Radiation induced photocurrent and quantum interference in n-p junctions. M.V. Fistul, S.V. Syzranov, A.M. Kadigrobov, K.B. Efetov.

Dirac spectrum

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. Previous study of irradiated graphene n-p junctions (PRL 98, (2007), PRB 78, , (2008))

Klein tunneling Full reflection in Schrodinger quantum mechanics but Perfect transmission in Dirac quantum mechanics

Now: n-p junctions in systems with a gap (bilayers, two-band semiconductors, etc.) Result: Ramsey-like oscillations of the photocurrent! Forbidden gap Carbon nanotubeMono- or bilayer graphene nanotube

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

ε Choice of coordinate system Resonant momenta ε Rotating reference frame in the pseudospin space Rotating-wave approximation close to - static Hamiltonian -quasiparticle spectrum with the gap Dynamical gap in homogeneous graphene However: it is difficult to probe the gap, especially in the presence of disorder.

Resonant momenta Dynamic gaps in the presence of a p-n junction U(r) The gap exists for a certain interval of momenta and is localized in space!

At the resonant point z 0 the resonant value of momentum is achieved Landau-Zener tunneling in the momentum space: Potential close to the resonance: -the probability of tunneling Tunneling through the dynamic gap (rotating frame) Cheianov, Falko (2006)

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

Electrons in the energy interval of the width can penetrate from the right to the left lead absorbing a photon! - moderate intensities Photocurrent and are Bessel and Struve functions, W is the width

High-intensity regime: Effect of elastic impurities: If, the photocurrent persists S-intensity Photocurrent vs. radiation intensity Low-intensity regime: (The tunneling exponent is much smaller than 1, )

Interference process in the presence of the gap between conduction and valence gaps. Energy as a function of the spatial coordinate. Energy versus momentum. The Hamiltonian of the homogeneous system in the rotating wave approximation. -dynamic gap

The accumulated phase. The total quantum mechanical probability of inelastic electron transmission. F-slope Current

Final expression for the photocurrent d-length of the junction Analogy to Ramsey fringes!

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

d=100nm W=1μm close to that in J.Huard et al., 2007 B.Oezyilmaz et al U 0 =0.1eV-the height of the potential barrier S=10kW/cm 2 -close to that in M.Freitag, Y. Martin, J. Misewich et al., 2003 Photocurrent is the largest, if The photocurrent is maximized when Exponent of tunneling through the gap Experimental parameters for Graphene.

Relevant experiment Xia et al (IBM), Nanoletters. (2009) Reduced photocurrent Maximum experimental value of the photocurrent: 25nA

Estimates for the “Ramsey fringes” The gap: Radiation frequency: A large number of the oscillations can be observed at

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 external radiation opens dynamical gaps in their spectrum, resulting in a strong modification 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.