Figure 1

(a) dc $I(V)$ curve measured for the SL when $B=0$ at temperature $T=293\mathrm{K}$. Inset: schematic diagram of the SL showing the emitter or collector contacts (green), barrier and quantum well layers (dark and light blue, respectively), and orientation of the applied electric field, $\mathbf{F}$, and magnetic field, $\mathbf{B}$, relative to the coordinate axes. (b) Color map (scale inset right calibrated in dBm) showing the spectrum of $I(t)$ oscillations measured over a range of $V$ and frequencies, $f$, near the first harmonic. Left inset: a typical frequency spectrum of the $I(t)$ oscillations measured around the first harmonic for $V=0.4\mathrm{V}$ and $T=293\mathrm{K}$.Reuse & Permissions

Figure 2

$I(V)$ characteristics (a) measured and (b) calculated for the SL at the $\theta$ values indicated when $B=7\mathrm{T}$ and $T=4.2\mathrm{K}$. Inset in (b) shows the regions of current instability (shaded) in the $I(V)$ curves calculated for $\theta =0°$ (lower trace) and $\theta =40°$ (upper trace, offset vertically by 20 mA for clarity). The maximum (minimum) values of the ac current correspond to the upper (lower) edges of the shaded areas. Dashed curves in inset indicate the time-averaged current.Reuse & Permissions

Figure 3

Color maps showing how the amplitude, $I_a$, of the $I(t)$ oscillations varies with $V$ and $\theta$ when $B=7\mathrm{T}$ and $T=4.2\mathrm{K}$: (a) experimental data—pixellation reflects discrete $V$ and $\theta$ values at which we measure $I(t)$ [inset shows amplitude of frequency spectra measured for $\theta =0$ at $V=0.3\mathrm{V}$ (lower trace) and $\theta =60°$ at $V=0.8\mathrm{V}$ (upper trace, offset vertically by 50 dBm for clarity) when $B=7\mathrm{T}$, arrows indicate first harmonics]; (b) and (c) are corresponding theoretical plots calculated, respectively, without and with the external resonant circuit shown in the inset of (c).Reuse & Permissions

Figure 4

Color map showing the single-electron drift velocity, $v_d$, calculated versus $F$ and $\theta$ for $B=7\mathrm{T}$. Islands of high $v_d$ (whose right-hand edges are regions of negative differential velocity) originate either from Bloch oscillations (near left-hand dashed line labeled ET) or from resonant coupling of Bloch and cyclotron motion when $r=1$ and 2, which occurs along the middle and right-hand dashed curves respectively. The inset shows a stroboscopic Poincaré section of the electron trajectories constructed by plotting the momentum components ($p_y$, $p_z$) (yellow dots) in the plane of the SL layers at integer multiples of the Bloch oscillation period $T_B=2\pi /{\omega }_B$ when $r=2$. Resonances between the cyclotron and Bloch oscillations create unbounded weblike structures, comprising interconnecting radial and ring-shaped chaotic filaments as shown in the inset, which are known in the literature as “stochastic webs” [19].Reuse & Permissions