Annotation of the results obtained in 2018
We have performed the first experimental observation of plasmon-enhanced terahertz detection in transistors based on high-quality graphene. We have also developed a theory of plasmon-enhanced photoresponse involving thermoelectric phenomena at the contacts that well describes the experimental data. The results have both fundamental and applied value. First, the reported detector displays internal responsivity up to 3 kV/W and noise equivalent power of 0.2 pW/Hz^{1/2} which make it competitive with, e.g. superconducting hot-electron bolometers. Second, electric tuning of resonant frequency enables the use of such detector as compact on-chip terahertz spectrometer. Third, the measured dependences of detector photocurrent on radiation frequency and gate voltage allow one to restore plasmon dispersion and damping in the channel material. As an example of the latter application, we have studied plasmons due to oscillations of carriers near the secondary Dirac points in Moire superlattices. These results were published in high-impact journal Nature Communications D. A. Bandurin, D. Svintsov, I. Gayduchenko, S. G. Xu, A. Principi, M. Moskotin, I. Tretyakov, D. Yagodkin, S. Zhukov, T. Taniguchi, K. Watanabe, I. V. Grigorieva, M. Polini, G. Goltsman,A. K. Geim, G. Fedorov “Resonant Terahertz Detection Using Graphene Plasmons” arXiv:1807.04703 (accepted for publication). Along with the studies of resonant THz detection in high-quality encapsulated graphene, we have studied the plasmonic properties of commercially available large-area CVD-grown graphene with modest carrier mobility ~10^3 cm^2/V s. We have measured the spectra of 5-10 THz transmission in the structures comprised of CVD graphene, dielectric layer and a metal grating gate. A polarization-dependent contribution to absorption was selected out; it scales with frequency according to ~n^{1/4} which confirms the plasmonic origin of such contribution. We have shown that the values of electron scattering rate, as determined from absorption spectra, can be 2-3 times lower than those from mobility measurements. The reason is weak sensitivity of optical methods to carrier scattering at grain boundaries and macroscopic defects. This fact enables the observation of plasmon resonance at 5-10 THz frequencies in moderate-quality CVD graphene. Comparison of the measured resonant frequencies with theory shows that plasmon field is tightly bound below individual metal stripes. Akin to the tight-binding theory in solids, we have proposed a simple analytical tight-binding theory for plasmons that explains well the experimental data. We have measured the photoresponse of “graphene-dielectric-grating” transistors in sub-THz (0.1-0.3 THz) and visible frequency ranges. The gate voltage dependences of sub-THz photocurrent confirm the photo-thermoelectric origin of the photoresponse. In the visible range, a significant contribution to photovoltage comes from internal photovoltaic effect in silicon substrate. The results were summarized in publication A. Bylinkin, E. Titova, V. Mikheev, E. Zhukova, S. Zhukov, M. Belyanchikov, M. Kashchenko, A. Miakonkikh, D. Svintsov “Tight-binding terahertz plasmons in chemical vapor deposited graphene” arxiv 1812.04028, submitted to Applied Physics Letters. We have studied the fundamental limits of plasmon quality factor in 2d materials (graphene and III-V heterostructures) due to electron-electron (e-e) scattering. To this end, we have developed an exactly solvable kinetic theory of high-frequency transport accounting for e-e scattering. In the limiting cases of low and high frequencies, the theory reduces to the hydrodynamic Navier-Stokes and free-particle ballistic transport equations. We have shown that e-e scattering prevents plasmon damping in the low-frequency hydrodynamic regime, and stimulates plasmon damping in the high-frequency ballistic regime. For wave frequencies comparable with e-e collision frequency (~1 THz at room temperature) the quality factor reaches its minimum value ~10-30 which depends on the phase velocity of the wave. The results are summarized in a published paper D. Svintsov "Hydrodynamic-to-ballistic crossover in Dirac materials", Physical Review B: Rapid Communications 97, 121405(R) (2018). We have theoretically identified the optimal conditions for the development of hydrodynamic asymmetry-driven plasma instabilities in the field-effect transistor (FET) channels. This result is the generalization of well-known Dyakonov-Shur instability to the case of arbitrary boundary conditions and arbitrary geometry of contacts. It is shown that asymmetry of plasmon field with respect to the FET mirror plane is necessary for instability development. However, too strong asymmetry