We consider a single-electron transistor in the form of a ferromagnetic dot in contact with normal-metal and pinned ferromagnetic leads. Microwave-driven precession by the dot induces a pumped electric current. In open circuits, this pumping produces a measurable reverse bias voltage, which can be enhanced and made highly nonlinear by Coulomb blockade in the dot. The dependence of this bias on the power and spectrum of microwave irradiation may be utilized to develop nanoscale microwave detectors analogous to single-electron transistor-based electrostatic sensors and nanoelectromechanical devices.
We consider the microwave dynamics and transport properties of a voltage-biased single-Cooper-pair transistor. The dynamics is shown to be strongly affected by interference between multiple microwave-induced inter-level transitions. As a result the magnitude and direction of the dc Josephson current are extremely sensitive to small variations of the bias voltage and to changes in the frequency of the microwave field.
Magnetic skyrmion is a topologically protected domain-wall structure at nanoscale, which could serve as a basic building block for advanced spintronic devices. Here, we propose a microwave field-driven skyrmionic device with the transistor-like function, where the motion of a skyrmion in a voltage-gated ferromagnetic nanotrack is studied by micromagnetic simulations. It is demonstrated that the microwave field can drive the motion of a skyrmion by exciting propagating spin waves, and the skyrmion motion can be governed by a gate voltage. We also investigate the microwave current-assisted creat…
We measure the small signal, 1 GHz source-drain dynamical conductance of a back-gated single-walled carbon nanotube field effect transistor at both low and high dc bias voltages. At all bias voltages, the intrinsic device dynamical conductance at 1 GHz is identical to the low frequency dynamical conductance, consistent with the prediction of a cutoff frequency much higher than 1 GHz. This work represents a significant step towards a full characterization of a nanotube transistor for RF and microwave amplifiers.
Resonant microwave-assisted and DC transport are investigated in degenerately doped silicon single electron transistors. A model based on hopping via localized impurity states is developed and first used to explain both the DC temperature dependence and the AC response. In particular, the non-monotonic power dependence of the resonant current under irradiation is proved to be consistent with spatial Rabi oscillations between these localized states.
We have developed metal-oxide graphene field-effect transistors (MOGFETs) on sapphire substrates working at microwave frequencies. For monolayers, we obtain a transit frequency up to ~ 80 GHz for a gate length of 200 nm, and a power gain maximum frequency of about ~ 3 GHz for this specific sample. Given the strongly reduced charge noise for nanostructures on sapphire, the high stability and high performance of this material at low temperature, our MOGFETs on sapphire are well suited for a cryogenic broadband low-noise amplifier.
Few-layer phosphorene MOSFETs with 0.3-um-long gate and 15-nm-thick Al2O3 gate insulator was found to exhibit a forward-current cutoff frequency of 2 GHz and a maximum oscillation frequency of 8 GHz after de-embedding for the parasitic capacitance associated mainly with the relatively large probe pads. The gate lag and drain lag of the transistor was found to be on the order of 1 us or less, which is consistent with the lack of hysteresis, carrier freeze-out or persistent photoconductivity in DC characteristics. These results confirm that the phosphorene MOSFET can be a viable microwave transi…
Cotunneling is an important error process in the application of single electron tunneling devices for metrological and electronic applications. Here we present an experimental investigation of the theory for adiabatic enhancement of cotunneling by coherent microwaves. The dependence is investigated as function of temperature, gate voltage, frequency, and applied microwave power. At low temperatures and applied power levels, the results are consistent with theory, using only the unknown damping in the microwave line as a free parameter. However, the results indicate that the effects of temperat…
We show that a single-Cooper-pair transistor (SCPT) electrometer emits narrow-band microwave radiation when biased in its sub-gap region. Photo activation of quasiparticle tunneling in a nearby SCPT is used to spectroscopically detect this radiation, in a configuration that closely mimics a qubit-electrometer integrated circuit. We identify emission lines due to Josephson radiation and radiative transport processes in the electrometer, and argue that a dissipative superconducting electrometer can severely disrupt the system it attempts to measure.
