Interaction of massless Dirac electrons with acoustic phonons in graphene at low temperatures

Kubakaddi, S. S.

doi:10.1103/physrevb.79.075417

Cited by 140 publications

(327 citation statements)

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“…We observe a peak in S at a gate voltage roughly corresponding to the electron-hole puddle carrier density n*, below which the value of S decreases due to cancellation of n-type and p-type Λ the phonon mean free path, and µ p is the phonon-limited carrier mobility 29 . We expect at high temperature Λ ~ 1/T, µ p ~ 1/nT [26], and thus S p ~ n/T, in sharp contrast to the experimental observation of additional thermopower independent of n and increasing with T (roughly proportional to T 2 at high T).…”

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confidence: 87%

Ambipolar Surface State Thermoelectric Power of Topological Insulator Bi₂Se₃

et al. 2014

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We measure gate-tuned thermoelectric power of mechanically exfoliated Bi 2 Se 3 thin films in the topological insulator regime. The sign of the thermoelectric power changes across the charge neutrality point as the majority carrier type switches from electron to hole, consistent with the ambipolar electric field effect observed in conductivity and Hall effect measurements. Near charge neutrality point and at low temperatures, the gate dependent thermoelectric power follows the semiclassical Mott relation using the expected surface state density of states, but is larger than expected at high electron doping, possibly reflecting a large density of states in the bulk gap. The thermoelectric power factor shows significant enhancement near the electron-hole puddle carrier density ~ 0.5 x 10 12 cm -2 per surface at all temperatures. Together with the 2 expected reduction of lattice thermal conductivity in low dimensional structures, the results demonstrate that nanostructuring and Fermi level tuning of three dimensional topological insulators can be promising routes to realize efficient thermoelectric devices.KEYWORDS Topological Insulators, Thermoelectric Power, Ambipolar Electric Field Effect, Bismuth Selenide, Charge Transfer Doping.The efficiency of thermoelectric devices is determined by the thermoelectric figure of merit ZT = σS 2 T/κ, where S is thermoelectric power (Seebeck coefficient) and σ and κ are electrical and thermal conductivity respectively. For a given thermal conductivity (typically dominated by phonons) and temperature, ZT is determined by the electronic structure of a material through the power factor σS 2 . Nanostructuring has long been seen as a promising route to increase ZT both through decreasing κ via phonon boundary scattering, and increasing the power factor through confinement-induced band structure effects 1 . The discovery that important thermoelectric materials Bi 1-x Sb x and Bi 2 (Se,Te) 3 [2][3][4] are in fact 3D topological insulators (TI) has triggered new directions to improve ZT via nanostructuring. The 3D TIs have an insulating bulk but metallic surface states with spin-momentum helicity which cannot be localized by nonmagnetic disorder 4,5 . Recent theoretical calculations 6,7 show that significant enhancement of ZT is expected in 3D TIs particularly in thin film geometry where top and bottom surfaces can hybridize and form a surface gap 8 .Thermoelectric power is also of great interest in understanding the electronic transport properties of Dirac electronic systems 9 , thus measurement of the thermoelectric properties of TI surface states can elucidate details of the electronic structure of the ambipolar nature of 3 topological metallic surface states that cannot be probed by conductance measurements alone 10 .Although there have been theoretical investigations of thermal and thermoelectric properties of Dirac materials including graphene and TIs 6,7,[11][12][13][14][15] and thermoelectric transport in carbon nanotubes 16 and graphene 9,17-19 have been studied expe...

