Many-body correlations in STM single molecule junctions

Transcription

1 Many-body correlations in STM single molecule junctions Andrea Donarini Institute of Theoretical Physics, University of Regensburg, Germany TMSpin Donostia

2 Many-body correlations in STM single molecule junctions Andrea Donarini Institute of Theoretical Physics, University of Regensburg, Germany TMSpin Donostia

3 Motivation T. Miyamachi et al. Nature comm. 3, 993 (2012) CuPc on Ag(100) is anionic (CuPc - ) The ground state is a triplet Triplet-singlet splitting: 21 mev A. Mugarza, et al. PRB 85, (2012)

4 Motivation Alteration of the molecular orbitals due electronic correlation STM experiments probe quasiparticle wavefunctions which differ from the single particle molecular orbitals D. Toroz, et al. PRL 110, (2013) Visualization of many-body transitions in STM experiments F. Schulz et al. Nat. Physics 11, 229 (2015)

5 Spectroscopy & Topography J.Repp et al. PRL 94, (2005)

6 HOMO LUMO Single particle vs. Many-body Substrate Tip LUMO HOMO The two approaches only agree for uncorrelated systems close to equilibrium

7 Non-equilibrium and correlation LUMO Non-equilibrium HOMO tunnelling HOMO topography Correlated system + tunnelling Superposition of HOMO & LUMO topography

8 The Hamiltonian The STM single molecule junction is described by the Hamiltonian The molecule: interacting Hamiltonian for a small set of frontier orbitals Frontier orbitals

9 Image charge effects This term incorporates the two main effects which stabilize the excess charge on the molecule Image charge effect Polaron formation K. Kaasbjerg and K. Flensberg PRB 84, (2011) F. E. Olsson et al., PRL 98, (2007)

10 Leads and tunnelling The tip and substrate are modeled as reservoirs of non interacting fermions The tunnelling Hamiltonian is calculated following the tunnelling theory of Bardeen. Tip tunnelling amplitudes follow the Chen s derivative rule. Substrate tunnelling amplitudes are proportional to the overlap of the molecule and substrate wavefunctions. S. Sobczyk, A. Donarini, and M. Grifoni, PRB 85, (2012)

11 Transport calculations The system dynamics is obtained by solving a generalized master equation for the reduced density matrix Coherent dynamics Effective internal dynamics Tunnelling dynamics Phenom. relaxation defines the stationary reduced density matrix. S. Sobczyk, A. Donarini, and M. Grifoni, PRB 85, (2012)

12 Grandcanonical energy Tunnelling Liouvillean N - 1 N N + 1 Particle Number S. Sobczyk, A. Donarini, and M. Grifoni, PRB 85, (2012)

13 Tunnelling rate matrix Effective Hamiltonian Current operator S. Sobczyk, A. Donarini, and M. Grifoni, PRB 85, (2012)

14 Many-body rate matrix The current is proportional to the transition rate between many-body states For uncorrelated and non-degenerate systems the many-body rate reduces to Close to equilibrium, the constant current map is the isosurface of a specific molecular orbital (Tersoff-Hamann theory of STM) S. Sobczyk, A. Donarini, and M. Grifoni, PRB 85, (2012)

15 Copper-Phthalocyanine Organic ligand Metal center Non-equilibrium spin crossover

16 Spin crossover Metal complex Configuration change Low Spin Change in the occupation of the metal d-orbitals: Interplay of: (Octahedral) ligand field splitting Exchange interaction Metal complex High Spin V. Meded, et al.prb 83, (2011)

17 Non equilibrium spin-crossover R tip,1 R tip,2 V b = 0 Low Spin Low Spin V b > V th Low Spin High Spin B. Siegert, A. Donarini, and M. Grifoni, PRB 93, (R) (2016) V b = 1.38 V