The ability to apply GHz frequencies to control the quantum state of a single $P$ atom is an essential requirement for the fast gate pulsing needed for qubit control in donor based silicon quantum computation. Here we demonstrate this with nanosecond accuracy in an all epitaxial single atom transistor by applying excitation signals at frequencies up to $\approx$ 13 GHz to heavily phosphorous doped silicon leads. These measurements allow the differentiation between the excited states of the single atom and the density of states in the one dimensional leads. Our pulse spectroscopy experiments co…
In quantum computation, information is processed by gates that must coherently couple separate qubits. In many systems the qubits are naturally coupled, but such an always-on interaction limits the algorithms that may be implemented. Coupling interactions may also be directed in devices and circuits that are provided with additional control wiring. This can be achieved by adjusting the gate voltage in a semiconductor device or an additional flux in a superconducting device. Such control signals must be applied adiabatically (limiting the speed) and the additional wiring provides pathways for n…
We report on DC and microwave electrical transport measurements in silicon-on-insulator CMOS nano-transistors at low and room temperature. At low source-drain voltage, the DC current and RF response show signs of conductance quantization. We attribute this to Coulomb blockade resulting from barriers formed at the spacer-gate interfaces. We show that at high bias transport occurs thermionically over the highest barrier: Transconductance traces obtained from microwave scattering-parameter measurements at liquid helium and room temperature is accurately fitted by a thermionic model. From the fits…
We show that the arguments in the posting cond-mat/0607432 by Flatte and Hall are flawed and untenable. Their spin based transistor cannot work as claimed because of fundamental scientific barriers, which cannot be overcome now, or ever. Their device is not likely to work as a transistor at room temperature, let alone outperform the traditional MOSFET, as claimed.
We have studied the microwave response of a single Cooper-pair transistor (CPT) coupled to a lumped-element microwave resonator. The resonance frequency of this circuit, $f_{r}$, was measured as a function of the charge $n_{g}$ induced on the CPT island by the gate electrode, and the phase difference across the CPT, $ϕ_{B}$, which was controlled by the magnetic flux in the superconducting loop containing the CPT. The observed $f_{r}(n_{g},ϕ_{B})$ dependences reflect the variations of the CPT Josephson inductance with $n_{g}$ and $ϕ_{B}$ as well as the CPT excitation when the microwaves induce …
We report on the on-chip detection of microwaves in the frequency range around 100GHz. For the purpose of detection, we employ a discrete transport channel triggered in a superconducting single-electron transistor by photon-assisted tunneling of quasiparticles. The technique is successfully applied to observe the spectrum of the dressed states of a model cQED system consisting of a superconducting coplanar resonator coupled to a quantum Josephson oscillator. The dressed states appear as typical resonance anticrossing exhibiting, in our case, an expectedly wide frequency splitting corresponding…
By operating the radio frequency single electron transistor (rf-SET) as a mixer we present measurements in which the RC roll-off of the tunnel junctions is observed at high frequencies. Our technique makes use of the non-linear rf-SET transconductance to mix high frequency gate signals and produce difference-frequency components that fall within the bandwidth of the rf-SET. At gate frequencies >15GHz the induced charge on the rf-SET island is altered on time-scales faster than the inverse tunnel rate, preventing mixer operation. We suggest the possibility of utilizing this technique to sense h…
A recent e-print (cond-mat/0604532) presented a proposed Comment to Applied Physics Letters on our publication Appl. Phys. Lett. 88, 162503 (2006), cond-mat/0603260. Here is our Response. As the proposed Comment has now been rejected by Applied Physics Letters, neither the Comment nor the Response will be published in Applied Physics Letters in this form.
