Tunneling decay in a magnetic field

Abstract

We provide a semiclassical theory of tunneling decay in a magnetic field and a three-dimensional potential of a general form. Because of broken time-reversal symmetry, the standard WKB technique has to be modified. The decay rate is found from the analysis of the set of the particle Hamiltonian trajectories in complex phase space and time. In a magnetic field, the tunneling particle comes out from the barrier with a finite velocity and behind the boundary of the classically allowed region. The exit location is obtained by matching the decaying and outgoing WKB waves at a caustic in complex configuration space. Different branches of the WKB wave function match on the switching surface in real space, where the slope of the wave function sharply changes. The theory is not limited to tunneling from potential wells which are parabolic near the minimum. For parabolic wells, we provide a bounce-type formulation in a magnetic field. The theory is applied to specific models which are relevant to tunneling from correlated two-dimensional electron systems in a magnetic field parallel to the electron layer.

Underbarrier interference

“…(19), iv(0, y) = y and therefore @rð0; yÞ=@y ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c þ a 2 ðyÞ p . To obtain the function r(x, y) one has to determine the function v(x,y) from Eq.…”

Multiscale twin hierarchy in NiMnGa shape memory alloys with Fe and Cu

“…Ferromagnetic off-stoichiometric Heusler-type NiMnGa-based (NMG) alloys recently attracted a lot of attention due to the unique combination of different properties, such as shape memory and magnetic memory, magnetocaloric effect, and large magnetoresistance [1][2][3][4][5][6]. These alloys have high potential for practical applications in actuators, sensors, and energy harvesters [5,7].…”

“…These alloys have high potential for practical applications in actuators, sensors, and energy harvesters [5,7]. With a temperature decrease the NMG alloys undergo the 1st order displacive (martensitic) transformation from L2 1 structure to a tetragonal, orthorhombic or monoclinic martensitic phase [8][9][10].…”

Cyclotron enhancement of tunneling

“…A decay of a metastable state was considered in Ref. [9]. The certain peculiarities of an underbarrier wave function were discussed in Refs.…”

“…The references [1,2,3,4,5,6,7,8,9] say that it is impossible. Indeed, when an electron enters under the barrier its velocity deviates, due to the cyclotron effect, from a tunneling path with no magnetic field.…”