tightbinding methodthe Hamiltonian matrix

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tight-binding methodthe Hamiltonian matrix
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tight-binding methodthe transfer matrix method
define
to obtain
transfer matrix
then
the eigen values are found from
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tight-binding methodadding the Aharonov-Bohm
flux
explicit example an ordered system, of three
sites, N3,
the eigen-value equation is
and the solutions are
For a general N,
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the transmission and reflection in the
tight-binding model
modelling a quantum dot attached to two leads
the energy is
the TB equations
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the transmission and reflection in the
tight-binding model (cont.)
the resulting scattering matrix
the transmission coefficient is
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the transmission and reflection in the
tight-binding model (cont.)
the behavior of the transmission
for a certain ka, as function of
gate-voltage (resonance at a certain gate-voltage)
as function of energy, gate-voltage within the
band
as function of energy, gate-voltage outside the
bandno resonance!
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tight-binding model for an Aharonov-Bohm ring
the energy is
the TB equations
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tight-binding model for an Aharonov-Bohm ring
(cont.)
the transmission amplitude is
the transmission is
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transmission of an Aharonov-Bohm ring
for a certain ka, as function of flux
as function of energy, at zero flux, showing Fano
resonance
disappearance of Fano resonance
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Solid-state interferometers threaded by a
magnetic flux (Aharonov-Bohm phase)
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Aharonov-Bohm interferometer
two-slit formula (WRONG!)
correct formula
the conductance is even in magnetic
field (Onsager relations)
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Solid-state interferometers threaded by a
magnetic flux (Aharonov-Bohm phase)
Onsager-Casimir relations unitarity
(conservation of electron number)
unitarity is broken
demonstrating coherent transport
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Summary 3
adding quantum conductors in series in 1D yields
localization at long length-scales L
The phenomenon of Coulomb-blockade-charge is
passing when the state of N elecs. has same
energy as that of N1
TB model (1D)
gauge transforming the AB phase
The Aharonov-Bohm ring
using transfer matrices
transmission of AB ring in TB model
Fano resonance
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Non-local effects in the conductance
the conductance of a side-scatterer
all elements are made of a perfect (ballistic)
wire
an optional AB flux in the ring
modelling the system by a TB description
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Non-local effects in the conductance (cont.)
the energy is
the TB equations
the solution
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Non-local effects in the conductance (results)
T as fn. of ka, no flux
checking the origin of the Fano resonances
T as fn. of ka, for a certain flux
as function of the flux