Ultrasensitive Photoresponse of Graphene Quantum Dot in the Coulomb Blockade Regime to THz Radiation
E. Riccardi, S. Massabeau, F. Valmorra, S. Messelot, M. Rosticher, J. Tignon, K. Watanabe, T. Taniguchi, M. Delbecq, S. Dhillon, R. Ferreira, S. Balibar, T. Kontos, J. Mangeney
UUltrasensitive Photoresponse of GrapheneQuantum Dot in the Coulomb Blockade Regimeto THz Radiation
Elisa Riccardi, † Sylvain Massabeau, † Federico Valmorra, † SimonMesselot, † Michael Rosticher, † Jérôme Tignon, † Kenji Watanabe, ‡ TakashiTaniguchi, ¶ Matthieu Delbecq, † Sukhdeep Dhillon, † Robson Ferreira, † Sébastien Balibar, † Takis Kontos, † and Juliette Mangeney ∗ , † † Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, UniversitÃl’ PSL, CNRS,Sorbonne UniversitÃl’, UniversitÃl’ de Paris, F-75005 Paris, France ‡ Research Center for Functional Materials, National Institute for Materials Science, Tsukuba,Ibaraki, 305-0047, Japan ¶ International Center for Materials Nanoarchitectonics, National Institute for Materials Science,Tsukuba, Ibaraki, 305-0047, Japan
E-mail: [email protected] a r X i v : . [ c ond - m a t . m e s - h a ll ] J un bstract Graphene quantum dots (GQDs) have recently attracted considerable attention, with ap-pealing properties for terahertz (THz) technology. This includes the demonstration of largethermal bolometric effects in GQDs when illuminated by THz radiation. However, the inter-action of THz photons with GQDs in the Coulomb blockade regime - single electron transportregime - remains unexplored. Here, we demonstrate the ultrasensitive photoresponse to THzradiation (from <0.1 to 10 THz) of a hBN-encapsulated GQD in the Coulomb blockade regimeat low temperature (170 mK). We show that THz radiation of ∼
10 pW provides a photocurrentresponse in the nanoampere range, resulting from a renormalization of the chemical potentialof the GQD of ∼ Keywords
THz, Graphene, Quantum Dot, Coulomb Blockade, Photogating2raphene quantum dots (GQDs) have attracted considerable attention in recent years due totheir unique optical and electrical properties that are directly related to their nanoscale structures.The potential of GQDs for the development of new quantum systems has been widely investigatedusing optical and transport experiments.
For instance, GQDs of a few nanometers in diameterare very appealing for applications in quantum metrology as GQDs can emit a single optical pho-ton at room temperature with high purity and high brightness. Further, GDQs of a few tens ofnanometers in diameter have been shown to possess very long relaxation times of electronic exci-tations (60 ns), paving the way for spin qubits with long coherence times. Such large GQDs havealso become very attractive for the development of new terahertz (THz) emitters and detectors as the quantum electron confinement permits characteristic energy level spacing to reach the fewmillielectron volt (meV) range (i.e. THz spectral range). For instance, the electronic confinementprovides a weak transport gap that can prevent undesirable large dark Zener Klein current that isobserved in graphene-based photodetectors. Moreover, nonradiative Auger recombination pro-cesses, which are detrimental for the development of THz lasers, can be potentially reduced inGQD as a result of limiting the final states available for electron-electron scattering. Recently, largebolometric effects have been demonstrated in nanostructured quantum dot constrictions in epitax-ial graphene grown on SiC when illuminated with THz photons. A huge variation of resistancewith temperature was obtained, > M Ω K − below K, owing to electronic confinement. However, as no gate electrodes were used to isolate the quantum dots from the leads and to controlthe chemical potential inside the quantum dots, the bolometric effect was limited to THz heat-ing. Although many interesting phenomena can be revealed in single electron transport regime,the investigation of the THz response of GQDs in the Coulomb blockade regime remains elusive.Here, we report on the photocurrent response of a hBN-encapsulated GQD to THz radiation inCoulomb blockade regime at low temperature (170 mK). We demonstrate that THz radiation (from<0.1 to 10 THz) of ∼
10 pW provides a renormalization of the chemical potential of the GQD of ∼ >