leads to the enhanced viscous dissipation. We have obtained a fundamental lower limit to the Reynolds number below which the instability in uniformly doped 2d channel cannot develop; it equals 2\sqrt{3}. Using the formalism of model integral of e-e collisions, we have calculated the viscosity of 2d electrons with parabolic dispersion law. At fixed electron density, the viscosity appears to be inversely proportional to carrier effective mass. We have theoretically studied the possibility of current-driven plasma instabilities in van der Waals heterostructures comprised of parallel graphene layers and in grating-gated graphene. We have shown that instabilities are possible only upon coincidence of carrier drift velocity and surface plasmon velocity. In turn, such coincidence is possible only in low-frequency (hydrodynamic) transport regime. In the high-frequency ballistic regime, electron plasma is stable under arbitrarily fast electron drift due to peculiarities of spatially-dispersive graphene conductivity. A publication is prepared, D. Svintsov, V. Ryzhii “Comment on "Negative Landau damping in bilayer graphene"” arXiv:1812.03764 (under review in Physical Review Letters, positive comments of the referees were received). Mercury-cadmium-telluride quantum wells have been theoretically studied as a gain medium for IR/THz injection lasers. Starting from bandstructures and wavefunctions found within the eight-band Kane-model, we have calculated the nonradiative recombination rates and the frequency dependence of optical conductivity at different values of parameters: well thickness, temperature, nonequilibrium carrier density. We have found lower Auger recombination rates than in graphene (by several times or more, depending on the band gap) due to the large permittivity of cadmium-mercury-telluride, the presence of a bandgap, and delocalization of wavefunctions along the growth direction. We have calculated threshold concentrations and currents required for achieving optical gain. The obtained threshold currents do not exceed several kA/cm^2 at room temperature for IR lasing and are of the same magnitude as the threshold currents of quantum cascade lasers. We have shown that achieving THz lasing at room temperature is hampered by the quick recombination with emission of optical phonons and intersubband absorption; nevertheless, it is still possible to achieve upper-THz (>4 THz, not covered by quantum cascade lasers due to strong absorption in AIIIBV semiconductors) lasing by using wells with a bandgap exceeding the optical phonon energies. The possibility of plasmon lasing in mercury-cadmium-telluride quantum wells was studied theoretically. We have found the threshold density of non-equilibrium carriers vs temperature at different well thickness. At near-room temperature, this density equals approximately 10^10 cm-2 at 50 meV bandgap which is easily achievable upon interband pumping. We have shown that the effect of intra-band Drude absorption and Landau damping on threshold density is weak when emission is expected in far-infrared range (~10 THz). In addition, plasmonic lasers can be more compact than their photonic-mode counterparts.

 

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Annotation of the results obtained in 2016
A theory of hydrodynamic plasma instabilities in field-effect transistors and plasmonic crystals with two-dimensional channels has been developed [A.S. Petrov et.al. “Amplified-reflection plasmon instabilities in grating-gate plasmonic crystals”, arXiv:1610.07035, submitted to Phys. Rev. B; A.S. Petrov et.al. “Plasma Instability of 2d Electrons in a Field Effect Transistor with a Partly Gated Channel”, accepted to International Journal of High Speed Electronics and Systems]. The instability occurs due to the amplified plasmon reflection from the boundary between gated and ungated parts of the channel in the presence of carrier drift. It is shown theoretically that the instability increment can exceed the collisional decrement of plasmons at realistic values of electron mobility in graphene and III-V compounds a room temperature. The proposed mechanism of instability can be responsible for the experimentally observed THz emission in transistors based on III-V semiconductors, and for the recently observed amplified transmission of electromagnetic waves through the structures “grating gate - boron nitride - graphene”. A theory of Auger recombination in narrow-gap semiconductors with quasirelativistic dispersion has been developed. This theory is applicable to a wide range of materials (graphene and its gapped derivatives, CdHgTe/HgTe quantum wells) that are promising candidates for creation of THz injection lasers. The effects of collision-induced broadening of the