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Constantinos Simserides Institute of Materials Science, NCSR Demokritos, Athens, Greece

NN09, Thessaloniki, Greece, 13-15 July 2009. Two-dimensional carriers under in-plane magnetic field : novel phenomena. Constantinos Simserides Institute of Materials Science, NCSR Demokritos, Athens, Greece. conduction band minimum (Ga,Al)As. conduction band minimum (Ga,Al)As.

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Constantinos Simserides Institute of Materials Science, NCSR Demokritos, Athens, Greece

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  1. NN09, Thessaloniki, Greece, 13-15 July 2009 Two-dimensional carriers under in-plane magnetic field: novelphenomena Constantinos Simserides Institute of Materials Science, NCSR Demokritos, Athens, Greece

  2. conduction band minimum (Ga,Al)As conduction band minimum (Ga,Al)As Barrier Barrier conduction band minimum GaAs conduction band offset NO applied fields, NO dopants quantum wells, QWs ☺ heterostructure QW (Ga,Al)As/GaAs/(Ga,Al)As Host crystals: III-V (e.g. GaAs), II-VI (e.g. CdTe)conduction band orvalence band

  3. (Ga,Al)As/GaAs/(Ga,Al)As heterostructure QW donors donors (Ga,Al)As conduction band minimum (Ga,Al)As conduction band minimum Β GaAs conduction band minimum with selective doping quasi two-dimensional carriers under parallel magnetic field(the elegant concept of Landau levels must be abandoned)

  4. For this orientation . . . Comparison with other carrier systems under magnetic / electric field Quantum mechanical properties & density of states (DOS) Examples of modified physical properties (magnetoresistance oscillations, N-type kink in photoluminescence, etc) Thermodynamic properties (population, entropy, internal & free energy, magnetization, magnetic susceptibility) Spintronic systems (with magnetic impurities): Spin-subband populations and spin-polarization Systems without magnetic impurities: a diamagnetic to paramagnetic transition of entirely orbital origin is predicted, while entropy...

  5. Comparison with other carrier systems under magnetic / electric field B//y B//y, E//z B=0, QW(z), [E//z] B//y, PQW(z) B//y, QW(z), [E//z] C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131–5141 C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y. Editors: Alfred Ruyter and Harper O'Mahoney,ISBN: 978-1-60692-557-7

  6. Free particle along y axis, while in thexz plane: Quasi two-dimensional carriers - Hamiltonian C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131–5141 C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y. Editors: Alfred Ruyter and Harper O'Mahoney,ISBN: 978-1-60692-557-7

  7. Quasi two-dimensional carriersForce on the electrons - Magnetic length C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131–5141 C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y. Editors: Alfred Ruyter and Harper O'Mahoney,ISBN: 978-1-60692-557-7

  8. DOS changes qualitatively & quantitatively DOS deviates from the well-known step-like form Equation holds for any type of competition between spatial and magnetic confinement LimitB → 0 or very narrow QWs Ei(kx) = Ei+ ħ2kx2/(2m*) DOS regains its step-like form Limit of a simple saddle point, Ei(kx) = Ei – ħ2kx2/(2n*), (n* > 0) DOS deviates logarithically ρ(ε) -ln|ε-Ei| Quasi two-dimensional carriers: density of states (DOS) Eiσ(kx) must be self-consistently calculated. The kx-dependence increases the numerical cost by 100-1000. The main features of this DOS, theVan Hove singularities, are not –generally- simple saddle points. The DOS, modification changes the physical properties. C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131 C. Simserides, Physica E 21 (2004) 956 C. Simserides, Phys. Rev. B 69 (2004) 113302

  9. Quasi two-dimensional carriers: Thermodynamic properties population internal energy entropy free energy magnetization C. Simserides, Phys. Rev. B 69 (2004) 113302 C. Simserides, J. Phys.: Condens. Matter 21 (2009) 015304

  10. Energy dispersion, DOS, subband concentrations, QW profile C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y. Editors: Alfred Ruyter and Harper O'Mahoney,ISBN: 978-1-60692-557-7

  11. Energy dispersion, DOS, subband concentrations, QW profile C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y. Editors: Alfred Ruyter and Harper O'Mahoney,ISBN: 978-1-60692-557-7

  12. Energy dispersion, DOS, subband concentrations, QW profile C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y. Editors: Alfred Ruyter and Harper O'Mahoney,ISBN: 978-1-60692-557-7

  13. Energy dispersion, DOS, subband concentrations, QW profile C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y. Editors: Alfred Ruyter and Harper O'Mahoney,ISBN: 978-1-60692-557-7

  14. Energy dispersion, DOS, subband concentrations, QW profile C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y. Editors: Alfred Ruyter and Harper O'Mahoney,ISBN: 978-1-60692-557-7