100 nm. TheGQD-based single electron transistor, shown in Fig. 1, consists in a large central GQD, with adiameter of nm, linked to the source and drain electrodes by two narrow constrictions ( nm)and surrounded by three lateral gates ( G , G and G ). As well as the GQD, all the electrodesand constrictions are made of hBN-encapsulated graphene, deposited on a SiO /Si substrate (seeFig. 1(a)). Owing to the encapsulation of the graphene layer with two hBN layers, the disorderin the GQD is reduced and the chemical potentials of the graphene leads µ S,D are expected tobe typically within ± meV. The graphene device is connected to the gold electrodes and toa THz bow-tie antenna as shown in Fig. 1(c). The whole area of the GQD-based device thatincludes the whole graphene area (leads and quantum dot) and the metallic bow tie antenna is x µ m . Further details on the sample fabrication are presented in the Supporting Information(Experimental details). To perform transport measurements under THz illumination, the GQD-based device is placed within a dilution He- He cryostat with THz optical access (three sapphirewindows). The device is cooled to a temperature of mK. The THz light source is a high-pressure mercury plasma arc-discharge lamp. The blackbody radiation emitted by the source isfiltered above 10 THz with a low pass filter so that the incident THz photon energies ¯ hω are lowerthan meV. To focus the THz beam onto the GQD-based device, a pair of parabolic mirrors areplaced in front of the fridge window (Fig. 1(c)). The incoherent incident radiation is mechanicallymodulated at a frequency of 330 Hz and we record the DC current with and without illumination(i.e. the mean value of the modulated current) and also the photocurrent, I photo , using a lock-inamplifier. For optical power-dependence measurements, we insert Si wafers in the THz beam pathto attenuate the incident THz power. Without any Si wafer, the estimated THz optical power of theincident THz radiation onto the GQD-based device is ∼
10 pW.4 bc SiO Au Si hBN-GrapheneS DG G G Bow-tie antenna Low-passfilterSi wafersSapphire windows20 μm Au
Figure 1: (a) Sketch of the devices made of the hBN/graphene/hBN heterostructure deposited onintrinsic silicon substrate with 500 nm thick SiO on top. We act on the two barriers and on theGQD using three lateral gates G , G and G separated from the constrictions and the island bya distance ∼
50 nm. We do not apply any backgate voltage using the Si substrate. (b) Scanningelectron microscopy (SEM) images of the graphene portion of the device, after the etching of thehBN-graphene-hBN heterostructure. The picture shows the GQD surrounded by the three lateralgates and linked to the source and drain electrodes. (c) Left: Optical image of the connected devicewith the gold bow-tie antenna. Right: sketch of the experimental setup: the GQD-based sample isplaced within a dilution cryostat at 170 mK equipped with three sapphire windows. The incoherentTHz radiation emitted by a Hg lamp, filtered using a low pass filter to frequencies < THz, isfocused on the GQD-based sample. Some high-resistivity silicon wafers are used to attenuate theincident THz radiation. 5e first perform transport measurements with the fridge’s window closed to explore the elec-tron confinement and excitation spectrum of the GQD. The plunger gate G mainly acts on thechemical potential of the quantum dot, µ dot , and the two side gates G and G control the transportthrough the two constrictions (see Fig. 1(a)). In order for the two constrictions to act as tunnelingbarriers, we set them in their respective transport gap at V G = V G = 11 . V. As observed inFig. 2(b), pronounced Coulomb-blockade peaks are observed in the differential conductance asa function of the plunger gate voltage V g , showing the regime of sequential tunneling where thetransport is allowed only if the chemical potential of the source (or drain) crosses one empty levelof the quantum dot. The Coulomb stability diagram of the GQD-based device, i.e. plots of thedifferential conductance G = dI/dV DS as a function of V DS and V g , is reported in Fig. 2(a). Weobserve well-defined and stable Coulomb diamonds, which correspond to the ground state of theGQD. The plunger gate voltage V g fills the quantum dot with electrons by moving the energy levels,while the bias voltage V DS shifts the chemical potential of the electron baths of source and drain.The conductance map is not centered at V DS = 0 V due to the offset voltage of the preamplifier onthe drain V = − . mV. The source-drain voltage applied to the GQD is V ∗ DS = V DS − V . Fromthe half-height of Coulomb diamond, we extract the addition energy needed to add an electronfrom a lead to the GQD, E add = 9 meV. This addition energy is expressed as E add = E c + δE with E c = e /C Σ as the charging energy, C Σ as the total capacitance of the device, and δE as theintrinsic level spacing of the GQD. We also observe quantum confinement effects as lines parallelto the edges of the diamonds in Fig. 2(a). The lines evidence the sequential tunneling of the elec-trons via the excited states of the GQD. From the vertical cut of the conductance map shown inFig. 2(c), we clearly see resonances due to the tunneling through the excited states around a regionwhere conductance is strongly suppressed. The energy separation of the excited states gives thesingle particle level spacing of the GQD, δE = 1 . meV, corresponding to a frequency spacingof . THz. This result confirms that large GQD (of diameter 150 nm) provide discretization ofelectronic states with energy spacing in the meV range (i.e THz range), as predicted by the litera-ture.
