Cyclotron decay time of a two-dimensional electron gas from 0.4 to 100 K

Jeremy A. Curtis, Takahisa Tokumoto, A. T. Hatke, Judy G. Cherian, John L. Reno, Stephen A. McGill, Denis Karaiskaj, and David J. Hilton

Phys. Rev. B 93, 155437 – Published 29 April 2016

Abstract

We have studied the cyclotron decay time of a Landau-quantized two-dimensional electron gas as a function of temperature (0.4–100 K) at a fixed magnetic field ( $\pm 1.25 T$ ) using terahertz time-domain spectroscopy in a gallium arsenide quantum well with a mobility of $μ_{d c} = 3.6 \times 10^{6} {cm}^{2} V^{- 1} s^{- 1}$ and a carrier concentration of $n_{s} = 2 \times 10^{11} {cm}^{- 2}$ . We find a cyclotron decay time that is limited by superradiant decay of the cyclotron ensemble and a temperature dependence that may result from both dissipative processes as well as a decrease in $n_{s}$ below $1.5 K$ . Shubnikov–de Haas characterization determines a quantum lifetime, $τ_{q} = 1.1 ps$ , which is significantly faster than the corresponding dephasing time, $τ_{s} = 66.4 ps$ , in our cyclotron data. This is consistent with small-angle scattering as the dominant contribution in this sample, where scattering angles below $θ \leq 13^{\circ}$ do not efficiently contribute to dephasing. Above $50 K$ , the cyclotron oscillations show a strong reduction in both the oscillation amplitude and lifetime that result from polar optical phonon scattering.

Received 2 July 2015
Revised 29 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.155437

Physics Subject Headings (PhySH)

Landau levels

Quantum wells Two-dimensional electron gas

Shubnikov-de Haas effect

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jeremy A. Curtis¹, Takahisa Tokumoto¹, A. T. Hatke², Judy G. Cherian², John L. Reno³, Stephen A. McGill², Denis Karaiskaj⁴, and David J. Hilton^1,*

¹Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294-1170, USA
²National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 30201, USA
³Center for Integrated Nanotechnologies, Sandia National Laboratory, Albuquerque, New Mexico 87185, USA
⁴Department of Physics, University of South Florida, Tampa, Florida 33620, USA

^*dhilton@uab.edu

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Vol. 93, Iss. 15 — 15 April 2016

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Images

Figure 1
(a) The apparatus used in the experiments and described in this paper is shown here [25]. Both the emitter and detector are zinc telluride (ZnTe), emitting linearly polarized terahertz pulses $\hat{x}$ . The detector is aligned to measure the cross-polarized component $\hat{y}$ of the terahertz electric field that is generated by $\vec{B}$ . OAP = off-axis parabolic mirror, QWP = quarter wave plate. (b) The application of an external magnetic field results in the formation of a spectrum of discrete Landau levels separated by the cyclotron energy $h ν_{c}$ . Adjacent levels have dipole-allowed optical transitions coupled by a circular polarized component of electromagnetic field [20, 21]. This results in both circular dichroism (elliptical polarization) and circular birefringence (polarization rotation) in the 2DEG and modifies the polarization of the transmitted terahertz pulse near $ν_{c}$ . (c) A Bloch sphere representation of the two-level system model used to describe our experiments, where the south pole is the highest filled Landau level $|n〉$ and the north pole is the lowest unfilled level $|n + 1〉$ .
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Figure 2
(a) Cyclotron resonance data $E (\pm B)$ that show oscillations at $B = \pm 1.25 T$ and at $T = 0.6 K$ . (b) Subtracted cyclotron resonance data, $Δ E = E (+ B) - E (- B)$ , for temperatures from $0.4 K$ (bottom curve) to $100 K$ (top curve), showing the increase in $τ_{C R}$ at low temperatures. Data shown here at $0.6 K$ also appear in their subtracted form in (b). The results of the fitting of these data to the multilayer transmission model are described in the text and in Ref. [29] and will be shown in Fig. 3. The secondary pulse located at approximately $\sim 15$ ps results from multiple reflections within the GaAs substrate.
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Figure 3
(a) Rightward-pointing triangles (right axis): The amplitude of the time-domain oscillations $A$ is shown as a function of temperature. Leftward-pointing triangles (left axis): The magnitude of the susceptibility ${\tilde{χ}}_{0}$ is shown as a function of temperature. (b) Circles: The cyclotron lifetime $τ_{C R}$ in EA0745 is shown as a function of temperature, which increases monotonically as the temperature is lowered from 100 to $0.4 K$ . Triangles: The low-frequency $τ_{D C}$ at $4.2 K$ was determined using transport characterization techniques. Solid line: The $τ_{D C}$ is calculated using Matthiessen's rule from the individual contributions, using the equations taken from Ref. [42]. Dot-dashed line: The polar optical phonon scattering contribution to $τ_{D C}$ is given by Eq. (31) in Ref. [42]. Dashed line: The combined remote ionized impurity scattering and interface charge contribution to $τ_{D C}$ , which is given by Eqs. (26) and (28) in Ref. [42]. Long- and short-dashed line: The contribution to $τ_{D C}$ due to acoustic phonon scattering is given by Eq. (34) in Ref. [42]. Dotted line: The contribution to $τ_{D C}$ due to piezoelectric scattering is given by Eq. (37) in Ref. [42]. Squares: The temperature-dependent component of $τ_{C R}$ , the result from acoustic phonon, polar optical phonon, and impurity scattering, with a potential second contribution from a reduction in carrier concentration at the lowest temperatures studied [see $A (T)$ in (a)]. Diamonds: The quantum lifetime, $τ_{q} = 1.1 ps$ , in this sample, which we determine from the Shubnikov–de Haas amplitude decay.
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Figure 4
Left axis: Magnetoresistance $Δ R$ of the sample at (a) $0.380 K$ (b) and $1.5 K$ . Right axis: The reduced oscillation amplitude $Δ R / D_{T}$ versus filling factor $ν$ from which we determine a quantum time, $τ_{q} = 1.1 ps$ .
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Figure 5
A three-interacting-systems model of this experiment. The Landau levels, induced by the perpendicular magnetic field on the 2DEG, are coupled to the terahertz field (absorption and superradiance) and to the lattice (scattering).
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