  15. Entirely orbital Thermodynamic properties of quasi two-dimensional carriersunder parallel magnetic fieldC. Simserides, J. Phys.: Condens. Matter 21 (2009) 015304 The magnetic susceptibility χm= ∂M/∂H oscillates between <0 (diamagnetic) and >0 (paramagnetic) values the NEW phenomenon is important in comparison with the ideal de Haas–van Alphen effect (the corresponding phenomenon under perpendicular magnetic field) Why increasing temperature, the diamagnetic to paramagnetic oscillation dies out... Entropy depends CLEARLY on the applied magnetic field

  16. Principal thermodynamic properties

  17. Principal thermodynamic properties

  18. change DOS => oscillation of M (II) MIN “cohesion”: occupiedE0(kx) splits in two parts ~ |kx| ≈ 0 (III) minima move apart (I) Depopulation of E1(kx) MAX “cohesion” Principal thermodynamic properties (IV) Increasing the magnitute of the system, S minimum increases. χm = ∂M/∂H between < 0 & >0 values: (purely orbital diamagnetic - paramagnetic oscillation) New phenomenon (under in-plane Β) corresponds to ideal de Haas–van Alphen effect (perpendicular Β). e.g. in case (γ΄), ΔM ~ 10 A/m~ 1/5of ideal de Haas–van Alphen effect.

  19. Ideal de Haas–van Alphen effect Θεωρία Peierls R 1933 Z. Phys. 81 186 Πείραμα Wilde M A, Schwarz M P, Heyn C, Heitmann D, Grundler D, Reuter D and Wieck A D 2006 Phys. Rev. B 73 125325

  20. End • Thank you for your attention!

  21. Relevant Literature C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131 C. Simserides, Journal of Computational Electronics 2 (2003) 459 C. Simserides, Physica E 21 (2004) 956 C. Simserides, Phys. Rev. B 69 (2004) 113302 C. Simserides, AIP Conf. Proc. 772 (2005) 341 C. Simserides, International Journal of Modern Physics B 18 (2004) 3745 C. Simserides, Journal of Physics: Conference Series 10 (2005) 143 C. Simserides, Phys. Rev. B 75 (2007) 195344 C. Simserides and I. Galanakis, Physica E 40 (2008) 1214 Diploma Thesis of Konstantinos Koumpouras:“Spintronics in dilute magnetic semiconductor quantum wells”. Materials Science Department, University of Patras (2008). C. Simserides, chapter in “Quantum Wells: Theory, Fabrication and Applications”, Nova Science Publishers, N.Y. Editors: Alfred Ruyter and Harper O'Mahoney,ISBN: 978-1-60692-557-7 C. Simserides, J. Phys.: Condens. Matter 21 (2009) 015304

  22. sheet electron concentration – internal energy Depopulation of E1(kx) forΒ ~ 13 T C. Simserides, chapter in "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, N.Y. Editors: Alfred Ruyter and Harper O'Mahoney,ISBN: 978-1-60692-557-7

  23. Β // in magnetoresistance Experimentally:- min of resistance (Rxx): step in DOS atEF(= subband depopulation) - max of resitance (Rxx): van Hove singularity in DOS atEF O. N. Makarovskii, L. Smrčka, P. Vašek, T. Jungwirth, M. Cukr, and L. Jansen, PRB 62 (2000) 10908

  24. Β // in photoluminescence (PL): N-type kink Huang D and Lyo S K 1999 Phys. Rev. B 59 7600 Orlita M, Grill R, Hlídek P, Zvára M, Döhler G H, Malzer S and Byszewski M 2005 Phys. Rev. B 72 165314 theory experiment

  25. Principal thermodynamic properties

  26. Principal thermodynamic properties Hence, increasing T, the diamagnetic to paramagnetic transition dies out.

  27. Περιοδικός πίνακας

  28. Ενεργειακή διασπορά, DOS, πληθυσμοί υποζωνών, μορφή QW C. Simserides, invited chapter in the book "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, NY. Editors: Alfred Ruyter and Harper O'Mahoney, in press

  29. Ενεργειακή διασπορά, DOS, πληθυσμοί υποζωνών, μορφή QW C. Simserides, invited chapter in the book "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, NY. Editors: Alfred Ruyter and Harper O'Mahoney, in press

  30. Ενεργειακή διασπορά, DOS, πληθυσμοί υποζωνών, μορφή QW C. Simserides, invited chapter in the book "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, NY. Editors: Alfred Ruyter and Harper O'Mahoney, in press

  31. Ενεργειακή διασπορά, DOS, πληθυσμοί υποζωνών, μορφή QW C. Simserides, J. Phys.: Condens. Matter 11 (1999) 5131 C. Simserides, invited chapter in the book "Quantum Wells: Theory, Fabrication and Applications", Nova Science Publishers, NY. Editors: Alfred Ruyter and Harper O'Mahoney, in press

  32. Question: What about Β // in spintronics?

  33. ☺DMS = dilute magnetic semiconductor,a semiconductor doped with (dilute) magnetic impurities Εικόνα από Ohno, Science281(1998) 951 Host crystals, doping, impurities Doping =introduction of impurities, on purpose - donors => electrons, e.g. N,P, As in host crystal Si, Ge - acceptors => holes, e.g. B, Al, Ga in host crystalSi, Ge Magnetic impurities, e.g. Mn( [Ar] 3d54s2) which provide(also) localized magnetic moments e.g. Mn in GaAs or in CdTe