The full-width at half-maximum of the excited state resonance at V g = − V is . meV6orresponding to a thermal broadening of T = 1 . K that is roughly consistent with the expectedelectronic temperature in the GQD under bias. From E add and δE , we deduce a charging energy E c = 7 . meV, which is smaller than the charging energy estimated from a metallic disk model E c = e / (4 (cid:15) (cid:15) eff d ) = 12 meV (with (cid:15) eff = ( (cid:15) SiO + 1) / . ) which is in agreement withprevious works on GQD-based devices. This deviation is attributed to the capacitive coupling ofthe GQD to the adjacent gates and leads, which increases the total capacitance C Σ . G d i ff ( / h ) V g (V) ab -10 -5 0 5 100.00.10.20.3 G d i ff ( / h ) V DS (mV) c δE Figure 2: (a) Differential conductance G as a function of the source-drain voltage V DS and of theplunger gate voltage V g , exhibiting Coulomb diamonds. Multiple resonances parallel to the edgesof the diamonds are clearly visible. (b) Differential conductance as a function of V g at V DS = 0 mV .The two side gates are V G = V G = 11 . V . (c) Differential conductance as a function of V DS (vertical cut along the dark dashed line in (b)). The width of the diamond allows to estimate theaddition energy, while the slope of the diamond edge is proportional to the electronic temperature.7e now turn to the transport investigation of the GQD-based device under THz light illumina-tion. We first focus on the effect of the THz illumination on the current flowing through the GQDat fixed V DS . Figures 3 (a) and (b) show Coulomb blockade peaks in the DC current measuredas a function of V g with (red) and without (black) illumination for P = 10 pW and V DS = 2 meV and V DS = − meV, respectively. The magnitude of the Coulomb blockade peaks reacha few nanoamperes. Note that the Coulomb peaks are significantly broadened when opening thefridge’s window even without THz illumination. This broadening may be due to the sensitivity ofthe GQD-based device to the electromagnetic environment. We observe that the magnitude and theshape of the Coulomb current peaks are not affected by the incoming THz photons. However, thecurrent peaks are shifted to lower V g when THz radiation is switched on. The shift, δV g , is as largeas ∼ I on − I off in the nanoampere range, as shown in 3(c) and (d).The I on − I off traces show consistently a bipolar behavior with a positive and a negative peak asa result of the peak current shift to lower V g . To get a more quantitative insight in the detectionprocess of the incoming THz photons, we calculate the net current through left and right leadsassuming that Γ R , Γ L < k B T with Γ R , Γ L representing the tunneling rate between the quantum dotand the left and right leads respectively. Without illumination, the current is given by I = − eA [ f F D ( α V g − eV ∗ DS ) − f F D ( α V g − eV ∗ DS )] (1)with A = Γ L Γ R Γ L +Γ R , α = C g C (cid:80) − C L , α = − C g C L , C g the capacitance from the GQD to its local gate, C L the capacitance from the GQD to left lead, C (cid:80) the sum of all capacitances on the GQD and f F D ( E ) = e E/ ( kBTe ) +1 the Fermi-Dirac distribution. The variables α = 0 . and α = 0 . areextracted from dark current measurements performed with a closed window (see SupplementaryNote 1). The dark current peaks around V g = 1 . V at V DS = 1 meV and V DS = 3 meVwithout THz illumination (black symbols) are well reproduced using equation (1) for T e = 10 K (black lines), as shown in Fig. 3(e) and (f) respectively. The parameter A only is adjustedbetween V DS = 1 meV and V DS = 3 meV since the tunneling rates depend on V DS . The good8greement between theoretical curves and measured dark DC current validate our description ofthe current flow through the GQD. By replacing V g with V g − δV g in equation (1), the DC currentpeaks under THz light illumination (red symbols) are remarkably well fitted (red lines) withoutchanging any other parameters (see Fig. 3(e) and (f)). This indicates