Giant photocurrents in a Dirac fermion system at cyclotron resonance

We report on the observation of the giant photocurrents in HgTe/HgCdTe quantum well (QW) of critical thickness at which a Dirac spectrum emerges. At an exciting QW of 6.6 nm width by terahertz (THz) radiation and sweeping magnetic field we detected a resonant photocurrent. Remarkably, the position of the resonance can be tuned from negative ($-$0.4 T) to positive (up to 1.2 T) magnetic fields by means of optical doping. The photocurrent data, accompanied by measurements of radiation transmission as well as Shubnikov–de Haas and quantum Hall effects, prove that the photocurrent is caused by cyclotron resonance in a Dirac fermion system, which allows us to obtain the effective electron velocity $v\approx 7.2\times {10}^5$ m/s. We develop a microscopic theory of the effect and show that the inherent spin-dependent asymmetry of light-matter coupling in the system of Dirac fermions causes the electric current to flow.

Figure 1

(a) Cross section of the investigated structures. (b) Experimental setup used for the photocurrent and transmission measurements. (c) Magnetotransport data obtained in the van der Pauw geometry for 6.6 nm HgTe/HgCdTe QW sample without (top) and with (bottom) optical doping. The change of slope in the Hall signal indicates that initially the $p$-type sample becomes $n$-type due to optical doping.

Figure 2

Signal normalized by the radiation power $U/P$ excited by ${\sigma }^{+}$ radiation vs $B_z$. The data are shown for magnetic fields lower than the full quantization limit.[41] The inset shows the photovoltage measured along the $y$-direction $U_y$ for linearly polarized light.

Figure 3

Transmissivity of circularly polarized light measured as a function of the magnetic field modulus $|B_z|$ and normalized by the zero-field transmissivity. Full lines are fits by a superposition of Lorentz functions. The inset shows the data obtained for ${\sigma }^{+}$ and ${\sigma }^{-}$ light for the $L_w=6.6$ nm samples.

Figure 4

Left panel: Magnetic field dependence of the signal $U/P$ excited by ${\sigma }^{+}$ light in the 21 nm sample. Right panel shows the magnetotransport data.

Figure 5

Microscopic model. (a) Energy dispersion with spin-up (left, blue) and spin-down (right, red) cones shifted due to Zeeman effect to higher and lower energies, respectively. (b) Nonequilibrium carrier distribution at Fermi energy caused by the spin-dependent scattering. Full and open circles sketch the electron distribution in $\mathit{k}$ space. (c) Energy relaxation of an electron gas heated as a result of the radiation absorption. Due to the spin-dependent scattering, the relaxation rates for electrons with positive and negative $\mathit{k}$ are different. Bent arrows show schematically a predominant energy relaxation in the spin-up (left) and spin-down (right) cones. The scattering asymmetry within each cone results in the oppositely directed fluxes ${\mathit{j}}_{+}$ and ${\mathit{j}}_{-}$ shown by horizontal arrows. As due to the Zeeman effect the spin-down cone is larger populated, the flux ${\mathit{j}}_{-}$ is stronger than ${\mathit{j}}_{+}$ and a dc electric current emerges.

Figure 6

Polarization dependence of the photovoltage normalized by radiation power $U_y/P$ excited with normal incident radiation in (a) $6.6$ nm and (b) 21 nm QWs at zero magnetic field. The normalized photosignal is shown for different carrier densities and fitted after $U_y\left(\alpha \right)/P=A+B\sin \left(2\alpha \right)+C\cos \left(2\alpha \right)$.