Bleaching of the Terahertz Magneto-Photogalvanic Effect in CdHgTe Crystals with Kane Fermions

Technical Summary: Bleaching of the Terahertz Magneto-Photogalvanic Effect in CdHgTe Crystals with Kane Fermions

Problem Statement
Bulk cadmium mercury telluride (CdHgTe) crystals host Kane fermions, which exhibit relativistic properties and allow for the study of both massive and massless fermions depending on band alignment (inverted vs. non-inverted). While the magneto-photogalvanic effect (MPGE) induced by terahertz (THz) radiation in these materials has been previously characterized at low intensities, the behavior of the MPGE under high-intensity irradiation remains unexplored. Specifically, the nonlinear intensity dependence of the photocurrent generated by various absorption mechanisms—cyclotron resonance (CR), interband transitions between Landau levels, impurity ionization, and Drude-like intraband absorption—requires a comprehensive theoretical and experimental investigation to understand the underlying saturation and bleaching processes.

Methodology
The study utilized two CdxHg1−xTe films grown by molecular-beam epitaxy: Sample A ($x=0.15$) with an inverted band structure and Sample B ($x=0.22$) with a non-inverted (normal) band structure. Experiments were conducted in a Voigt geometry using a high-power pulsed molecular laser ($f = 1.07$ THz, $\hbar\omega = 4.4$ meV) capable of generating intensities ranging from $10^{-3}$ to $4 \times 10^4$ W/cm$^2$.

The experimental setup allowed for the controlled variation of radiation intensity using crossed wire-grid polarizers and calibrated Teflon attenuators, as well as the variation of the polarization angle $\alpha$ relative to the in-plane magnetic field ($B_y$). Measurements were performed at liquid helium temperatures (4.2 K) and higher temperatures (110 K, 300 K). The photocurrent ($J_x$) was measured as the voltage drop across a 50 $\Omega$ load resistor in unbiased structures. The study focused on two configurations: Cyclotron Resonance Active (CRA, $E \perp B$) and Cyclotron Resonance Passive (CRP, $E \parallel B$).

Key Contributions and Theoretical Framework
The authors developed a microscopic theoretical framework to describe the nonlinear MPGE. The core finding is that the complex intensity dependence of the photocurrent arises from the bleaching of radiation absorption (saturation) across different channels. The total photocurrent is modeled as a superposition of contributions from distinct absorption mechanisms, each characterized by a specific low-intensity slope ($A_i$) and a saturation intensity ($I_s^i$):

$$J_{MPGE} = \sum_i \frac{A_i I}{1 + I/I_s^i}$$

The paper derives specific expressions for the saturation intensity ($I_s$) for four distinct mechanisms:

1. Cyclotron Resonance (CR): Saturation occurs due to the slow relaxation of photoexcited carriers back to the initial Landau level state. The theory predicts a significant difference in saturation intensity between active and passive polarizations.
2. Interband Transitions (Landau Levels): Saturation is governed by the relaxation time of carriers between valence and conduction band Landau levels.
3. Impurity Ionization: Saturation results from the depletion of impurity states, governed by the capture time to impurity states.
4. Drude-like (Intraband) Absorption: Saturation is caused by electron-gas heating (bolometric effect), where the absorption coefficient decreases as the electron temperature rises.

Experimental Results

• Inverted Band Structure ($x=0.15$): At low intensities, the photocurrent is dominated by resonant interband transitions between Landau levels and Drude absorption. As intensity increases, the interband component saturates first (at $I_s \approx 3.8$ W/cm$^2$), followed by the Drude component at much higher intensities. At the highest intensities ($>10^4$ W/cm$^2$), a transition from sublinear to superlinear behavior is observed, attributed to THz impact ionization of impurity states.
• Non-Inverted Band Structure ($x=0.22$): The photocurrent is a superposition of CR, impurity ionization, and Drude absorption. The data reveals a hierarchy of saturation intensities: $I_s^{CR} \ll I_s^{imp} \ll I_s^{Dr}$. Consequently, the CR resonance vanishes at very low intensities, followed by impurity ionization, leaving only the non-resonant Drude background at high intensities.
• Temperature Dependence: At elevated temperatures (110 K), thermal ionization of impurities eliminates resonant features, leaving a smooth, non-monotonic Drude-like response. The intensity dependence becomes linear across the entire range due to increased energy relaxation rates (phonon scattering) and reduced electron temperature deviation.

Significance and Claims
The paper claims to provide the first comprehensive study of the nonlinear intensity dependence of the MPGE in CdHgTe crystals over a dynamic range of seven orders of magnitude. The primary significance lies in:

1. Mechanism Identification: Demonstrating that absorption bleaching is the universal cause of MPGE nonlinearity, but that different mechanisms (CR, interband, impurity, Drude) possess vastly different saturation intensities.
2. Independent Analysis: The large disparity in saturation intensities allows researchers to analyze these mechanisms independently by selecting specific intensity regimes, effectively decoupling the contributions.
3. Parameter Extraction: By fitting the theoretical model to the experimental data, the authors determined energy relaxation times for Kane fermions. Specifically, they estimated the interband relaxation time $\tau_{ib} \approx 1.3$ ps and the cyclotron resonance relaxation time $\tau_{CR} \approx 16$ ns.
4. New Phenomena: The observation of superlinear photocurrent growth at extreme intensities suggests the onset of THz impact ionization, a phenomenon previously unreported in CdHgTe films.

The authors conclude that these findings, supported by a theory that accurately fits data across all intensity regimes, offer valuable insights for the development of CdHgTe-based electronic devices operating in the THz spectral range.