that δV g is independent of V DS . Moreover, T e is kept constant with and without illumination indicating that the electronictemperature in the GQD is not significantly changed by the incoming THz photons, which is incontrast with previous works on GQD illuminated by THz photons. This analysis confirms thatthe THz detection process is fully described by an additional gate voltage δV g that leads to areduction of the GQD chemical potential µ dot with respect to those of the leads. The responsivityof the GQD-based device reaches ∼ A/W at T = 170 mK, demonstrating the high sensitivityfor THz photon detection of the GQD-based device at low temperature.We further investigate the photoresponse of the GQD-based device as a function of both V DS and V g reported as a I photo map in Fig. 4(b) for P = 10 pW. For comparison, we also report in Fig.4(a) the differential conductance stability diagram measured without THz illumination but withfridge’s window open. The Coulomb diamonds of the dark differential conductance are smallerthan those with the window closed (Fig. 2(a)), which may be because of the sensitivity of the addi-tion energy and also the capacitance of the GQD-based device to the electromagnetic environment.The dark differential conductance and I photo maps show very similar features such as commondiamond-shaped structures. The bipolar features observed only in the I photo map emphasized bythe positive and negative slopes of the Coulomb diamonds edges point out significant modificationof the resonance conditions induced by THz illumination for charging and discharging the GQD tothe respective leads. Thus, the I photo profile in the axis of V DS reflects the tuning, induced by THzlight illumination, of the chemical potential in the GQD, µ dot , with respect to those of the leads(Fig. 4(c)). We attribute the asymmetry of I photo with respect to V ∗ DS to different capacitancesfrom the GQD to the left and right leads. No distortion of the Coulomb diamonds is observedin the I photo map indicating that this chemical potential shift is independent of V g and V DS , i.e.,that is constant over the whole charge stability diagram. Thus, illuminating the GQD-based device9 .92 1.94 1.96 1.9801234 V* DS =2.35 mV I DC ( n A ) V g (V) V* DS =-1.65 mV I DC ( n A ) V g (V) a bc de f I DC ( n A ) V g (V)V* DS =1.35 mV T e =10 K d V g V* DS =3.35 mV I DC ( n A ) V g (V) d V g T e =10 K V* DS =2.35 mV I on - I o ff ( n A ) V g (V) V* DS =-1.65 mV I on - I o ff ( n A ) V g (V) Figure 3: (a) DC current Coulomb peaks as a function of V g at V ∗ DS = 2 . mV (a) and V ∗ DS = − . mV (b) with (red) and without (black) THz illumination. We defined V ∗ DS as the source-drain voltage applied to the GQD after subtracting the preamplifier offset voltage V = − . mV.The difference I on − I off as a function of V g at V ∗ DS = 2 . mV (c) and V ∗ DS = − . mV (d).DC current Coulomb peaks around V g = 1 . V at V ∗ DS = 1 . mV (e) and V ∗ DS = 3 . mV(f) with (red) and without (black) THz illumination. Data are reported by diamond symbols, andtheoretical fits using equation (1) are represented by plain lines.10 g (V) V D S ( m V ) V g (V) V DS (mV) -10 100 I photo (a.u.)G diff (2e /h) -10100 2 2.12.05 I pho t o ( a . u ) -0.010.010 1.9 1.95 20.511.5 V D S ( m V ) -10100 a b c Figure 4: (a) Dark differential conductance G as a function of V DS and V g with fridge’s windowopen. (b) Map of I photo as a function of V DS and V g . (c) Vertical cuts of I photo taken in the dashedbox of the photocurrent map (b)). The spectra, as a function of V DS , exhibit a change in signwhen the sign of V DS is changed, and this trend is inverted when the system pass from the left side(green) to the right side (blue) of the Coulomb diamonds.with incoherent THz photons results in a renormalization of the chemical potential of the GQD, µ dot , relative to those of the source and drain leads. Using the lever arm of . extracted fromthe dark differential conductance map with open fridge window, we deduce