The Cooper-pair transistor (CPT), a small superconducting island enclosed between two Josephson weak links, is the atomic building block of various superconducting quantum circuits. Utilizing gate-tunable semiconductor channels as weak links, the energy scale associated with the Josephson tunneling can be changed with respect to the charging energy of the island, tuning the extent of its charge fluctuations. Here, we directly demonstrate this control by mapping the energy level structure of a CPT made of an indium arsenide nanowire (NW) with a superconducting aluminum shell. We extract the dev…
The reduced switching current of an excited energy-band in a Bloch transistor can be used to detect microwave-induced interband transitions. Spectroscopic measurements of the band-gap are performed by mapping the frequency dependence of the excitation threshold where the microwave photon energy and band-gap are equal. This excitation threshold also provides a probe of charge-state mixing on the island of the transistor. Any asymmetry in the junctions of the transistor makes the coherent mixing of charge-states appear as a finite gap-splitting at the electrostatic degeneracy point between state…
We investigate the dynamical control of the heat flux exchanged in near-field regime between a membrane made with a phase-change material and a substrate when the temperature of the membrane is tuned around its critical value. We show that in interaction with an external source of thermal radiation, this system is multistable and behaves as a thermal transistor, being able to dynamically modulate and even amplify super-Planckian heat fluxes. This behavior could be used to dynamically control heat fluxes exchanged at the nanoscale in systems out of thermal equilibrium and to process thermal inf…
Here, we report the photoconducting response of field-effect transistors based on three atomic layers of chemical vapor transport grown WSe$_2$ crystals mechanically exfoliated onto SiO$_2$. We find that tri-layered WSe$_2$ field-effect transistors, built with the simplest possible architecture, can display high hole mobilities ranging from 350 cm$^2$/Vs at room temperature (saturating at a value of ~500 cm$^2$/Vs below 50 K) displaying a strong photocurrent response which leads to exceptionally high photo responsivities up to 7 A/W under white light illumination of the entire channel for powe…
The current through ferromagnetic single-electron transistors (SET's) is considered. Using path integrals the linear response conductance is formulated as a function of the tunnel conductance vs. quantum conductance and the temperature vs. Coulomb charging energy. The magneto-resistance of ferromagnet-normal metal-ferromagnet (F-N-F) SET's is almost independent of the Coulomb charging energy and is only reduced when the transport dwell time is longer than the spin-flip relaxation time. In all-ferromagnetic (F-F-F) SET's with negligible spin-flip relaxation time the magneto-resistance is calcul…
We propose a microwave frequency single photon transistor which can operate under continuous wave probing, and represents an efficient single microwave photon detector. It can be realized using an impedance matched system of a three level artificial ladder-type atom coupled to two microwave cavities connected to input/output waveguides. Using a classical drive on the upper transition, we find parameter space where a single photon control pulse incident on one of cavities can be fully absorbed into hybridized excited states. This subsequently leads to series of quantum jumps in the upper manifo…
The quantum efficiency, which characterizes the quality of information gain against information loss, is an important figure of merit for any realistic quantum detectors in the gradual process of collapsing the state being measured. In this work we consider the problem of solid-state charge qubit measurements with a single-electron-transistor (SET). We analyze two models: one corresponds to a strong response SET, and the other is a tunable one in response strength. We find that the response strength would essentially bound the quantum efficiency, making the detector non-quantum-limited. Quantu…
We report a new method to study two level fluctuators (TLFs) by measuring the offset charge induced after applying a sudden step voltage to the gate electrode of a single electron transistor. The offset charge is measured for more than 20 hours for samples made on three different substrates. We find that the offset charge drift follows a logarithmic increase over four orders of magnitude in time and that the logarithmic slope increases linearly with the step voltage. The charge drift is independent of temperature, ruling out thermally activated TLFs and demonstrating that the charge fluctuatio…
We present a scheme for photonic transistors based on photons and phonons in a cavity electromechanical system, which is consisted of a superconducting microwave cavity coupled to a nanomechanical resonator. Control of the propagation of photons is achieved through the interaction of microwave field (photons) and nanomechanical vibrations (phonons). By calculating the transmission spectrum of the signal field, we show that the signal field can be efficiently attenuated or amplified, depending on the power of a second `gating'(pump) field. This scheme may be a promising candidate for single-pho…
High electron mobility transistors are widely used as microwave amplifiers owing to their low microwave noise figure. Electronic noise in these devices is typically modeled by noise sources at the gate and drain. While consensus exists regarding the origin of the gate noise, that of drain noise is a topic of debate. Here, we report a theory of drain noise as a type of partition noise arising from real-space transfer of hot electrons from the channel to the barrier. The theory accounts for the magnitude and dependencies of the drain temperature and suggests strategies to realize devices with lo…
