Time-dependent electron tunneling through time-dependent tunnel barriers

Abstract

A plane electron wave incident on a tunnel-transparent potential barrier formed by the potential V͑x , t͒ = V 0 ͑x͒ + V 1 ͑x͒cos t generates, in addition to the usual stationary transmitted and reflected stationary waves, also "transmitted" and "reflected" electron waves oscillating with the same frequency. The transmitted oscillating wave can serve as the basis for transit-time microwave generators oscillating in the terahertz range. (Such oscillators are ballistic analogs of the tunnel-emission transit-time diode oscillators suggested almost half a century ago.) In the special case of a rectangular potential barrier, we describe the dependence of a small transmitted oscillating wave amplitude on the frequency and the value of V 1 ͑x͒. We consider two forms of V 1 ͑x͒: (1) homogeneous oscillation of the height of the rectangular barrier and (2) V 1 ͑x͒ = a␦͑x − x 1 ͒ [where ␦͑x͒ is the Dirac delta function and 0 Ͻ x 1 Ͻ w; w is the barrier thickness]. For sufficiently high frequencies determined by the time for tunneling, a much higher emission of the transmitted oscillating wave takes place in comparison with the results of quasistatic calculations.

Non-adiabatic quantum pumping by a randomly moving quantum dot

“…Another important feature shared by all such types of CTRW is that if one is only interested in the average survival amplitude (or Weyl differential) of the initial eigenstate |k 0 then as we have seen from Fig.1(c,d), Eqs. (15) are in excellent agreement with the numerics for each realization. Therefore one can average these formulae directly and arrive at the following amazing statement: Regardless of the nature of the symmetric CTRW of a narrow potential barrier the average survival amplitude f (k 0 , t) of an eigenstate |k 0 is just the characteristic function Φ(k 0 , t) of the current position of the scatterer γ(t).…”

Differential tunnel transparency of a rectangular heterostructural barrier for the terahertz frequency range

“…1 In the case of the rectangular barrier with a time-dependent height B = 0 + ͑1͒ cos t, the formula, which is analogous to Eq. We can hope that the optimal working regime for the high-frequency tunnel emitters can be realized if ͑A /2Qw͒exp Qw Ϸ 1 or ͓eE B ͑␦ − ͒ / gប͔exp͓បgw /2͑␦ − ͔͒ Ϸ 1.…”

“…In a previous article, 1 we considered several models relating to a time-dependent electron tunneling through nonstationary tunnel emitter barriers. As is known, 2-5 the quasistatic approach based on the use of the static tunneling equations becomes incorrect if a characteristic frequency tends to the terahertz range.…”

“…As in the previous article, 1 we consider here the simplest quantum-mechanical problem relating to transmission and reflection of a single-electron wave. A certain field should exist there: it is caused by the continuity of a normal component of the electric induction vector D x = D E x in the interface of the barrier/region 2 where D is a dielectric constant.…”

Exploring the non-equilibrium fluctuation relation for quantum mechanical tunneling of electrons across a modulating barrier

“…The part left back evolves within the modulated barrier and part of it tunnels across the periodically modulated barrier [5]. Typically for a barrier modulated at a frequency , the solutions for the reflected and transmitted waves not only have the usual stationary wave solution, but also have waves which are reflected and transmitted at frequency  [2,5,6,7]. It has also been suggested that under certain conditions, a continuous drive may lead to localization and completely destroy coherent tunneling across the barrier [8,9,10].…”