that δV g of ± . mV corresponds to a ∆ µ dot of ∼ . ± . meV. This very low-energy physical effect is clearlyobservable here owing to the extremely high-energy resolution provided by the low temperatureexperiment. Besides, the absence of any additional photocurrent lines induced by THz light intoor out of the Coulomb blockaded regions suggests that any intersublevel transition in the GQD orany photon-assisted tunneling effect (electrons exchange photons in the quantum dot) are drivenby the incident photons due to the incoherence of the THz radiation.Let us now discuss the physical mechanism responsible for the renormalization of the chemicalpotential of the GQD. THz photons, incoming from the incoherent and broadband source, are ab-sorbed by both the whole graphene area (including the quantum dot, the leads and gate electrodesthat are made in encapsulated graphene) and by the silicon substrate. Let us first consider if theabsorption of THz radiation by the graphene area could be responsible for the µ dot renormalization.THz photons are preferentially coupled to the leads due to their larger size and their linear disper-sion relation (in contrast to the quantum dot) that provides stronger absorption of the broad THz11adiation. At these frequencies the absorbed energy results in an increase of the electronic temper-ature and consequently, the chemical potentials of the graphene leads are reduced. (for detailssee Supplementary Note 5). The observed gate renormalization in the stability diagram can thenreflect a relative shift between the dot discrete levels and the chemical potential of the grapheneleads (see Figure S5(a)). From our analysis described in Supplementary Note 5, we estimate theincrease of the electronic temperature for ∆ µ dot = 0 . meV to be ∆ T e > K. However, our dataare qualitatively and quantitatively inconsistent with such temperature increase. Indeed, the currentpeaks with and without illumination are well reproduced using equation (1) for a constant temper-ature T e = 10 K; increasing T e to >
17 K would significantly broaden the current peak under THzillumination. Moreover, by resolving the heat flow, we estimate ∆ T e in our experimental conditionto remain below . K. Details of the calculation based on the Wiedemann-Franz law are providedin the Supporting Information (Supplementary Note 4). Consequently, even if a renormalization ofthe GQD chemical potential is expected from the absorption of the THz photons by the grapheneleads, its magnitude would be significantly lower than . meV and thus could not account forthe large photocurrent response of the GQD-based device.Another effect that can be pointed out is the photogating effect. It relies on the absorptionof THz photons in the silicon substrate. Absorption of typically . − . cm − in the THz spec-tral range have been recorded in high-resistivity silicon due to shallow impurity absorption (sincesilicon bandgap energy is high compared to the THz photon energy). This absorption processcreates photoexcited carriers in silicon from the ground states of impurities into the valence andconduction bands. This is in contrast with free carrier absorption that does not create free carriersand is extremely low in high-resistivity silicon ( α Drude = 0 . cm − due to the low free carrierconcentration, n = 10 cm − ). The photogating effect relies also on the existence of a band bend-ing at the SiO /Si interface due to charges in the oxide (fixed-oxide charge, oxide-trapped chargeand mobile ionic charge) and traps at the interface (interface-trapped charge). In our case of thesilicon substrate with residual N-type doping (see the Supporting Information, Experimental de-tails), the energy bands in silicon bend upward, leading to a triangular potential well for the holes12t the interface and a built-in electric field near the interface. The electric field can separate thephotoexcited carriers absorbed in silicon, electrons diffuse toward the bulk silicon, and holes ac-cumulate at the interface.
