Magnetophotogalvanic Effects Driven by Terahertz Radiation in CdHgTe Crystals with Kane Fermions

Technical Summary: Magnetophotogalvanic Effects Driven by Terahertz Radiation in CdHgTe Crystals with Kane Fermions

Problem and Context
Three-dimensional topological semimetals exhibit unique electronic structures characterized by bulk band crossings and gapless excitations. While Dirac and Weyl fermions are well-studied, massless 3D Kane fermions represent a distinct class of pseudo-relativistic quasiparticles identified in bulk Cd$_x$Hg$_{1-x}$Te near the semiconductor-to-semimetal topological phase transition (critical concentration $x_C \approx 0.17$ at 2 K). Unlike Dirac fermions, Kane fermions are not protected by symmetry but respect time-reversal symmetry and possess an energy dispersion where cones are intersected by an additional flat band. Despite theoretical predictions regarding their unique properties, such as inverted rest mass and universal relativistic behavior, their experimental characterization via opto-electronic techniques remains an active area of exploration. Specifically, the magnetophotogalvanic effect (MPGE)—the generation of a dc electric current from an ac electric field under an external magnetic field—had not been comprehensively studied in bulk CdHgTe crystals hosting these fermions.

Methodology
The study employed molecular beam epitaxy (MBE) grown CdxHg$_{1-x}$Te films with two distinct cadmium concentrations: $x = 0.15$ (Sample A, inverted band structure) and $x = 0.22$ (Sample B, non-inverted band structure). The samples were subjected to normally incident, linearly polarized terahertz (THz) radiation generated by an optically pumped pulsed molecular laser (frequencies: 0.6, 1.07, 2.02, and 3.33 THz).

Experiments were conducted in the Voigt geometry, where an in-plane magnetic field ($B$) was applied perpendicular to the radiation propagation direction. Measurements were performed across a temperature range from 4.2 K to 300 K, with magnetic fields up to 4 T. The photocurrent ($J_x$) was measured as a voltage drop across a load resistance in unbiased structures. Theoretical analysis utilized an eight-band $k \cdot p$ Kane Hamiltonian to calculate the band structure and Landau levels, alongside a microscopic theory of MPGE based on spin-dependent scattering probabilities containing terms cubic in momentum.

Key Contributions and Results

1. Observation of MPGE: The authors report the first observation of THz-induced MPGE in bulk CdHgTe crystals. The effect was detected in both samples, with the photocurrent exhibiting a non-monotonic dependence on the magnetic field and a specific polarization dependence ($J \propto \cos(2\alpha)$).

2. Resonant vs. Non-Resonant Currents:

   • Non-Resonant MPGE: A non-resonant photocurrent was observed, attributed to Drude-like intraband absorption assisted by phonon scattering. This current increases linearly at low magnetic fields, reaches a maximum, and decreases at high fields ($\propto 1/B^3$). It is measurable up to room temperature but decreases drastically as temperature rises.
   • Resonant MPGE: At liquid helium temperatures (4.2 K), multiple resonances appeared in the photocurrent upon variation of the magnetic field. These resonances were significantly larger (by orders of magnitude) than the non-resonant background.

3. Identification of Resonance Mechanisms:

   • Sample A ($x=0.15$, Inverted Band Structure): Two types of resonances were identified:
     • Cyclotron Resonance (CR): Polarization-dependent resonances ($E \perp B$) arising from transitions between electron Landau levels in the conduction band.
     • Interband Transitions (R-type): Polarization-independent resonances resulting from optical transitions between the valence band (heavy holes) and the conduction band. These are enabled by the gapless energy spectrum of Kane fermions in this composition.
   • Sample B ($x=0.22$, Non-Inverted Band Structure):
     • Cyclotron Resonance (CR): Similar to Sample A, observed for $E \perp B$.
     • Impurity Ionization (R-type): A single polarization-independent resonance per frequency, attributed to photoionization from an impurity level to the first Landau level, as the interband gap (~100 meV) exceeds the photon energies used.

4. Theoretical Validation: The positions of all observed resonances (CR and R-type) were perfectly described by the band structure calculated using the Kane model. The theory demonstrates that the MPGE current arises from asymmetric spin-dependent scattering (cubic in momentum terms), generating a pure spin current which is converted into an electric current via the Zeeman effect.

Significance and Claims
The paper claims that the developed theory and experimental results confirm that MPGE in these materials is driven by spin current excitation in the bulk, converted to charge current by the Zeeman effect. A primary finding is the exceptionally large magnitude of the resonant and non-resonant MPGE currents at low temperatures, reaching several milliamperes per Watt. The authors state that this magnitude exceeds THz-radiation-induced photogalvanic currents in other known systems by several orders of magnitude.

Furthermore, the study provides a comprehensive mapping of the optical transitions in Kane fermion systems, distinguishing between inter-Landau level transitions, interband transitions, and impurity ionization based on band structure engineering (Cd content). The work validates the utility of the eight-band $k \cdot p$ Kane Hamiltonian in describing the complex Landau level spectra and optical selection rules in these topological semimetals. The results highlight the potential of Kane fermions for studying relativistic quantum phenomena and suggest that the specific origin of these electrons (suppressing non-radiative Auger recombination) could be relevant for future THz applications, though the paper focuses primarily on the fundamental characterization of the MPGE mechanism.