We derive self-consistent expressions of current and noise for single-electron transistors driven by time-dependent perturbations. We take into account effects of the electrical environment, higher-order co-tunneling, and time-dependent perturbations under the two-charged state approximation using the Schwinger-Kedysh approach combined with the generating functional technique. For a given generating functional, we derive exact expressions for tunneling currents and noises and present the forms in terms of transport coefficients. It is also shown that in the adiabatic limit our results encompas…
A single-electron transistor (SET) in a magnetic field irradiated with microwaves is studied theoretically in non-equilibrium Kondo regime. The two fold effect of frequency--Ω--microwaves is considered as follows: the oscillations in the voltage with frequency Ωand in the coupling parameters with frequency Ω/p (p\in\mathbb{N}). We describe the system by the Kondo model at a specific point in the Toulouse limit. A non-perturbative technique is proposed, namely, the non-equilibrium Green's functions and physical observables are averaged over a period of 2πp/Ω. When the microwave irradiation is c…
Single donors in semiconductor nanostructures represent a key element to develop spin related quantum functionalities in atomic scale devices. Quantum transport through a single Arsenic donor in the channel of a Silicon nano-field effect transistor under microwave irradiation is investigated. The device is characterized at mK temperatures in the regime of Coulomb-blockade. Photon assisted tunneling and microwave induced electron pumping regimes are revealed respectively at low and high microwave power. At sufficiently high power, the microwave irradiation induces tunneling through the first ex…
We have analyzed the response and noise-limited sensitivity of the radio-frequency single-electron transistor (RF-SET), extending the previously developed theory to the case of arbitrary large quality factor Q of the RF-SET tank circuit. It is shown that while the RF-SET response reaches the maximum at Q roughly corresponding to the impedance matching condition, the RF-SET sensitivity monotonically worsens with the increase of Q. Also, we propose a novel operation mode of the RF-SET, in which an overtone of the incident rf wave is in resonance with the tank circuit.
The InGaAs-InAlAs-InP high electron mobility transistor (InP HEMT) is the preferred active device used in a cryogenic low noise amplifier (LNA) for sensitive detection of microwave signals. We observed that an InP HEMT 0.3-14GHz LNA at 2K, where the in-going transistors were oriented perpendicular to a magnetic field, heavily degraded in gain and average noise temperature already up to 1.5T. Dc measurements for InP HEMTs at 2K revealed a strong reduction in the transistor output current as a function of static magnetic field up to 14T. In contrast, the current reduction was insignificant when …
We report on microwave operation of top-gated single carbon nanotube transistors. From transmission measurements in the 0.1-1.6 GHz range, we deduce device transconductance gm and gate-nanotube capacitance Cg of micro- and nanometric devices. A large and frequency-independent gm of about 20 microSiemens is observed on short devices, which meets the best dc results. The capacitance per unit gate length of 60 aF/micrometer is typical of top gates on a conventional oxide with a dielectric constant equal to 10. This value is a factor of 3-5 below the nanotube quantum capacitance which, according t…
We implemented experimentally an interferometer-type charge qubit consisting of a single-Cooper-pair transistor closed by a superconducting loop that is in flip-chip configuration inductively coupled to a radio frequency tank circuit. The tank permits to readout the qubit state, acting as inductance measuring apparatus. By applying continuous microwave power to the quantum device, we observed inductance alterations caused by redistributions of the energy level populations. From the measured data, we extracted the energy gap between ground and upper levels as a function of the transistor quasic…
In our previous paper, we reported on switchable monolayer MoS2 transistors with a high on-off ratio and we claim that dielectric screening can be used to increase the mobility of monolayer MoS2. We estimated its mobility using a method previously applied by Lemme et al. to top-gated graphene nanoribbons. We discuss here the comments raised by M. Fuhrer and J. Hone in their post 1301.4288 and give our own estimates of the possible errors in previous mobility measurements and their origins.
Starting from the Kubo formula for conductance, we calculate the frequency-dependent response of a single-electron transistor (SET) driven by an ac signal. Treating tunneling processes within the lowest order approximation, valid for a wide range of parameters, we discover a finite reactive part even under Coulomb blockade due to virtual processes. At low frequencies this can be described by an effective capacitance. This effect can be probed with microwave reflection measurements in radio-frequency (rf) SET provided that the capacitance of the surroundings does not completely mask that of the…
We analyze the response of a nanomechanical resonator to an external drive when it is also coupled to a single-electron transistor (SET). The interaction between the SET electrons and the mechanical resonator depends on the amplitude of the mechanical motion leading to a strongly non-linear response to the drive which is similar to that of a Duffing oscillator. We show that the average dynamics of the resonator is well-described by a simple effective model which incorporates damping and frequency renormalization terms which are amplitude dependent. We also find that for a certain range of para…
We present an approach for time-dependent quantum transport based on a self-consistent non-equilibrium Green function formalism. The technique is applied to a ballistic carbon nanotube transistor in the presence of a time harmonic signal at the gate. In the ON state the dynamic conductance exhibits plasmonic resonant peaks at terahertz frequencies. These vanish in the OFF state, and the dynamic conductance displays smooth oscillations, a signature of single particle quantum effects. We show that the nanotube kinetic inductance plays an essential role in the high-frequency behavior.