quasiparticle spectrum were shown to be crucial to obtain a correct value of the Auger recombination rate: in the absence of scattering, the Auger recombination rate turns to zero. The calculated Auger recombination lifetime in graphene on a SiC substrate was found to be around 300 fs at room temperature, in a good agreement with experimental data [Gierz, I. et al. J. Phys. Condens. Matter 27, 164204 (2015)]. We have demonstrated theoretically the possibility to control the recombination time not only by opening a small gap in graphene-spectrum (e.g. induced by substrate), but also by changing the dielectric environment. In particular, placing graphene near a metal gate can increase the lifetime of nonequilibrium carriers up to 1.5 ps, which is sufficient for maintaining the population inversion in THz injection lasers. A theory of optical conductivity in graphene with population inversion was developed within the framework of the quantum kinetic equation with indirect interband and intraband transitions caused by impurity scattering scattering taken into account. It was shown that the absorption induced by intraband transitions is suppressed if the carrier scattering occurs on a smoothly decaying impurity potential. For such type of scattering potentials, the contribution from the indirect interband transitions surpasses by absolute value the intraband contribution and has a negative sign. Delta-doping of the 2D systems could form such scattering potential. Thus, we have shown the principle possibility of optical gain enhancement in active media by the means of introducing extra scattering centers into the system. This possibility is unique to the narrow-gap semiconductors - graphene, bilayer graphene and CdHgTe/HgTe quantum wells. A theory of plasmon- and photon-assisted inelastic tunnelling in “graphene-insulator-graphene” structures was developed [D. Svintsov et.al. Phys. Rev. B 94 (2016), http://journals.aps.org/prb/abstract/10.1103/PhysRevB.94.115301 ]. It was theoretically shown that with a proper selection of the barrier layer material and thickness, the photon and surface plasmon gain due to the resonant tunnelling can exceed the absorption caused by the interband and intraband transitions. The most important difference of the “graphene-insulator-graphene” structures from the analogous quantum cascade structures based on massive 2d electrons lies in the resonant nature of plasmon-assisted tunnelling. This resonance can be traced back to the linear electron spectrum in graphene and a strong tunnelling between the states with collinear momenta. Due to such resonance, the plasmon loss compensation becomes feasible in the “graphene-insulator-graphene” samples with carrier mobilities of the order 10^4 cm2/(V s) at room temperature. It was also shown that the spontaneous plasmon emission under inelastic tunnelling may be responsible for the THz electroluminescence in van-der-Waals heterostructures, which was experimentally observed by our colleagues form Tohoku University, Japan [D.Yadav et al, 2D Materials 3, 045009 (2016)]. The optimization of the quantum cascade laser resonators with active graphene bilayer structures was conducted using the developed theory of resonant tunnelling supplemented by numerical calculations of the electromagnetic modes [A.A. Dubinov et.al. “Ultra-compact injection terahertz laser using the resonant inter-layer radiative transitions in multi-graphene-layer structure” Optics Express 24б pp. 29603-29612 (2016), https://www.osapublishing.org/oe/abstract.cfm?uri=oe-24-26-29603]. For the TM-mode surface plasmonic waveguide, which provides the most efficient field localization, the gain coefficient at 8 THz peaks to 500 cm-1 which corresponds to the resonator threshold length of 50 micrometers. The proposed lasers are capable of operating in the 5-15 THz frequency range, where the A3B5 QCL operation is hindered by the optical phonon absorption; in addition, the proposed lasers can surpass the existing QCLs in compactness. The basic technological procedures towards the creation of transistor structures “graphene-insulator-graphene” were developed, aiming at studying and providing proof to new physical principles of plasmon detection of THz radiation. The electrical properties of graphene were measured and the obtained mobilities reached the value of μ=1100 cm^2/(V s). Also, the dependences of THz (v=2 cm^-1 - 120 cm^-1) transmission spectra of the graphene transistor structures “graphene-semiconductor-planar gate” on the gate voltage were studied in order to obtain the optical properties of graphene. Experimental results show that the transmission spectra dependence on the gate voltage is well described by the Drude model for graphene conductance in this range of frequencies.