Holes are moreover trapped in the potential well. This accumulationof photon-generated holes at the SiO /Si interface provides an additional positive gate voltage bycapacitive coupling. In other words, the photogating effect would cause a negative shift in the I DS - V G characteristic under laser illumination. This interfacial photogating effect is qualitatively fullyconsistent with our observations. Indeed, we observe a negative shift of the I DS - V G characteristicunder THz illumination, independent of V DS and V G . In addition, the photocurrent is the differencebetween the source-drain currents in dark and illumination regime. δ � � m e V ) Incident power (pW) V g =1.99 VV g =1.96 VV g =1.91 VV g =1.87 V 0.00.20.40.60.81.0 I pho t o ( a . u . ) | Δ μ do t | Figure 5: | ∆ µ dot | and I photo as a function of the incident power P onto the GQD-based device for V DS = 2 mV and V g = 1 . V; V g = 1 . V, V g = 1 . V and V g = 1 . V.Several other mechanisms can be responsible for the conversion of absorbed THz photons intoa photocurrent in graphene-based devices such as the photovoltaic effect, the photothermoelectriceffect and the bolometric effect. However, all these mechanisms generate photocurrents or photo-voltages without any shift in gate voltage. Moreover, photothermoelectric and bolometric effectsrely on an increase of the electronic temperature that is extremely weak in this work due to the lowincident power as discussed previously. Consequently, we attribute the photocurrent originatingfrom the gate voltage shift measured when the GQD-based device is illuminated by THz photons13o the interfacial photogating effect. Since the Coulomb blockade current at low temperature isextremely sensitive to the gate voltage, the GQD acts as a very sensitive electrometer operating inthe THz spectral range. To further investigate the properties of the THz photoresponse, we mea-sure I photo and ∆ µ dot as a function of P , as displayed in Fig. 5. The same set of measurements isrepeated at several positions of the Coulomb diamonds map, i.e., for 4 different values of V g . Weobserve that I photo and | ∆ µ dot | increase monotonously as P is increasing with a nonlinear depen-dence. I photo and | ∆ µ dot | also start to saturate at high power. We found a very robust nonlineardependency between ∆ µ , I photo and the incident power for all V g . These tendencies are not com-patible with a ∆ µ dot induced by the intraband absorption of the THz photons in the graphene leadssince at such low incident THz electric field and low temperature, ∆ µ dot is expected to evolvelinearly with P (see Supporting Information). On the contrary, both the nonlinearity and satu-ration features are consistent with interfacial photogating effect. Indeed, as trapped photocarrierlifetime in silicon depends on the incident optical power, the photoexcited carrier density in thesteady-state regime contributing to the photogating effect is expected to evolve nonlinearly with P . The observed saturation can be attributed to a decrease of the height of the potential well at theSiO /Si interface as the THz incident power is increased. This feature has been observed in severalprevious works in graphene-based photodetectors dominated by the photogating effect and at-tributed to the trapped charges at the interface that induce an opposite build-in electric field. Thus,these power-resolved measurements provide an additional evidence that interfacial photogating isthe main physical mechanism involved in the THz photoresponse of the GQD-based device.In conclusion, we have investigated a hBN-encapsulated GQD in Coulomb blockade regimeunder THz illumination at low temperature. The hBN encapsulation enables to fabricate lowroughness GQD with excited states at energy ∼ and THz light-matter couplingby the insertion of the GQD in a THz resonator. Furthermore, owing to their great flexibility inelectronic states engineering, these large GQDs are very promising for the developments of THzemitters and detectors. Acknowledgement
The authors thank Bernard Plaçais for valuable discussions.
Funding : This project has receivedfunding from the European Research Council (ERC) under the European Unionâ ˘A ´Zs Horizon2020 research and innovation program (grant agreement No. 820133). K.W. and T.T. acknowledgesupport from the Elemental Strategy Initiative conducted by the MEXT, Japan ,Grant Number JP-MXP0112101001, JSPS KAKENHI Grant Numbers JP20H00354 and the CREST(JPMJCR15F3).
Author contributions : E.R. fabricated the sample and acquired and interpreted the experimentaldata. S.B, F.V. set up the cryogenic experiment. M.D. and T.K. set up the transport experimentaquisition. S.M. K.W. and T.T. participated in sample fabrication. J.M., T.K., R.F interpreted theexperimental data. S.M. contributed to THz power and absorption estimation, heat diffusion cal-culations and antenna FEM simulation. The manuscript was written and the data were interpretedby E.R., T.K., R.F., S.B., J.M., S.D., J.T. and T.K. provided insights into manuscript writing. Allwork was coordinated and overseen by J.M. All authors contributed to the discussion and to thefinal preparation of the manuscript.
