Andrea Donarini P.Yu, N. Kocic, B.Siegert, Jdoa17296/fisica/...SFB Workshop, Neumarkt 04.10.2016...
Transcript of Andrea Donarini P.Yu, N. Kocic, B.Siegert, Jdoa17296/fisica/...SFB Workshop, Neumarkt 04.10.2016...
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SFB Workshop, Neumarkt 04.10.2016
Entangled
ground state
Apparent reversal of molecular orbitals reveals
entanglement Andrea Donarini
P.Yu, N. Kocic, B.Siegert, J.Repp
University of Regensburg and Shanghai Tech University
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SFB Workshop, Neumarkt 04.10.2016
Spectroscopy & Topography
J.Repp et al. PRL 94, 026803 (2005)
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Motivation Alteration of the molecular orbitals due to electronic correlation
D. Toroz, et al. PRL 110, 018305 (2013)
F. Schulz et al. Nat. Physics 11, 229 (2015)
Visualization of intramolecular many-body correlation in STM experiments
STM experiments probe
quasiparticle
wavefunctions
single particle
molecular orbitals
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Particle-in-a-box like states in oligothiophenes
J. Repp et al., Nat. Phys. 6, 975 (2010)
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-1 nodes.
LUMO of thiophene
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Orbital engineering
Quinquethiophene
(5T)
Dicyanovinyl-
quinquethiophene
(DCV5T)
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Orbital inversion
No explanation within single particle picture
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pair hopping
exchange
inter-orbital Coulomb
kinetic term
intra-orbital Coulomb
The many-body Hamiltonian ● choose LUMO (S) and LUMO+1 (AS) as basis
● freeze other orbitals
HOMO
LUMO+1
LUMO
LUMO+1 (AS)
HOMO
LUMO (S)
E 5T DCV5T
Other interaction terms are forbidden by symmetry
DFT and experiment:
LUMO and LUMO+1 move
together + large gap to
HOMO
S
AS
S
AS
S
AS
S
AS
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similar spatial distrubution
real MOs
comparatively large fit to the experiment
S
AS
The many-body Hamiltonian
• Some simplifications
• Coulomb integrals are calculated numerically from MOs:
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Interaction with the substrate
grand canonical potential
image charge/polaron shift
• incorporates two effects which stabilize the charge on the molecule:
image charge effect
K. Kaasbjerg and K. Flensberg, PRB 84, 115457 (2011)
polaron formation
F. E. Olsson et al., PRL 98, 176803 (2007)
• the interaction between the molecule and the substrate is described by two additional terms:
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DCV5T on NaCl/Cu(111)
● The molecule is neutral on this substrate
● The order of the anionic states is in agreement with
the single particle picture
N
EG(e
V)
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SFB Workshop, Neumarkt 04.10.2016
DCV5T on NaCl/Cu(311)
N
EG(e
V)
● The molecule is doubly charged on this substrate
● The two particle sates are correlated
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The two-particle spectrum
singlet
triplet
In DCV5T
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Orbital reversal: qualitative explanation
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Single particle vs. Many-body
N0 N0+1 N0-1
HO
MO
LU
MO
Tip Substrate
HOMO
LUMO
The two approaches coincide only for uncorrelated systems close to equilibrium
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Tunnelling and correlation
+
tunnelling
?
Uncorrelated
system
Correlated
system tunnelling
or
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Mechanism of orbital reversal
dI/dV
(a.u
.)
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Mechanism of orbital reversal
dI/dV
(a.u
.)
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Mechanism of orbital reversal
dI/dV
(a.u
.)
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Mechanism of orbital reversal
dI/dV
(a.u
.)
This transition is forbidden if
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• &
Mechanism of orbital reversal
dI/dV
(a.u
.)
&
The antisymmetric component would not be detected in presence of strong relaxation
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Double charging
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-1 -0.5 0 0.5 1.0 1.5
Sample bias (V)
Charging energy
Charging energy
of DCV5T
• From transport characteristics on NaCl/Cu(311)
How can the molecule be possibly neutral on NaCl/Cu(111)
and doubly charged on NaCl/Cu(311) ?
• Change of crystallographic orientation of the
substrate from NaCl/Cu(111) to NaCl/Cu(311)
Work function
change
For the addition of an electron into a quantum dot, at least its charging energy is required.
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Addition energies
N0 N0+1 N0-1
A variation of the substrate work function
can change the charge state of the molecule.
The stability of a given charge is
given by ist addition energy
Addition energies for the two orbital model of DCV5T:
The singly charged DCV5T
is extremely unstable
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Stability diagram
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Quantitative description of transport
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Leads and tunnelling
The tip and substrate are modeled as reservoirs of non
interacting fermions
Sub: no xy-confinement
Tip: parabolic xy-confinement
x
y z
The tunnelling Hamiltonian is calculated following the tunnelling theory of Bardeen.
S. Sobczyk, AD, and M. Grifoni, PRB 85, 205408 (2012)
The tunnelling amplitudes are proportional to the overlap of the molecule and substrate
wavefunctions.
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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.
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Tunnelling Liouvillean
Gra
ncanonic
al energ
y
Particle Number
N N + 1 N - 1
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Tunnelling rate matrix
Current
operator
Effective
Hamiltonian
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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)
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Theory vs. Experiment
DCV5T/NaCl/Cu(111)
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SFB Workshop, Neumarkt 04.10.2016
Theory vs. Experiment
DCV5T/NaCl/Cu(311)
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SFB Workshop, Neumarkt 04.10.2016
Intramolecular relaxation
Experiment
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SFB Workshop, Neumarkt 04.10.2016
Conclusions The chemical engineering of the single-particle level spacing
between two frontier orbitals can control electronic-correlation in
single molecule junctions
With the help of a STM, the apparent reversal in the orbital
sequence of a dicyanovinyl-quinquethiophene (DCV5T) has been
observed, upon changing the crystallographic orientation of the
insulator-coated copper substrate
The orbital reversal is the signature of the formation of an
entangled ground state which we understand interms 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
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Thank you for your attention