Variable-wavelength frequency-domain terahertz ellipsometry

Hofmann, Tino; Herzinger, C. M.; Boosalis, A.; Tiwald, Thomas E.; Woollam, John A.; Schubert, M.

doi:10.1063/1.3297902

Cited by 80 publications

(49 citation statements)

References 38 publications

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“…The last step towards a full characterization of the SIT is to develop an understanding of the behavior of the AC conductivity. This is a powerful probe of fluctuations on both long and short length and time scales, and it is of great interest especially as recent technological developments begin to open up more windows of the electromagnetic spectrum for measurement [18][19][20][21].One of the most important questions concerns the AC conductivity in the "collisionless DC" limit [22,23] [52], σ * = lim ω→0 lim T →0 σ(ω, T ). This has been the subject of a large body of work, including analytical arguments involving charge-vortex duality arguments, quantum Monte Carlo calculations in various representations, and experiments [1,4,16,23,[25][26][27][28][29][30][31][32].…”

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confidence: 99%

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confidence: 99%

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Divergence of dynamical conductivity at certain percolative superconductor-insulator transitions

Loh¹,

Dhakal²,

Neis³

et al. 2014

J. Phys.: Condens. Matter

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Random inductor-capacitor (LC) networks can exhibit percolative superconductor-insulator transitions (SITs). We use a simple and efficient algorithm to compute the dynamical conductivity σ(ω, p) of one type of LC network on large (4000 × 4000) square lattices, where δ = p − pc is the tuning parameter for the SIT. We confirm that the conductivity obeys a scaling form, so that the characteristic frequency scales as Ω ∝ |δ| νz with νz ≈ 1.91, the superfluid stiffness scales as Υ ∝ |δ| t with t ≈ 1.3, and the electric susceptibility scales as χE ∝ |δ| −s with s = 2νz − t ≈ 2.52. In the insulating state, the low-frequency dissipative conductivity is exponentially small, whereas in the superconductor, it is linear in frequency. The sign of Im σ(ω) at small ω changes across the SIT. Most importantly, we find that right at the SIT Re σ(ω) ∝ ω t/νz−1 ∝ ω −0.32 , so that the conductivity diverges in the DC limit, in contrast with most other classical and quantum models of SITs. [4,5]. As a quantum phase transition occurring at zero temperature, this superconductor-insulator transition (SIT) has attracted much interest. Early work focused on the most easily measurable quantity, the DC conductivity.[1-3, 6-10] Recently, due to the availability of local scanning probes, attention has turned to the tunneling behavior [11][12][13][14][15]. In the case of the disorder-tuned SIT [15], it has become clear that the SIT is ultimately due to a bosonic mechanism [16] rather than a fermionic one [17]. The last step towards a full characterization of the SIT is to develop an understanding of the behavior of the AC conductivity. This is a powerful probe of fluctuations on both long and short length and time scales, and it is of great interest especially as recent technological developments begin to open up more windows of the electromagnetic spectrum for measurement [18][19][20][21].One of the most important questions concerns the AC conductivity in the "collisionless DC" limit [22,23] [52], σ * = lim ω→0 lim T →0 σ(ω, T ). This has been the subject of a large body of work, including analytical arguments involving charge-vortex duality arguments, quantum Monte Carlo calculations in various representations, and experiments [1,4,16,23,[25][26][27][28][29][30][31][32]. It is often claimed that at the SIT σ * is finite and takes a universal value of the order of σ Q = 4e 2 /h, but there are large discrepancies between the "universal" values from various studies, and it is not clear whether there really is a universal value.

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confidence: 99%

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confidence: 99%

Divergence of dynamical conductivity at certain percolative superconductor-insulator transitions

Loh¹,

Dhakal²,

Neis³

et al. 2014

J. Phys.: Condens. Matter

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“…The magnetic field strength was varied between B = −1.5 to +1.5 T with a field direction oriented perpendicular to the sample surface. 7,17 The MIR-SE measurements have been carried out using a commercial Fourier transformbased MIR ellipsometer ͑J.A. Woollam Co. Inc., Lincoln, Nebraska͒ in the spectral range from 10 to 45 THz ͑333 to 1500 cm −1 ͒ with a resolution of 60 GHz ͑2 cm −1 ͒.…”