Competing interests : The authors declare that they have nocompeting interest.
Data and materials availability : All data needed to evaluate the conclusionsin the paper are present in the paper and/or the Supporting Information. Additional data related tothis paper may be requested from the authors.
Supporting Information
The supporting information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.0c0180015 eferences (1) Güttinger, J.; Molitor, F.; Stampfer, C.; Schnez, S.; Jacobsen, A.; Dröscher, S.; Ihn, T.; En-sslin, K. Transport through graphene quantum dots.
Reports on Progress in Physics , ,:1753.(2) B.Trauzettel,; Bulaev, D. V.; Loss, D.; Burkard, G. Spin qubits in graphene quantum dots. Nature Physics , , 192.(3) Ponomarenko, L. A.; Schedin, F.; Katsnelson, M. I.; Yang, R.; Hill, E. W.; Novoselov, K. S.;Geim, A. K. Chaotic Dirac billiard in graphene quantum dots. Science , , 356–358.(4) Zhao, S.; Lavie, J.; Rondin, L.; Orcin-Chaix, L.; Diederichs, C.; Roussignol, P.; Chassag-neux, Y.; Voisin, C.; Mullen, K.; Narita, A.; Campidelli, S.; Lauret, J. S. Single photonemission from graphene quantum dots at room temperature. Nature Communications , , 3470.(5) Volk, C.; Neumann, C.; Kazarski, S.; Fringes, S.; Engels, S.; Haupt, F.; Muller, A.;Stampfer, C. Probing relaxation times in graphene quantum dots. Nature Communications , , 073113.(6) Sheng, W.; Korkusinski, M.; Güçlü, A.; Zielinski, M.; Potasz, P.; Kadantsev, E. S.;Voznyy, O.; Hawrylak, P. Electronic and optical properties of semiconductor and graphenequantum dots. Frontiers of Physics , , 328–352.(7) Koppens, F.; Mueller, T.; Avouris, P.; Ferrari, A. C.; Vitiello, M. S.; Polini, M. Photodetectorsbased on graphene, other two-dimensional materials and hybrid systems. Nature Nanotech-nology , , 780.(8) Vicarelli, L.; Vitiello, M.; Coquillat, D.; Lombardo, A.; Ferrari, A. C.; Knap, W.; Polini, M.;Pellegrini, V.; Tredicucci, A. Graphene field-effect transistors as room-temperature terahertzdetectors. Nature materials , , 865.169) Mittendorff, M.; Wendler, F.; Malic, E.; Knorr, A.; Orlita, M.; Potemski, M.; Berger, C.;Heer, W. A. D.; Schneider, H.; Helm, M., et al. Carrier dynamics in Landau-quantizedgraphene featuring strong Auger scattering. Nature Physics , , 75.(10) Gierz, I.; Petersen, J.; Mitrano, M.; Cacho, C.; Turcu, I.; Springate, E.; A. Stöhr, A. K.;Starke, U.; Cavalleri, A. Snapshots of non-equilibrium Dirac carrier distributions in graphene. Nature materials , , 1119.(11) Yadav, D.; Tamamushi, G.; Watanabe, T.; Mitsushio, J.; Tobah, Y.; Sugawara, K.; Dubi-nov, A.; Satou, A.; Ryzhii, M.; Ryzhii, V., et al. Terahertz light-emitting graphene-channeltransistor toward single-mode lasing. Nanophotonics , , 741–752.(12) Fatimy, A. E.; Myers-Ward, R.; Boyd, A. K.; Daniels, K. M.; Gaskill, D. K.; Barbara, P.Epitaxial graphene quantum dots for high-performance terahertz bolometers. Nature nan-otechnology , , 335.(13) Fatimy, A. E.; Nath, A.; Kong, B. D.; Boyd, A.; Myers-Ward, R.; Daniels, K.; Jadidi, M.;Murphy, T.; Gaskill, D.; Barbara, P. Ultra-broadband photodetectors based on epitaxialgraphene quantum dots. Nanophotonics , , 735.