Time-domain terahertz spectroscopy in high magnetic fields

doi:10.1007/s12200-020-1101-4

Front. Optoelectron.

2021, Vol. 14

Issue (1) : 110-129 https://doi.org/10.1007/s12200-020-1101-4

REVIEW ARTICLE

Time-domain terahertz spectroscopy in high magnetic fields

Andrey BAYDIN¹(

), Takuma MAKIHARA², Nicolas Marquez PERACA², Junichiro KONO^1,^2,³(

)

¹. Department of Electrical and Computer Engineering, Rice University, Houston, TX 70005, USA
². Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
³. Department of Materials Science and NanoEngineering, Rice University, Houston, Texas 77005, USA

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Abstract

There are a variety of elementary and collective terahertz-frequency excitations in condensed matter whose magnetic field dependence contains significant insight into the states and dynamics of the electrons involved. Often, determining the frequency, temperature, and magnetic field dependence of the optical conductivity tensor, especially in high magnetic fields, can clarify the microscopic physics behind complex many-body behaviors of solids. While there are advanced terahertz spectroscopy techniques as well as high magnetic field generation techniques available, a combination of the two has only been realized relatively recently. Here, we review the current state of terahertz time-domain spectroscopy (THz-TDS) experiments in high magnetic fields. We start with an overview of time-domain terahertz detection schemes with a special focus on how they have been incorporated into optically accessible high-field magnets. Advantages and disadvantages of different types of magnets in performing THz-TDS experiments are also discussed. Finally, we highlight some of the new fascinating physical phenomena that have been revealed by THz-TDS in high magnetic fields.

Keywords high magnetic field terahertz time-domain spectroscopy (THz-TDS)

Corresponding Author(s): Andrey BAYDIN,Junichiro KONO

Just Accepted Date: 20 November 2020 Online First Date: 16 December 2020 Issue Date: 19 April 2021

Cite this article:

Andrey BAYDIN,Takuma MAKIHARA,Nicolas Marquez PERACA, et al. Time-domain terahertz spectroscopy in high magnetic fields[J]. Front. Optoelectron., 2021, 14(1): 110-129.

URL:

https://academic.hep.com.cn/foe/EN/10.1007/s12200-020-1101-4
https://academic.hep.com.cn/foe/EN/Y2021/V14/I1/110

Fig.1 Free-space THz time-domain spectroscopy (THz-TDS) system combined with a superconducting magnet. The generation and detection of THz radiation is achieved via optical rectification and the electro-optic effect, respectively, using ZnTe crystals. A pellicle beamsplitter (PBS) is used to combine the THz and near-infrared probe beams. A quarter-wave plate (QWP) and a Wollaston prism (WP) are commonly used to detect the polarization rotation of the probe beam

Fig.2 Free-space THz time-domain spectroscopy system combined with the Split-Florida Helix Magnet [⁶⁸]. The broadband THz pulses are generated by mixing the fundamental and its second-harmonic laser field (generated from a frequency-doubling BBO crystal) in a nitrogen-purged atmosphere. Laser pulses are focused and collimated using off-axis parabolic (OAP) mirrors. The THz wavevector is perpendicular to the applied magnetic field (Voigt geometry). For detection, THz pulses are focused onto a THz-air breakdown coherent detector (THz-ABCD). A portion of the fundamental beam is used to gate the THz-ABCD to recover the full electric field waveform

Fig.3 Free-space single-shot THz time-domain spectroscopy system combined with a pulsed magnet [⁴¹,⁴²]. THz pulses strong enough for single-shot detection are generated using LiNbO₃. Detection is performed in a single-shot manner using a reflective echelon, which stretches the probe pulse in the time domain. The inset at the top shows that for a 1-kHz repetition-rate laser, three measurements can be done on the rising edge of the magnetic field pulse. A pellicle beamsplitter (PBS) is used to combine the THz and near-infrared probe beams. A quarter-wave plate (QWP) and a Wollaston prism (WP) are commonly used to detect the polarization rotation of the probe beam

	superconducting	resistive	pulsed
magnetic field	$< ~$ 10 T	$< ~$ 25 T	$< ~$ 30 T
THz sampling mechanism	delay stage [⁴⁷–⁵⁸]	delay stage [⁶⁸]	ECOPS [³³,⁷⁵], ASOPS [²⁹], reflective echelons [⁴¹,⁴²], rotating delay line [³⁴]
additional notes	Superconducting magnets are easiest to implement and benefit from having static fields, albeit the weakest fields.	Resistive magnets provide the strongest static fields but are only available at national laboratories due to their demand for resources.	Pulsed magnets provide the strongest magnetic fields but require sophisticated protocols for THz sampling.

