED Defense Technical Information Center Compilation Part Notice ADP013124 TITLE: Resonant Acceptors States in Ge/Ge[1-x]Si[x] MQW Hetero structures DISTRIBUTION: Approved for public release,
More informationSupplementary Materials
Supplementary Materials Sample characterization The presence of Si-QDs is established by Transmission Electron Microscopy (TEM), by which the average QD diameter of d QD 2.2 ± 0.5 nm has been determined
More informationarxiv:cond-mat/ v1 [cond-mat.str-el] 9 May 2001
Positively charged magneto-excitons in a semiconductor quantum well. C. Riva and F. M. Peeters Departement Natuurkunde, Universiteit Antwerpen (UIA), B-2610 Antwerpen, Belgium arxiv:cond-mat/0105192v1
More informationSpin-Orbit Interactions in Semiconductor Nanostructures
Spin-Orbit Interactions in Semiconductor Nanostructures Branislav K. Nikolić Department of Physics and Astronomy, University of Delaware, U.S.A. http://www.physics.udel.edu/~bnikolic Spin-Orbit Hamiltonians
More informationQuantum transport through graphene nanostructures
Quantum transport through graphene nanostructures S. Rotter, F. Libisch, L. Wirtz, C. Stampfer, F. Aigner, I. Březinová, and J. Burgdörfer Institute for Theoretical Physics/E136 December 9, 2009 Graphene
More informationarxiv:cond-mat/ v1 [cond-mat.mes-hall] 26 Sep 2001
Effects of an electron gas on the negative trion in semiconductor quantum wells arxiv:cond-mat/09505v1 [cond-mat.mes-hall] 26 Sep 2001 Luis C.O. Dacal 1, José A. Brum 1,2 (1) DFMC-IFGW, Universidade Estadual
More informationCoulomb-interaction induced incomplete shell filling in the hole system of InAs quantum dots
Coulomb-interaction induced incomplete shell filling in the hole system of InAs quantum dots D. Reuter 1,2, P. Kailuweit 1, A. D. Wieck 1, U. Zeitler 2, O. S. Wibbelhoff 3, C. Meier 3, A. Lorke 3, and
More informationISSN: [bhardwaj* et al., 5(11): November, 2016] Impact Factor: 4.116
ISSN: 77-9655 [bhardwaj* et al., 5(11): November, 016] Impact Factor: 4.116 IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY EXCITON BINDING ENERGY IN BULK AND QUANTUM WELL OF
More informationEXCITONS, PLASMONS, AND EXCITONIC COMPLEXES UNDER STRONG CONFINEMENT IN QUASI-1D SEMICONDUCTORS. Theory and Perspectives
EXCITONS, PLASMONS, AND EXCITONIC COMPLEXES UNDER STRONG CONFINEMENT IN QUASI-1D SEMICONDUCTORS. Theory and Perspectives Igor Bondarev Math & Physics Department North Carolina Central University Durham,
More informationHarju, A.; Siljamäki, S.; Nieminen, Risto Two-electron quantum dot molecule: Composite particles and the spin phase diagram
Powered by TCPDF (www.tcpdf.org) This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Harju, A.; Siljamäki, S.; Nieminen,
More informationMean-field concept. (Ref: Isotope Science Facility at Michigan State University, MSUCL-1345, p. 41, Nov. 2006) 1/5/16 Volker Oberacker, Vanderbilt 1
Mean-field concept (Ref: Isotope Science Facility at Michigan State University, MSUCL-1345, p. 41, Nov. 2006) 1/5/16 Volker Oberacker, Vanderbilt 1 Static Hartree-Fock (HF) theory Fundamental puzzle: The
More informationQuantum Physics in the Nanoworld
Hans Lüth Quantum Physics in the Nanoworld Schrödinger's Cat and the Dwarfs 4) Springer Contents 1 Introduction 1 1.1 General and Historical Remarks 1 1.2 Importance for Science and Technology 3 1.3 Philosophical
More informationSpin entanglement induced by spin-orbit interactions in coupled quantum dots
Spin entanglement induced by spin-orbit interactions in coupled quantum dots Nan Zhao, 1 L. Zhong, Jia-Lin Zhu, 1 and C. P. Sun 1 Department of Physics, Tsinghua University, Beijing 100084, China Institute
More informationOptics and Quantum Optics with Semiconductor Nanostructures. Overview
Optics and Quantum Optics with Semiconductor Nanostructures Stephan W. Koch Department of Physics, Philipps University, Marburg/Germany and Optical Sciences Center, University of Arizona, Tucson/AZ Overview