(14) Güçlü, A. D.; Potasz, P.; Hawrylak, P. Excitonic absorption in gate-controlled graphene quan-tum dots. Phys. Rev. B , , 155445.(15) Schnez, S.; Molitor, F.; Stampfer, C.; GÃijttinger, J.; Shorubalko, I.; Ihn, T.; Ensslin, K.Observation of excited states in a graphene quantum dot. Applied Physics Letters , ,012107.(16) Mics, Z.; Tielrooij, K.; Parvez, K.; Jensen, S.; Ivanov, I.; Feng, X.; Müllen, K.; Bonn, M.;Turchinovich, D. Thermodynamic picture of ultrafast charge transport in graphene. Naturecommunications , , 7655. 1717) Shimatani, M.; Yamada, N.; Fukushima, S.; Okuda, S.; Ogawa, S.; Ikuta, T.; Maehashi, K.High-responsivity turbostratic stacked graphene photodetectors using enhanced photogating. Applied Physics Express , , 122010.(18) Fang, H.; Hu, W. Photogating in Low Dimensional Photodetectors. Advanced Science , , 1700323.(19) Dai, J.; Zhang, J.; Zhang, W.; Grischkowsky, D. Terahertz time-domain spectroscopy charac-terization of the far-infrared absorption and index of refraction of high-resistivity, float-zonesilicon. J. Opt. Soc. Am. B , , 1379.(20) Palik, E. D. Handbook of Optical Constants of Solids ; New York: Academic, 1998.(21) Jiang, Y.; Vijayraghavan, K.; Jung, S.; Demmerle, F.; Boehm, G.; Amann, M.; Belkin, M. A.External cavity terahertz quantum cascade laser sources based on intra-cavity frequency mix-ing with 1.2–5.9 THz tuning range.
Journal of Optics , , 094002.(22) Hubers, H.-W.; Pavlov, S.; Rummeli, M.; Zhukavin, R.; Orlovab, E.; Riemann, H.; Shastin, V.Terahertz emission from silicon doped by shallow impurities. Physica B: Condensed Matter , , 232.(23) Guo, X.; Wang, W.; Nan, H.; Yu, Y.; Jiang, J.; Zhao, W.; Li, J.; Zafar, Z.; Xiang, N.; Ni, Z.,et al. High-performance graphene photodetector using interfacial gating. Optica , ,1066.(24) Liu, Y.; Xia, Q.; He, J.; Liu, Z. Direct Observation of High Photoresponsivity in PureGraphene Photodetectors. Nanoscale Research Letters , , 93.(25) Ogawa, S.; Shimatani, M.; Fukushima, S.; Okuda, S.; Kanai, Y.; Ono, T.; Matsumoto, K.Broadband photoresponse of graphene photodetector from visible to long-wavelength in-frared wavelengths. Optical Engineering , , 1.1826) Hafez, H. A.; Kovalev, S.; Deinert, J.; Mics, Z.; Green, B.; Awari, N.; Chen, M.; German-skiy, S.; Lehnert, U.; Teichert, J., et al. Extremely efficient terahertz high-harmonic genera-tion in graphene by hot Dirac fermions. Nature , , 507.(27) Vinh, N. Q.; Redlich, B.; van der Meer, A. F. G.; Pidgeon, C. R.; Greenland, P. T.;Lynch, S. A.; Aeppli, G.; Murdin, B. N. Time-Resolved Dynamics of Shallow AcceptorTransitions in Silicon. Phys. Rev. X , , 011019.(28) Luo, F.; Zhu, M.; Tan, Y.; Sun, H.; Luo, W.; Peng, G.; Zhu, Z.; Zhang, X.-A.; Qin, S. Highresponsivity graphene photodetectors from visible to near-infrared by photogating effect. AIPAdvances , , 115106.(29) Kawano, Y.; Fuse, T.; Toyokawa, S.; Uchida, T.; Ishibashi, K. Terahertz photon-assistedtunneling in carbon nanotube quantum dots. Journal of Applied Physics ,103