Tab.1 Summary of magnets for high-field THz time-domain magnetospectroscopy

Fig.4 Superradiant decay of cyclotron resonance in ultrahigh-mobility two-dimensional electron gases [⁶³]. (a) Magnetic field dependence of CR oscillations in the time domain, showing peaks (blue) and valleys (red). (b) Frequency-domain version of (a). Black dashed line: a linear fit with a cyclotron mass of 0.069m₀. (c) Magnetic field dependence of the CR decay time, t_CR at 3 K. (d) Temperature dependence of t_CR at 2.5 T and the DC scattering time, t_DC, determined from the DC mobility, µ = et_DC/m^*. (e) CR oscillations in the time domain for samples with different densities by controlling the illumination time. (f) CR decay rate as a function of electron density. Blue solid circle: sample 2 (low density). Red solid circles: sample 1 (high density). The blue dashed line represents a theoretical relation expected from the phenomenon of superradiance [¹⁰²] without any adjustable parameter (with n_GaAs = 3.6 and m^* = 0.069m₀)

Fig.5 Magneto-optical Kerr rotation in monolayer graphene. (a) Schematic of the experimental configuration depicting the transmission of a THz pulse through the sample. (b) Time-domain waveform of the THz pulse transmitted through the sample. (c) Magnetic field dependence of the Kerr rotation at 1 THz for the sample with a Fermi energy of 70 meV. The inset shows Kerr rotation spectra at the indicated magnetic fields. Adapted from Ref. [¹¹⁶]

Fig.6 Quantized Faraday rotation of topological surface states in Bi₂Se₃. (a) Schematic diagram of the Faraday rotation experimental setup. P1, P2, and P3 are polarizers. The polarization acquires an ellipticity simultaneously, as shown in (b). (c) Real part of the Faraday rotation of 10-QL Bi₂Se₃ films with MoO₃ at 4.5 K at various magnetic fields [color-coded as in (d)]. The dash-dotted line is the theoretical expectation. (d) Imaginary part of the Faraday rotation. A representative cyclotron frequency is marked by a red arrow for data at 2.5 T. (e) Quantized Faraday rotation for different samples. Dashed black lines are theoretical expectation values assuming certain values for the filling factor of the surface states. (f) DC Hall resistance of a representative 8-QL sample. Adapted from Ref. [⁵⁸]

Fig.7 Ultrastrong coupling between THz split-ring resonators and the CR of a high-mobility 2DEG. (a) Transmission as a function of B at 10 K. (b) A vertical cut from panel (a) in the anticrossing region at B = 1.2 T. Both the upper-polariton and lower-polariton modes are observed together with the free-space CR (CYC) arising from the uncovered regions of the 2DEG. (c) Polariton branches plotted as a function of magnetic field. Solid lines are theoretical calculations. Inset: schematic of the 500 GHz resonator deposited on the sample surface. Adapted from Ref. [⁵⁵]

Fig.8 Vacuum Bloch–Siegert shift in Landau polaritons with ultrahigh cooperativity [⁶⁵]. Transmission spectra in the vicinity of the anticrossing region between CR and the first cavity mode (red dashed line) for simulations using the full Hamiltonian (solid lines) is shown. The counter-rotating and A² terms have to be included in the full Hamiltonian. Experimental data points are shown as open circles

Fig.9 THz-TDS of magnon-magnon ultrastrong coupling in YFeO₃ evidencing dominant vacuum Bloch−Siegert shifts [⁴²]. (a) Schematic of THz magnetospectroscopy studies of YFeO₃ in a tilted magnetic field. H_DC was applied in the b-c plane at an angle of q with respect to the c-axis, with k_THz//H_DC and H_THz polarized in the b-c plane. (b) Transmitted THz waveform for q = 20° at µ₀|H_DC| = 12.60 T displaying beating in the time domain and two peaks in the frequency domain. (c) Magnon power spectra for q = 20° and q = 40° at different H_DC, displaying larger frequency splitting for larger q. (d) Experimentally measured magnon frequencies for q = 0°, 40°, 90° versus µ₀|H_DC| (black dots) with calculated resonance magnon frequencies (solid red lines) and decoupled qFM and qAFM magnon frequencies (black dashed-dotted lines). The upper mode frequency becomes lower than the qAFM frequency at q = 90°, indicating a dominant vacuum Bloch−Siegert shift compared to the vacuum Rabi splitting-induced shift

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