18 HOMO LUMO? Anomalous current maps Standard Anomalous sub N 0-1 N 0 N 0 +1 N 0-1 N 0 N 0 +1 N 0-1 N 0 N 0 +1 The anomalous current map depends on the nature of the excited state J.Repp et al. PRL 94, (2005) The population inversion relies on the strong asymmetry between substrate and tip tunneling rates and on the weak relaxation rate

19 Minimal basis set The single particle Hamiltonian is constructed following LCAO schemes of Harrison [1] and Slater-Koster [2]. b 1g a 1u e g SOMO HOMO LUMO+ LUMO- 4 frontier orbitals C.Uhlmann et al., Nano Lett. 13, 777 (2013) [1] S. Froyen and W.A. Harrison, PRB 20, 2420 (1979) [2] J. C. Slater and G. F. Koster, Phys. Rev. 94, 1498 (1954)

20 Many-body spectrum B. Siegert, A. Donarini, and M. Grifoni, PRB 93, (R) (2016)

21 Low energy eigenstates + LUMO + SOMO + HOMO B. Siegert, A. Donarini, and M. Grifoni, PRB 93, (R) (2016)

22 Topography of CuPc B. Siegert, A. Donarini, and M. Grifoni, PRB 93, (R) (2016)

23 Standard Current and spin maps with B. Siegert, A. Donarini, and M. Grifoni, PRB 93, (R) (2016)

24 Anomalous Standard Standard vs. anomalous B. Siegert, A. Donarini, and M. Grifoni, PRB 93, (R) (2016)

25 Anomalous Standard Population inversion Current and topographic maps of an anionic transition resembles the HOMO The average spin of the molecule varies with the tip position and does not correspond to the one of the molecular ground state Standard Anomalous The molecule undergoes a population inversion which depends on the tip position B. Siegert, A. Donarini, and M. Grifoni, PRB 93, (R) (2016)

26 The anomalous current map B. Siegert, A. Donarini, and M. Grifoni, PRB 93, (R) (2016)

27 Is CuPc so special? Necessary and sufficient conditions for the appearance of non equilibrium spin-crossover: The energy of the excited neutral state should be lower than the ones of the cationic and anionic ground states C g N e N g A g The spin of the ground and the excited neutral state should be different S Ng S Ne The (tip) transitions between the ground anionic state and the the neutral ground and excited states should involve different molecular orbitals C g N e A g The tip and substrate tunnelling rates should be strongly asymmetric The (intrinsic) relaxation rate of the molecule on the substrate should be low (i.e. comparable or lower than the tip tunnelling rate) B. Siegert, A. Donarini, and M. Grifoni, PRB 93, (R) (2016)

28 A class of single molecule junctions Substrate workfunction B. Siegert, A. Donarini, and M. Grifoni, PRB 93, (R) (2016)

29 Conclusions I We developed a minimal model for the Cu-Phthalocyanine in terms of four interacting frontier orbitals. For an experimentally accessible substrate workfunction of 5 ev, we predict the appearance, close to the anionic resonance of non equilibrium spincrossover. Dramatic changes in the current and topographical maps with respect to standard LUMO resonances are found as fingerprints of the spin-crossover A class of single molecule junctions candidates for the observation of non equilibrium spin-crossover is defined in terms of relations between transport gap, optical gap and substrate workfunction. B. Siegert, A. Donarini, and M. Grifoni, PRB 93, (R) (2016)

30 Dicyanovinyl-quinquethiophene Oligothiophene Dicyanovinyl groups Entanglement in the two particles groundstate

31 Particle-in-a-box like states In oligothiophenes LUMO of thiophene General statement of the Sturm-Liouville theory for differential equations: In a one dimensional system the eigenfunction of the n-th excited state has n nodes. J. Repp et al., Nat. Phys. 6, 975 (2010)

32 Level-spacing engineering AS S Quinquethiophene (5T) Dicyanovinylquinquethiophene (DCV5T)

33 Orbital reversal P. Yu, N. Kocić, J. Repp, B. Siegert, and A. Donarini, PRL 119, (2017)

34 The many-body Hamiltonian We concentrate on the dynamics of two orbitals only S AS AS S and freeze the occupation of the other single particle states exchange pair-hopping AS AS AS AS S S S S fit to the experiment calculated from the molecular orbitals