We present results for time-dependent electron transport in a ballistic graphene field-effect transistor with an ac-driven gate. Nonlinear response to the ac drive is derived utilizing Floquet theory for scattering states in combination with Landauer-Büttiker theory for transport. We identify two regimes that can be useful for applications: (i) low and (ii) high doping of graphene under source and drain contacts, relative to the doping level in the graphene channel, which in an experiment can be varied by a back gate. In both regimes, inelastic scattering induced by the ac drive can excite qua…
We have analyzed numerically the response and noise-limited charge sensitivity of a radio-frequency single-electron transistor (RF-SET) in a non-superconducting state using the orthodox theory. In particular, we have studied the performance dependence on the quality factor Q of the tank circuit for Q both below and above the value corresponding to the impedance matching between the coaxial cable and SET.
Cryogenic low noise amplifiers based on high electron mobility transistors (HEMTs) are widely used in applications such as radio astronomy, deep space communications, and quantum computing, and the physical mechanisms governing the microwave noise figure are therefore of practical interest. In particular, the contribution of thermal noise from the gate at cryogenic temperatures remains unclear owing to a lack of experimental measurements of thermal resistance under these conditions. Here, we report measurements of gate junction temperature and thermal resistance in a HEMT at cryogenic and room…
We analyze the effect of bichromatic microwave irradiation on the magnetoresistivity of a two dimensional electron system. We follow the model of microwave driven Larmor orbits in a regime where two different microwave lights with different frequencies are illuminating the sample ($w_{1}$ and $w_{2}$). Our calculated results demonstrate that now the electronic orbit centers are driven by the superposition of two harmonic oscillatory movements with the frequencies of the microwave sources. As a result the magnetoresisitivity response presents modulated pulses in the amplitude with a frequency o…
We experimentally characterise the impedance of a single electron transistor (SET) at an excitation frequency comparable to the electron tunnel rate. Differently from usual rf-SET operations, the excitation signal is applied to the gate of the device. At zero source-drain bias the single electron transistor displays both resistive (Sisyphus resistance) and reactive (tunnelling capacitance) components to its impedance. We study the bias dependence of the complex impedance, investigating its response as the electron tunnel rate becomes large with respect to the driving frequency. The experimenta…
We have designed and built a near-field scanning microwave microscope, which has been used to measure the local microwave response and the local density-of-states (LDOS) in the area including the boundary between the gold deposited and the non-deposited region on highly-orientated pyrolytic graphite at a frequency of about 7.3 GHz. We have succeeded in measuring the spatial variation of both the LDOS and the surface resistance. It can be observed that the surface resistance in gold deposited region with the metallic tunneling spectra is smaller than that in the non-deposited region with the U-…
Semiconductor transistors are essential elements of electronic circuits as they enable, for example, the isolation or amplification of voltage signals. While conventional transistors are point-type (lumped-element) devices, it may be highly interesting to realize a distributed transistor-type optical response in a bulk material. Here, we show that low-symmetry two-dimensional metallic systems may be the ideal solution to implement such a distributed-transistor response. To this end, using the semiclassical Boltzmann equation approach, we characterize the optical conductivity of a two-dimension…
We analyze theoretically the dependence of the microwave polarization sate and sense on the magnetoresistivity response of two-dimensional electron systems. Linear and circular polarization have been considered with different senses and directions. We discuss the polarization dependence of the longitudinal magnetoresistivity and propose an explanation for the experimentally observed polarization immunity, i.e., resistivity oscillations and zero resistance state regions are unaffected by the sense of circular polarization or by the direction of microwave electric field.
We investigate charge qubit measurements using a single electron transistor, with focus on the backaction-induced renormalization of qubit parameters. It is revealed the renormalized dynamics leads to a number of intriguing features in the detector's noise spectra, and therefore needs to be accounted for to properly understand the measurement result. Noticeably, the level renormalization gives rise to a strongly enhanced signal-to-noise ratio, which can even exceed the universal upper bound imposed quantum mechanically on linear-response detectors.