More informationEnergy spectrum for a short-range 1/r singular potential with a nonorbital barrier using the asymptotic iteration method
Energy spectrum for a short-range 1/r singular potential with a nonorbital barrier using the asymptotic iteration method A. J. Sous 1 and A. D. Alhaidari 1 Al-Quds Open University, Tulkarm, Palestine Saudi
More informationΨ t = ih Ψ t t. Time Dependent Wave Equation Quantum Mechanical Description. Hamiltonian Static/Time-dependent. Time-dependent Energy operator
Time Dependent Wave Equation Quantum Mechanical Description Hamiltonian Static/Time-dependent Time-dependent Energy operator H 0 + H t Ψ t = ih Ψ t t The Hamiltonian and wavefunction are time-dependent
More informationSupplementary documents
Supplementary documents Low Threshold Amplified Spontaneous mission from Tin Oxide Quantum Dots: A Instantiation of Dipole Transition Silence Semiconductors Shu Sheng Pan,, Siu Fung Yu, Wen Fei Zhang,
More informationElectrons in a periodic potential
Chapter 3 Electrons in a periodic potential 3.1 Bloch s theorem. We consider in this chapter electrons under the influence of a static, periodic potential V (x), i.e. such that it fulfills V (x) = V (x
More informationUNCLASSIFIED UNCLASSIFIED
UNCLASSIFIED Defense Technical Information Center Compilation Part Notice ADP012814 TITLE: Optical Effect of Electric Field on Indirect Exciton Luminescence *n Double Quantum Wells of GaAs DISTRIBUTION:
More informationLECTURES ON QUANTUM MECHANICS
LECTURES ON QUANTUM MECHANICS GORDON BAYM Unitsersity of Illinois A II I' Advanced Bock Progrant A Member of the Perseus Books Group CONTENTS Preface v Chapter 1 Photon Polarization 1 Transformation of
More informationChapter 28 Sources of Magnetic Field
Chapter 28 Sources of Magnetic Field In this chapter we investigate the sources of magnetic of magnetic field, in particular, the magnetic field produced by moving charges (i.e., currents). Ampere s Law
More informationMagnetic field induced confinement-deconfinement transition in graphene quantum dots
Magnetic field induced confinement-deconfinement transition in graphene quantum dots G. Giavaras, P. A. Maksym, and M. Roy Department of Physics and Astronomy, University of Leicester, Leicester LE1 7RH,
More informationFIR Absorption in CdSe Quantum Dot Ensembles
phys. stat. sol. (b) 224, No. 2, 599 604 (2001) FIR Absorption in CdSe Quantum Dot Ensembles M.I. Vasilevskiy 1 ) (a), A.G. Rolo (a), M.V. Artemyev (b), S.A. Filonovich (a, c), M.J.M. Gomes (a), and Yu.P.
More informationExcitons confined in Single Semiconductor Quantum Rings: Observation and Manipulation of Aharonov-Bohm-type Oscillations
Excitons confined in Single Semiconductor Quantum Rings: Observation and Manipulation of Aharonov-Bohm-type Oscillations F. Ding, B. Li, F. M. Peeters, A. Rastelli, V. Zwiller and O. G. Schmidt Abstract
More informationAbsorption-Amplification Response with or Without Spontaneously Generated Coherence in a Coherent Four-Level Atomic Medium
Commun. Theor. Phys. (Beijing, China) 42 (2004) pp. 425 430 c International Academic Publishers Vol. 42, No. 3, September 15, 2004 Absorption-Amplification Response with or Without Spontaneously Generated
More informationChapter 28 Sources of Magnetic Field
Chapter 28 Sources of Magnetic Field In this chapter we investigate the sources of magnetic field, in particular, the magnetic field produced by moving charges (i.e., currents), Ampere s Law is introduced
More informationPHYS 3313 Section 001 Lecture # 22
PHYS 3313 Section 001 Lecture # 22 Dr. Barry Spurlock Simple Harmonic Oscillator Barriers and Tunneling Alpha Particle Decay Schrodinger Equation on Hydrogen Atom Solutions for Schrodinger Equation for
More information