Radiation induced photocurrent and quantum interference in n-p junctions.

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Radiation induced photocurrent and quantum
interference in n-p junctions.
M.V. Fistul, S.V. Syzranov, A.M. Kadigrobov, K.B.
Efetov.
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Dirac spectrum
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Previous study of irradiated graphene n-p
junctions (PRL 98, 256803 (2007), PRB 78, 045407,
(2008))
Effect of radiation on quasiparticles spectra
opening of dynamical gaps, proportional to the
amplitude of EF
strong modification of current-voltage
characteristics

1. Photocurrent through the junction without any DC
   bias voltage applied (Elastic impurities
   weakly influence the photocurrent for
   experimentally relevant parameters)
2. Suppression of tunneling by strong enough
   radiation.

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Klein tunneling
Full reflection in Schrodinger quantum mechanics
but
Perfect transmission in Dirac quantum mechanics
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Now n-p junctions in systems with a gap
(bilayers, two-band semiconductors, etc.)
Result Ramsey-like oscillations of the
photocurrent!
Forbidden gap
Carbon nanotube
Mono- or bilayer graphene nanotube
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Floquet Theorem (analogue of Bloch theorem)
V(t)-periodic with period T
General Solution
is periodic with the same period T
Scattering from energy to energy
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Dynamical gap in homogeneous graphene
e
Choice of coordinatesystem
Resonantmomenta
Rotating reference frame in the pseudospin space
e
Rotating-waveapproximation closeto
-static Hamiltonian
-quasiparticlespectrum
However it is difficult to probe the gap,
especially in the presence of disorder.
with the gap
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Dynamic gaps in the presence of a p-n junction
U(r)
Resonantmomenta
The gap exists for a certain interval of momenta
and is localized in space!
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At the resonant point z0 the resonant value of
momentum is achieved
Tunneling through the dynamic gap (rotating
frame)
Potential close to the resonance
Landau-Zener tunneling in the momentum space
-the probability of tunneling
Cheianov, Falko (2006)
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General formulae for the current
-Energy and angle characterizing the state
The state scatters from to
-lead
t -scattering amplitude
Current I through the strip of width W
Photocurrent is possible if
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- moderate intensities
Photocurrent
and are Bessel and Struve functions, W
is the width
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Low-intensity regime (The tunneling exponent is
much smaller than 1,
)
S-intensity
High-intensity regime
Effect of elastic impurities
If
, the photocurrent persists
Photocurrent vs. radiation intensity
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Interference process in the presence of the gap
between conduction and valence gaps.
The Hamiltonian of the homogeneous system in the
rotating wave approximation.
-dynamic gap
Energy as a function of the spatial coordinate.
Energy versus momentum.
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The accumulated phase.
F-slope
The total quantum mechanical probability of
inelastic electron transmission.
Current
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Final expression for the photocurrent
d-length of the junction
Analogy to Ramsey fringes!
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Ramsey fringes in atomic physics
Norman F. Ramsey, Phys. Rev. 78, 699 (1950)
Nobel Prize in Physics (1989)
What is a best way to observe Ramsey
fringes? Variation of
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Experimental parameters for Graphene.
close to that inJ.Huard et al., 2007 B.Oezyilmaz
et al. 2007
d100nmW1µm
U00.1eV
-the height of the potential barrier
-close to that in M.Freitag, Y. Martin, J.
Misewich et al., 2003
S10kW/cm2
Photocurrent is the largest, if
The photocurrent is maximized when
Exponent of tunneling through the gap
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Relevant experiment
Xia et al (IBM), Nanoletters. (2009)
Reduced photocurrent
Maximum experimental value of the photocurrent
25nA
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Estimates for the Ramsey fringes
The gap
Radiation frequency
A large number of the oscillations can be
observed at
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• Transport properties of graphene bilayers,
  graphene ribbons, etc,.. p-n junctions irradiated
  by monochromatic electromagnetic field (EF) were
  studied.
• The resonant interaction of propagating
  quasiparticles with an externalradiation opens
  dynamical gaps in their spectrum, resulting in a
  strongmodification of current-voltage
  characteristics.
• A photocurrent flows in all the situations
  considered.
• If the conduction and valence gap are separated
  by a gap, the photocurrent oscillates as a
  function of the split gate or the external
  frequency, which is analogous to Ramsey
  oscillations.