Here, we report the observation of a hitherto unreported optoelectronic effect, namely a light-induced diode-like response in multi-layered MoSe$_2$ field-effect transistors whose sense of current rectification is controllable through a gate voltage. We argue, through numerical simulations, that this behavior results from the difference in the size of the Schottky barriers between drain and source metal contacts. Each barrier can be modeled as a Schottky diode but with opposite senses of current rectification between them, with the diode response resulting from the light induced promotion of p…
Electromagnetic response of a finite-width two-dimensional electron stripe is theoretically studied. It is shown that retardation and radiative effects substantially modify the absorption spectrum of the system at microwave frequencies, leading to a non-trivial zigzag behavior of the magnetoplasmon-polariton modes in magnetic fields, similar to that recently observed by Kukushkin et al. [Phys. Rev. Lett. {\bf 90}, 156801 (2003)].
We report electrically detected magnetic resonance of phosphorus donors in a silicon field-effect transistor. An on-chip transmission line is used to generate the oscillating magnetic field allowing broadband operation. At milli-kelvin temperatures, continuous wave spectra were obtained up to 40 GHz, using both magnetic field and microwave frequency modulation. The spectra reveal the hyperfine-split electron spin resonances characteristic for Si:P and a central feature which displays the fingerprint of spin-spin scattering in the two-dimensional electron gas.
We have directly measured the quantum noise of a superconducting single-electron transistor (S-SET) embedded in a microwave resonator consisting of a superconducting LC tank circuit. Using an effective bath description, we find that the S-SET provides damping of the resonator modes proportional to its differential conductance and has an effective temperature that depends strongly on the S-SET bias conditions. In the vicinity of a double Cooper pair resonance, when both resonances are red detuned the S-SET effective temperature can be well below both the ambient temperature and the energy scale…
We study electron transport through single-electron spin-valve transistors in the presence of non-local exchange between the ferromagnetic leads and the central normal-metal island. The Coulomb interaction is described with the orthodox model for Coulomb blockade and we allow for noncollinear lead magnetization directions. Two distinct exchange mechanisms that have been discussed in the literature are shown to be of comparable strength and are taken into account on equal footing. We present results for the linear conductance as a function of gate voltage and magnetic configuration, and discuss…
We theoretically analyzed the microwave-induced modification of the Hall magnetoresistivity in high mobility two-dimensional electron systems. These systems present diagonal magnetoresistivity oscillations and zero-resistance states when are subjected to microwave radiation. The most surprising modification of the Hall magnetoresistivity is a periodic reduction which correlates with a periodic increase in the diagonal resistivity. We present a model that explains the experimental results considering that radiation affects directly only the diagonal resistivity and the observed Hall resistivity…
There is growing interest in exploring nanomagnetic devices as potential replacements for electronic devices (e.g. transistors) in digital switching circuits and systems. A special class of nanomagnetic devices are switched with electrically generated mechanical strain leading to electrical control of magnetism. Straintronic magneto-tunneling junctions (s-MTJ) belong to this category. Their soft layers are composed of two-phase multiferroics comprising a magnetostrictive layer elastically coupled to a piezoelectric layer. Here, we show that a single straintronic magneto-tunneling junction with…
Radio-frequency (rf)- operated single-electron transistors (SETs) are high-sensitivity, fast-response electrometers, which are valuable for developing new insights into single-charge dynamics. We investigate high-frequency (up to 1 MHz) charge noise in an AlGaAs/GaAs quantum dot using a transmission-type rf-SET technique. The electron capture and emission kinetics on a trap in the vicinity of the quantum dot are dominated by a Poisson process. The maximum bandwidth for measuring single trapping events is about 1 MHz, which is the same as that required for observing single-electron tunneling os…
A concurrent remote sensing and magneto-transport study of the microwave excited two dimensional electron system (2DES) at liquid Helium temperatures has been carried out using a carbon detector to remotely sense the microwave activity of the 2D electron system in the GaAs/AlGaAs heterostructure during conventional magnetotransport measurements. Various correlations are observed and reported between the oscillatory magnetotransport and the remotely sensed reflection. In addition, the oscillatory remotely sensed signal is shown to exhibit a power law type variation in its amplitude, similar to …
