Magnetically tuned resonant photon-assisted tunneling

We present evidence of a new channel for electronic conduction in a multi-quantum well type superlattice in the presence of a magnetic field applied parallel to the quantum well layers. Electrons in one potential well that are photo-excited to anti-crossings of the dispersion curves of the conduction subbands tunnel resonantly to the neighboring wells without intrasubband relaxation. This tunneling mechanism must be distinguished from tunneling involving states located around the energy minimum of the conduction subbands. We show that the new tunneling channel can only be understood from a nonperturbative calculation of the energy levels of the multi-quantum well structure in the presence of the magnetic field, since first order perturbation theory predicts the same energy dispersion for all conduction subbands, thus making this tunneling channel indistinct from standard intersubband excitation. Measurements of $\mathrm{THz}$ photocurrent show that both tunneling processes co-exist in a $\mathrm{GaAs}∕\mathrm{AlGaAs}$ multi-quantum well superlattice.

Figure 1

(Color online) Current as a function of the magnetic field parallel to the MQW layers, measured at a fixed bias of $15\mathrm{mV}$ without illumination. A broad peak is seen around $0.49\mathrm{T}$, the field for the resonance condition shown in Fig. 2. The sharper features are not reproducible and should be understood as noise.

Figure 2

(Color online) The lowest energy levels of three adjacent potential wells as a function of $-\hslash k_y∕eB$, the so-called cyclotron orbit center, at a magnetic field of $0.49\mathrm{T}$ and a voltage drop of $0.4\mathrm{mV}$ per period, calculated by the numerical nonperturbative calculation described in the text (solid line) and using first-order perturbation theory (dotted lines). For these values of magnetic and electric fields the first subband of the right well is at resonance with the bottom of the first subband of the center well, near $k_y=0$.

Figure 3

(Color online) Dispersion relations of a three well structure at $B=3.1\mathrm{T}$ and a voltage drop of $0.4\mathrm{mV}$ per period, calculated using first order perturbation theory (dotted lines) and by the numerical nonperturbative calculation described in the text (solid line). In this case, there are anti-crossings at the bottom of the second subbands with the first subbands of the neighboring wells.

Figure 4

(Color online) Dispersion relations of a three well structure at $B=5.1\mathrm{T}$ and a voltage drop of $0.4\mathrm{mV}$ per period, calculated using first-order perturbation theory (dotted lines) and by the numerical nonperturbative calculation described in the text (solid line). The arrows show the excitation energy from the first subband of the center well into extended states at the anti-crossings between the second subband of this same well and the first subbands of the neighboring wells.

Figure 5

(Color online) Calculated resonant frequency for the magnetically tuned resonant photon-assisted tunneling, MTRPAT (open circles) and for the excitation between states at the bottom of the lowest subband and of the second one (closed squares). The dependence on the magnetic field of the intersubband excitation frequency given by first-order perturbation theory is also shown (solid line). The horizontal dashed lines show the frequencies used in the measurements. The intersection of them with the MTRPAT curve gives the resonance fields for magnetically tuned resonant photon-assisted tunneling at these frequencies.

Figure 6

(Color online) Photocurrent as a function of magnetic field applied parallel to the MQW layers, for three radiation frequencies. The arrows show the expected field positions for MTRPAT at $f=3.54\mathrm{THz}$ (solid arrow), at $f=3.72\mathrm{THz}$ (dashed arrow) and at $f=3.90\mathrm{THz}$ (dotted arrow). The dash-dotted vertical line at $3.1\mathrm{T}$ shows the field at which another maximum in the photocurrent should occur due to the anti-crossings at the bottom of the second subbands with the first subbands of the neighboring wells. The observed broad (linewidth larger than $1\mathrm{T}$) peaks are a result of the convolution of this peak with the MTRPAT resonance, as explained in the text. For the sake of clarity, the curves for $f=3.72\mathrm{THz}$ and $f=3.90\mathrm{THz}$ were moved up $0.4$ and $0.8\mathrm{nA}$, respectively.

Figure 7

(Color online) Schematic representation of the $k_x$ dispersion curve for electron states at two different $k_y$’s, at the same subband. It represents states, at the first subband of a well, with $k_y$’s coincident with the edge of the forward and backward MTRPAT channels.