 

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Annotation of the results obtained in 2017
This year’s work was devoted to the (1) Development of models for new THz detectors and sources based on two-dimensional materials; (2) Initiation of collaboration with experimental groups capable of fabrication and measurement of such devices; (3) Development of fabrication and measurement technology for graphene-based THz detectors in MIPT. Three prospective classes of terahertz electronic devices based on two-dimensional systems are studied within the project: 1. Sources and detectors of THz radiation exploiting the excitation of plasmons in field-effect transistors with two-dimensional electronic channels. Within this topic, we have developed numerical and analytical models for simulation and optimization of THz sources based on plasmon excitation in two-dimensional electronic systems. For the first time, we have revealed a key role for asymmetry of field-effect transistor structures for excitation of plasmons by direct current. Namely, we have shown that the direct hydrodynamic flow of electrons in arbitrary asymmetric transistor structure is unstable with respect to the self-excitation of plasma waves. It is important that this plasmon instability is thresholdless in the absence of electron scattering by impurities and phonons, i.e. it develops at arbitrarily small velocity of carrier drift. Previously, the role of asymmetry was studied in detail only in the problem of THz detection, while its role in the formation of plasmon instabilities in transistors remained unclear. At the same time, we have developed the programs for calculations of spectra and growth rates of plasma instabilities in single-gate and multi-gate transistor structures. In our calculations, we have taken into account the experimentally relevant factors of edge and contact effects, electron scattering and viscosity. The programs were used to establish the optimal gating geometry and doping profiles in transistors ensuring the maximum instability growth rates. In collaboration with experimental groups of the Manchester University and Moscow State Pedagogical University, we have fabricated and measured the characteristics of sub-THz detectors based on graphene field-effect transistors (FETs) [D.A. Bandurin, I. Gayduchencko, Y. Cao, M. Moskotin, A. Principi, G. Goltsman, G. Fedorov, D. Svintsov “Dual Origin of Room Temperature Sub-Terahertz Photoresponse in Graphene Field Effect Transistors” arXiv:1712.02144]. Graphene films in these transistors are encapsulated in hexagonal boron nitride, which allows us to achieve electron transport limited by phonon (not impurity!) scattering. Transistors were integrated with THz antennas, and the dependences of photovoltage on frequency, carrier density and temperature were measured in these devices. The responsivity in our devices reaches 30 V/W at room temperature, which exceeds by an order of magnitude a similar quantity for non-encapsulated transistors [L. Vicarelli et.al. Nat. Mater. 11, 865 (2012)]. The comparison of the obtained photovoltage signals with the predictions of theory allowed us to disentangle the relative role of various photoresponse mechanisms: rectification due to resistive self-mixing (non-resonant Dyakonov-Shur mechanism), rectification due to contact p-n-junctions, and photo-thermoelectric effect. We have shown that the main mechanism of photoresponse in graphene FETs with asymmetric feeding of signal between source and gate is the photo-thermoelectric effect. Once the Viedemann-Frantz law for electrons is fulfilled, the photo-thermoelectric voltage is proportional to (Sch-Scont)/T, where Sch and Scont are the Seebeck coefficients in the channel and near-contact regions, T is the absolute temperature. Further, if electron system is highly degenerate, the responsivity appears to be temperature-independent, while under weak degeneracy (near the Dirac point) the response grows with lowering the temperature. The response due to resistive self-mixing is strongly suppressed provided (\omega R C)<<1, where R is the resistance of the top-gated part of the channel, and C is the top gate-to-channel capacitance. Under these conditions, the response due to resistive self-mixing counter-intuitively grows with increasing the frequency of electron-phonon collisions. We have shown that non-uniform doping of the channel induced under selective application of DC voltage to the top gate induces extra p-n junctions in the FET channel. The rectification of signal by these junctions also contributes to the photovoltage, this contribution is pronounced below the temperature of liquid nitrogen. 