35 The two-particle spectrum triplet singlet In DCV5T

36 di/dv (a.u.) Mechanism of orbital reversal P. Yu, N. Kocić, J. Repp, B. Siegert, and A. Donarini, PRL 119, (2017)

37 di/dv (a.u.) Mechanism of orbital reversal This transition would be forbidden if P. Yu, N. Kocić, J. Repp, B. Siegert, and A. Donarini, PRL 119, (2017)

38 Theory vs. Experiment DCV5T/NaCl/Cu(311) P. Yu, N. Kocić, J. Repp, B. Siegert, and A. Donarini, PRL 119, (2017)

39 Conclusions II By chemical engineering of the single-particle level spacing between two frontier orbitals we control the degree of electroniccorrelation in single molecule junctions We observe the apparent reversal in the orbital sequence of a dicyanovinyl-quinquethiophene (DCV5T) in STM upon changing the crystallographic orientation of the insulator-coated copper substrate The orbital reversal is the signature of an entangled ground state which we understand in terms of a minimal interacting model Criteria for such entanglement are clearly formulated in terms of the parameters in the minimal model and allow us to predict and control its occurrence for other molecules. Correlation P. Yu, N. Kocić, J. Repp, B. Siegert, and A. Donarini, PRL 119, (2017)

40 Aknowledgments Theory Experiment Milena Grifoni Benjamin Siegert Sandra Sobczyk Nemania Kocić Ping Yu Jascha Repp GRK 1570 SFB 689 Lichtenberg Programm

41 Thank you for your attention Entangled ground state

42 Additional Slides

43 di/dv (a.u.) Mechanism of orbital reversal & & The antisymmetric component is a strictly non-equilibrium effect

44 Intramolecular relaxation Experiment

45 log Basics on STM The signal is the tunnelling current between a metallic tip and the conducting sample z tip A The tunnelling current depends exponentially on the tip-sample distance sample x I Constant height The microscope can be used in two fundamental modes: constant height or constant current. One expects to record in both cases the topography of the sample z tip x Constant current x

46 Spectroscopy & Topography tip A z Molecule sample Insulator Substrate J.Repp et al. PRL 94, (2005) x

47 Intramolecular correlation Alteration of the molecular orbitals due to electronic correlation. STM experiments probe quasiparticle wavefunctions single particle molecular orbitals D. Toroz, et al. PRL 110, (2013) Visualization of intramolecular many-body correlation in STM experiments F. Schulz et al. Nat. Physics 11, 229 (2015)

48 Interaction with the substrate the interaction between the molecule and the substrate is described by two additional terms: grand canonical potential image charge/polaron shift incorporates two effects which stabilize the charge on the molecule: image charge effect polaron formation K. Kaasbjerg and K. Flensberg, PRB 84, (2011) F. E. Olsson et al., PRL 98, (2007)

49 E G (ev) DCV5T on NaCl/Cu(111) N The molecule is neutral on this substrate The order of the anionic states is in agreement with the single particle picture (and Sturm-Liouville theory)

50 E G (ev) DCV5T on NaCl/Cu(311) N The molecule is doubly charged on this substrate The two particle states are correlated

51 Orbital reversal: qualitative explanation TMSpin Donostia

52 Double charging TMSpin Donostia

53 Charging energy For the addition of an electron into a quantum dot, at least its charging energy is required. From transport characteristics on NaCl/Cu(311) Charging energy of DCV5T Change of crystallographic orientation of the substrate from NaCl/Cu(111) to NaCl/Cu(311) Sample bias (V) Work function change How can the molecule be possibly neutral on NaCl/Cu(111) and doubly charged on NaCl/Cu(311)?