  34. Spintronics = spin + electronics: use carrier charge as well as spin Carriers (holes, electrons)induce ferromagnetism! Εικόνες από MacDonald Schiffer Samarth, Nature Materials 4 (2005) 195

  35. “M” Figure from Ohno, J. Crystal Growth 251 (2003) 285 DMS:Electric field control of ferromagnetism. αλλάζουμε τάσηπύλης αλλάζει συγκέντρωση οπών αλλάζει βρόγχος υστέρησης

  36. Αντικατάσταση MnGa (καλό =>οπές κ εντοπισμένες μαγνητικές ροπές ΕνδοπλεγματικόMnI (κακό! διπλός δότης) Mn σεημιαγωγούς III-V GaAs • Εικόνα από Jungwirth et al., Rev. Mod. Phys. 78 (2006) 809 Αντικατάσταση AsGa antisite (κακό! Διπλός δότης)

  37. II Cd, Zn, Mg VI Se, Te Mn σεημιαγωγούς II-VΙ Το Mn αντικαθιστάκατιόντα (Cd, Zn, Mg, . . .) Καλό, δίνει μόνοεντοπισμένες μαγνητικές ροπές! Εισάγουμε φορείςΑΝΕΞΑΡΤΗΤΑ, εμπλουτίζοντας τα φράγματατων δομών! π.χ.. n- ή p- DMS ZnSe / Zn1-x-yCdxMnySe / ZnSe QWs

  38. Όρος Zeeman Όρος ανταλλαγής σπιν-σπιν μεταξύ s- (p-)ηλεκτρονίων ζώνης αγωγιμότητας (σθένους) και d- ηλεκτρονίωντωνκατιόντων Μn Σπιν πόλωση Για ηλεκτρόνια ζώνης αγωγιμότητας Ns = Ns,up + Ns,down (επιφανειακές συγκεντρώσεις) Η παρουσία μαγνητικών προσμίξεων αυξάνει το spin-splitting των φορέων, Uοσ. Θεωρία μέσου πεδίου (II) Υψηλότερες θερμοκρασίες. Το spin-splitting μικραίνει Αυξάνεται η συνεισφορά των φορέωνμειονότητας Μηχανισμός ανάδρασηςλόγωndown(r) - nup(r). (I) Χαμηλές θερμοκρασίες Μέγιστο spin-splitting ~ 1/3 της ασυνέχειας ζώνης αγωγιμότητας C. Simserides, Phys. Rev. B 69, 113302 (2004) C. Simserides, Phys. Rev. B 75(2007) 195344

  39. (I) Χαμηλές θερμοκρασίες. Μέγιστο spin-splitting, ~ 1/3 τηςασυνέχειας ζώνης αγωγιμότητας Απλά κβαντικά φρέατα με μαγνητικές προσμίξεις στη ζώνη αγωγιμότηταςυπό παράλληλομαγνητικό πεδίο (μη κλιμακοειδής DOS) • ταλάντωσητης M (ΕΑΝ ισχυρός ανταγωνισμόςχωρικούκαιμαγνητικού εντοπισμού) • Αλλαγές στις φυσικές ιδιότητες π.χ. • Πληθυσμοί σπιν-υποζωνών και σπιν-πόλωση • Εσωτερική ενέργεια, U, και Ελεύθερη ενέργεια, F • Εντροπία, S • Μαγνήτιση, M C. Simserides, Phys. Rev. B 69, 113302 (2004)

  40. C. Simserides, Phys. Rev. B 69, 113302 (2004)

  41. C. Simserides, Phys. Rev. B 69, 113302 (2004)

  42. C. Simserides, Phys. Rev. B 69, 113302 (2004)

  43. Magnetization considerable fluctuation of M (if vigorous competition between spatial and magnetic confinement) Magnetization fluctuation: 5 A/m (as adding 1017 cm-3 Mn).

  44. (II) Υψηλότερες θερμοκρασίες. Απλά κβαντικά φρέατα με μαγνητικές προσμίξεις στη ζώνη αγωγιμότηταςυπό παράλληλομαγνητικό πεδίο (μη κλιμακοειδής DOS) Σχετική επίδραση όρου Zeeman – όρου ανταλλαγής C. Simserides, Phys. Rev. B 75(2007) 195344

  45. C. Simserides, Phys. Rev. B 75, 195344 2007

  46. C. Simserides, Phys. Rev. B 75, 195344 2007

  47. Quasi-two-dimensional carriers in dilute-magnetic-semiconductorquantum wells under in-plane magnetic field

  48. Conduction band –valence band (bulk) From Winkler, http://www.niu.edu/~rwinkler/teaching/spin-04/wh1.pdf

  49. Conduction band–valence band (bulk-quantum wells) Spin orientation of holes in quantum wells, R. Winkler, D. Culcer, S. J. Papadakis, B. Habiband M. Shayegan, Semicond. Sci. Technol. 23 (2008) 114017

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