Terahertz Emission from Quantum Cascade Lasers in the Quantum Hall Regime: Evidence for Many Body Resonances and Localization Effects

A terahertz quantum cascade laser, operating at $\lambda =159\mu \mathrm{m}$ and exploiting the in-plane confinement arising from perpendicular magnetic field, is used to investigate the physics of electrons confined on excited subbands in the regime of a large ratio of the magnetic field confinement energy to the photon energy. As the magnetic field is increased above about 6 T, and the temperature lowered below 20 K, the devices are characterized by a very low threshold current density, with values as low as $J_{\mathrm{t}\mathrm{h}}=1\mathrm{A}/{\mathrm{c}\mathrm{m}}^2$, and an increase of gain by five times the low field value. We show that, as with the quantum Hall effect, the key physical process is the localization of the carriers. Evidences for resonant electron-electron scattering processes are directly obtained from light intensity and transport measurements.

Figure 1

(a) Light emission in pulsed mode as a function of magnetic field for various applied biases for a 3.5 mm long, $520\mu \mathrm{m}$ wide laser stripe with backfacet high reflection (HR) coating at 4.2 K. Inset: band structure of one period of the active region; the layer sequence in nm starting from the injection barrier is (from right to left) as follows: $\mathbf{2.5}\mathbf{/}3.5/\mathbf{1.2}/55.0/\mathbf{3}/21.0/\mathbf{1.0}/20.0/\mathbf{3.2}/\underline{16.4/\mathbf{3.2}/16.0}/\mathbf{3.5}/15.8/\mathbf{1.0}/3.8/$ (underlined layers are Si doped at $1.5\times {10}^{16}{\mathrm{c}\mathrm{m}}^{-3}$; figures in bold type are ${\mathrm{A}\mathrm{l}}_{0.15}{\mathrm{G}\mathrm{a}}_{0.85}\mathrm{A}\mathrm{s}$ layers). (b) Threshold current density as a function of magnetic field for the same device as in (a). (c) Conductance (black line), together with its second derivative (grey line), as a function of magnetic field at 4.2 K measured on a $320\times 400\mu {\mathrm{m}}^2\mathrm{\text{mesa}}$ at 1.5 V applied bias. (d) Landau fan plot of the active region: the dashed line is the cyclotron energy. Note the crossing at 9.3 T of the cyclotron energy with the horizontal wide dashed line representing two times the photon energy $2E_{32}$.

Figure 2

(a) Waveguide losses as a function of magnetic field for a ridge width of $420\mu \mathrm{m}$. Inset: intensity profile for the $n=2\mathrm{T}\mathrm{M}$ mode (black line) which has a calculated value of losses of $7.9{\mathrm{c}\mathrm{m}}^{-1}$ and a mode overlap of $\Gamma =0.29$. (b) Left axis (disks): modal gain as a function of applied magnetic field for a ridge width of $420\mu \mathrm{m}$. Right axis (full line): lifetime deduced from the magnetotransport of the diagonal terahertz emitter studied in Ref. 16. Inset: laser spectra recorded at six and 12 T for a 3.4 mm long, $220\mu \mathrm{m}$ wide cavity at $T=4.2\mathrm{K}$ with an FTIR spectrometer (resolution $0.125{\mathrm{c}\mathrm{m}}^{-1}$).

Figure 3

Dependence of threshold current density on temperature and magnetic field for a 3.5 mm, $320\mu \mathrm{m}$ wide device. The change in lasing regime is evident above 6 T and below 20 K. The measurements at 4.2 K are performed with the sample immersed in liquid He.