2. Terahertz sources and detectors based on resonant tunneling in “graphene – insulator- graphene” heterostructures We have developed a theory of electron resonant tunneling accompanied by the spontaneous emission of plasmons in graphene-based heterostructures. We have revealed the manifestations of plasmon-assisted tunneling in the (1) current-voltage curves of the tunnel structure (2) tunneling electroluminescence spectra. We have calculated the probability of radiative decay for emitted plasmons in the double graphene layer structures and shown that it can be as large as 10% in optimized systems coupled to antennas. We have shown that the frequency dependence of electroluminescence possesses resonances appearing due to enhanced tunneling between electronic states with collinear momenta. Moreover, the integrated luminescence possesses resonances at certain interlayer voltages corresponding to the coincidence of group velocities for plasmons and interlayer single-particle excitations. The latter resonance is unique to the tunnel-coupled layers of two-dimensional systems with linear electron dispersion, and is absent in the antenna-coupled “metal-insulator-metal” junctions. We have compared the probability of inelastic plasmon-assisted tunneling and elastic tunneling, and shown that plasmon-assisted current can dominate under resonant conditions. We have proposed and simulated a novel type of photodetectors based on multilayer “graphene-insulator-graphene” structures [V.Ryzhii, M.Ryzhii, D.Svintsov, V.Leiman, V.Mitin, M.S.Shur, T.Otsuji "Infrared photodetectors based on graphene van der Waals heterostructures", Infrared Physics and Technology 84, p. 72-81 (2017)]. The detector can demonstrate high responsivity (~5 A/W at the 3 mkm wavelength), detectivity exceeding >10^10 cm Hz^1/2 / W and record-high photoelectric gain coefficient (~100). The possibility of photoelectric gain in the proposed type of detectors is due to the formation of positive space charge of holes under illumination. The presence of space charge increases the electric field strength near the emitter layer and leads to the enhancement of injection current. The latter can surpass the current of photoexcited carriers themselves, which is the manifestation of gain. To simulate the detector characteristics we have developed a microscopic model of photodetection in van der Waals heterostructures. The theory includes the processes of photon absorption, tunneling ionization, electron energy relaxation and capture. We have performed the optimization of photodetectors aiming at the lowering of operation frequency down to units of terahertz. 3. Injection lasers based on graphene and its narrow-gap derivatives The main work on this topic was concentrated on modeling of Auger recombination and studies of pathways for its suppression in narrow-gap two-dimensional systems. It is known that the shortening of non-radiative Auger recombination lifetimes with shrinking the band gap is the main obstacle to the creation of long-wavelength semiconductor lasers. Within this project, we study the materials for THz lasing with quasi-relativistic spectra of electrons and holes, where the first-order Auger process is prohibited by the energy and momentum conservation laws. We have developed a method for calculation of Auger recombination rates in such materials [G. Alymov, D. Svintsov, V. Vyurkov, V. Ryzhii, A. Satou “Auger recombination in Dirac materials: A tangle of many-body effects” https://arxiv.org/pdf/1709.09015v2.pdf]. The method is applicable to graphene, quantum wells based on CdHgTe alloys, and Weyl semimetals. The method fully takes into account the many-body effects of dynamic screening, Coulomb renormalization of dispersion, and its collisional broadening. We have shown that all these effects are important to obtain the values of recombination time in graphene consistent with experimental data. We have shown that the recombination time in gapless graphene sub-linearly depends on the dielectric constant of the substrate and does not exceed 1-2 ps at room temperature. Using the additional screening by metal gates, one can reduce the recombination rate in graphene by ~7 times at gate-to-graphene separation equal to 1 nm. We have demonstrated a considerable contribution to Coulomb recombination in graphene due to the emission of surface plasmons. This fact can be used for creation of plasmonic THz lasers using the grating gates for plasmon-to-photon conversion. The developed method of recombination rate calculations was applied to the multilayer structures with misoriented graphene layers. It was shown that the increase in the number of layers in the stack leads to (1) extra screening of Coulomb interaction (2) emergence of the new recombination channels, where the energy and momentum from electron-hole annihilation in one layer are absorbed in the neighboring layer. The role of screening, according to the performed calculations, is dominant, and the increase in the number of layers leads to a monotonous increase in non-radiative lifetime. This lifetime saturates at the layer number N ~ h v / d k T, where d = 2.5 A is the interlayer distance in misoriented graphene, v = 10^6 m/s – is the Fermi velocity, h is the Planck’s constant and kT is the thermal energy. For temperatures T~1500 K relevant to pump-probe experiments, the saturation of recombination occurs at N~30, the corresponding non-radiative lifetime has the order of 300 fs. We have evaluated the energy threshold of Auger recombination in mercury cadmium telluride (MCT) quantum wells for different values of band gap and electron and hole effective masses. These parameters can be controlled by varying the composition and thickness of the quantum well. It is shown that the energy threshold tends to infinity, and the first-order Auger progess becomes prohibited for equal effective masses of electrons and holes. During the next year, these results will be used for the optimization of semiconductor lasers based on MCT quantum wells fabricated in the Institute of Semiconductor Physics RAS (Novosibirsk) and Institute for Physics of Microstructures RAS (Nizhny Novgorod).

 

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