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confidence: 99%

“…16 A custombuilt frequency-domain terahertz ellipsometer was used for the THz-OHE measurements in the spectral range from 0.65 to 1.00 THz with a resolution of 1 GHz. 17 The THz-OHE measurements were carried out at an angle of incidence ⌽ a = 74.5°. The magnetic field strength was varied between B = −1.5 to +1.5 T with a field direction oriented perpendicular to the sample surface.…”

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Terahertz optical-Hall effect characterization of two-dimensional electron gas properties in AlGaN/GaN high electron mobility transistor structures

Schöche

Shi

Boosalis

et al. 2011

Applied Physics Letters

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“…Subsequent to the growth of a 2 µm thick [11]. The THz-OHE data presented here were obtained using a custom-built THz ellipsometer [2,12]. THz-OHE data were measured in the spectral range from 830 to 930 GHz with a resolution of 2 GHz at an angle of incidence Φ a = 45…”

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Cavity-enhanced optical Hall effect in two-dimensional free charge carrier gases detected at terahertz frequencies

et al. 2015

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The effect of a tunable, externally coupled Fabry-Pérot cavity to resonantly enhance the optical Hall effect signatures at terahertz frequencies produced by a traditional Drude-like two-dimensional electron gas is shown and discussed in this communication. As a result, the detection of optical Hall effect signatures at conveniently obtainable magnetic fields, for example by neodymium permanent magnets, is demonstrated. An AlInN/GaN-based high electron mobility transistor structure grown on a sapphire substrate is used for the experiment. The optical Hall effect signatures and their dispersions, which are governed by the frequency and the reflectance minima and maxima of the externally coupled Fabry-Pérot cavity, are presented and discussed. Tuning the externally coupled Fabry-Pérot cavity strongly modifies the optical Hall effect signatures, which provides a new degree of freedom for optical Hall effect experiments in addition to frequency, angle of incidence and magnetic field direction and strength.The optical Hall effect (OHE) in semiconductor layer structures is the occurrence of magneto-optic birefringence detected in response to incident electromagnetic radiation, caused by movement of free charge carriers under the magnetic field-induced influence of the Lorentz force [1]. In general, this birefringence leads to polarization mode coupling which is conveniently detected by generalized ellipsometry at oblique angle of incidence and at terahertz (THz) frequencies, for example. THz-OHE has recently been demonstrated as non-contact and therefore valuable tool for the investigation of free charge carrier properties in semiconductor heterostructures [2][3][4][5][6][7][8][9]. Previous instrumental approaches, discussed more detailed in Refs. 2 and 9, rely on high magnetic fields provided either by conventional, water-cooled or superconducting, liquid He-cooled electromagnets resulting in comparably large and costly experimental setups. In general, OHE configurations capable of detecting signals at low and conveniently obtainable magnetic fields are desirable. The use of small magnetic fields for THz magnetooptic measurements was demonstrated recently by Ino et al. for bulk-like InAs [10]. Due to low effective mass and high charge carrier concentration, the low field still yielded large enough signals for detection. The signalto-noise separations of the OHE signatures depend on many factors, the most important are low effective mass, high mobility and high carrier density, but also crucial is the thickness of the physical layer that contains the charge carriers. The OHE signatures scale, in first approximation, linearly with the magnetic field amplitude. Hence, the first approach to detect OHE signatures in samples with very thin layers, or low-mobile, heavy-mass and low-density charge carriers where the OHE signatures are weak is to increase the magnetic field amplitude.In this communication, we demonstrate and exploit the enhancement of the OHE signal obtained from samples IG. 1. Schematic drawing of the beam pa...

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Variable-wavelength frequency-domain terahertz ellipsometry

Cited by 80 publications

References 38 publications

Divergence of dynamical conductivity at certain percolative superconductor-insulator transitions

Divergence of dynamical conductivity at certain percolative superconductor-insulator transitions

Terahertz optical-Hall effect characterization of two-dimensional electron gas properties in AlGaN/GaN high electron mobility transistor structures

Cavity-enhanced optical Hall effect in two-dimensional free charge carrier gases detected at terahertz frequencies

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