54 Addition energies A variation of the substrate work function can change the charge state of the molecule. The stability of a given charge is given by its addition energy N 0-1 N 0 N 0 +1 Addition energies for the two orbital model of DCV5T: The singly charged DCV5T is extremely unstable

55 Stability diagram

56 Quantitative description of transport

57 Leads and tunnelling z x y The tip and substrate are modeled as reservoirs of non interacting fermions Sub: no xy-confinement Tip: parabolic xy-confinement The tunnelling Hamiltonian is calculated following the tunnelling theory of Bardeen. The tunnelling amplitudes are proportional to the overlap of the molecule and substrate wavefunctions. S. Sobczyk, A. Donarini, and M. Grifoni, PRB 85, (2012)

58 Transport calculations The dynamics is calculated via a generalized master equation for the reduced density matrix Coherent dynamics Effective internal dynamics Tunnelling dynamics Phenom. relaxation defines the stationary reduced density matrix.

59 Grancanonical energy Tunnelling Liouvillean N - 1 N N + 1 Particle Number

60 Tunnelling rate matrix Effective Hamiltonian Current operator Single particle tunnelling rate matrix

61 Many-body rate matrix The current is proportional to the transition rate between many-body states For uncorrelated and non-degenerate systems the many-body rate reduces to Close to equilibrium, the constant current map is the isosurface of a specific molecular orbital (Tersoff-Hamann theory of STM)

62 The many-body Hamiltonian Coulomb integrals are calculated numerically from MOs: S AS Some simplifications fit to the experiment similar spatial distrubution real MOs comparatively large

63 Non-equilibrium spin-crossover

64 Spin-orbit interaction (SOI) and Magnetic anisotropy

65 Motivation Metal organic complexes Cr 8 Spin-orbit coupling Specific organic ligand Fe + 4 on the metal center(s) configuration (ligand and crystal fields) Magnetic anisotropy in high spin molecular magnets Monolayers of single molecule magnets are promising high density information storage devices and exhibit interesting many-body phenomena D. Gatteschi, R. Sessoli, J. Villain, Molecular Nanomagnets, Oxford University Press, (2006) A. Chiesa, S. Carretta, P. Santini, G. Amoretti, E. Pavarini, Phys. Rev. Lett., 110, (2013) M. N. Faraggi. V. N. Golovach, et al., J. Phys. Chem C 119, 547 (2015)

66 SOI in the frontier orbitals basis The dominat contribution is given by the third shell of Cu Projection onto the frontier orbital basis yields where and

67 Low energy spectrum of CuPc contains three different energy scales To first order in the spin orbit coupling B. Siegert, A. Donarini and M. Grifoni, Beilstein J. of Nanotech. 6, 2452 (2015)

68 External magnetic field Orbital component described by the Peierls phase By adding also the Zeeman term we obtain the effective Hamiltonian where, and B. Siegert, A. Donarini and M. Grifoni, Beilstein J. of Nanotech. 6, 2452 (2015)

69 Magnetotransport B. Siegert, A. Donarini and M. Grifoni, Beilstein J. of Nanotech. 6, 2452 (2015)

70 Magnetic anisotropy B. Siegert, A. Donarini and M. Grifoni, Beilstein J. of Nanotech. 6, 2452 (2015)

71 Magnetic anisotropy B. Siegert, A. Donarini and M. Grifoni, Beilstein J. of Nanotech. 6, 2452 (2015)

72 Conclusions II We developed a minimal model which captures the interplay of organic ligand configuration and spin orbit interaction in CuPc The low energy spectrum is characterized in terms of spin and pseudo-spin quantum numbers The calculated transport characteristics of an STM single molecule junction show signatures of sizeable magnetic anisotropy

73 Outlook Incorporate a quantitative treatment of the electrostatic interactions within the junction Calculate the magnetotransport characteristics in presence of non-collinearly polarized ferromagnetic contacts Investigate the position resolved spin and/or orbital Kondo effect Study the time resolved evolution of electronic and spin excitations within an electronic or optoelectronic pumpprobe scheme

74 Thank you for your attention! TMSpin Donostia

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