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confidence: 87%

Ambipolar Surface State Thermoelectric Power of Topological Insulator Bi₂Se₃

et al. 2014

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“…13 The acoustic phonon cooling in graphene is a fairly weak mechanism which allows carriers to attain temperatures far in excess of that of the lattice, 13,14 and at low temperatures in the Bloch-Grüneisen limit this process is strongly temperature dependent. This "hot-carrier" effect can be described using the theory of Kubakaddi,25 which has been shown experimentally to predict the energy loss rates very accurately. 13,14 Using this theory, we can calculate the effective minimum carrier temperature T e,min that can be obtained for a given device for each current.…”

Section: Maximum Currentsmentioning

confidence: 99%

“…Using the numerical values suggested by Kubakaddi 25 we calculate α = 5.36 × 10 −18 W K −4 / √ n, where n is in units of 10 12 cm −2 . Figure 4 shows data from one of our epitaxial samples which exhibits a saturation in the measured value of L ϕ with decreasing temperature.…”

Section: Maximum Currentsmentioning

confidence: 99%

“…Further evidence for electron temperature saturation in graphene has been observed recently through measurements of bolometric response in noise power 26,27 and resistivity 28 which require energy loss rates similar to those used here. 13,14,25 By way of illustration we calculate the currents required to achieve a given carrier temperature for three different examples of typical samples used here and in the literature which we present in Fig. 5.…”

Section: Maximum Currentsmentioning

confidence: 99%

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Weak localization scattering lengths in epitaxial, and CVD graphene

et al. 2012

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Weak localization in graphene is studied as a function of carrier density in the range from 1 × 10 11 cm −2 to 1.43 × 10 13 cm −2 using devices produced by epitaxial growth onto SiC and CVD growth on thin metal film. The magnetic field dependent weak localization is found to be well fitted by theory, which is then used to analyze the dependence of the scattering lengths L ϕ , L i , and L * on carrier density. We find no significant carrier dependence for L ϕ , a weak decrease for L i with increasing carrier density just beyond a large standard error, and a n −1/4 dependence for L * . We demonstrate that currents as low as 0.01 nA are required in smaller devices to avoid hot-electron artifacts in measurements of the quantum corrections to conductivity.

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“…The arguments above are valid under the condition T ≥ T BG . At temperatures lower than T BG , another regime of standard electron-phonon interaction without phase space constraints will play an important role [22,23]. T BG is estimated from k B T BG ¼ ℏsk F (s is the sound velocity in graphene) to be 12 K for the low density curves and 24 K for the high density curve in Fig.…”

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Competing Channels for Hot-Electron Cooling in Graphene

et al. 2014

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We report on temperature-dependent photocurrent measurements of high-quality dual-gated monolayer graphene p-n junction devices. A photothermoelectric effect governs the photocurrent response in our devices, allowing us to track the hot-electron temperature and probe hot-electron cooling channels over a wide temperature range (4 to 300 K). At high temperatures (T > T Ã ), we found that both the peak photocurrent and the hot spot size decreased with temperature, while at low temperatures (T < T Ã ), we found the opposite, namely that the peak photocurrent and the hot spot size increased with temperature. This nonmonotonic temperature dependence can be understood as resulting from the competition between two hot-electron cooling pathways: (a) (intrinsic) momentum-conserving normal collisions that dominates at low temperatures and (b) (extrinsic) disorder-assisted supercollisions that dominates at high temperatures. Gate control in our high-quality samples allows us to resolve the two processes in the same device for the first time. The peak temperature T Ã depends on carrier density and disorder concentration, thus allowing for an unprecedented way of controlling graphene's photoresponse. Slow electron-lattice thermal equilibration is responsible for a plethora of new optoelectronic [1][2][3][4], transport [5,6], and thermoelectronic [7,8] phenomena in graphene. The wide temperature ranges (lattice temperature, 4 to 300 K) and long spatial scales in which hot carriers proliferate make graphene an ideal candidate for electronic energy transduction and numerous applications. Central to these are the unusual electron-phonon scattering pathways that dominate the cooling channels of graphene [7,[9][10][11][12][13].Unlike other materials, electron-lattice cooling at room temperature in graphene is dominated by an extrinsic threebody process [10]. This occurs when acoustic phonon emission is assisted by disorder scattering, called "supercollisions" (SC). SC dominates over the intrinsic momentumconserving emission of acoustic phonons (normal collisions [NC]) for high temperatures. At low temperatures, the intrinsic process is expected to be dominant. However, the intrinsic NC process has never been experimentally observed before [11,14].Here, we report on temperature-dependent spatially resolved photocurrent measurements of high-quality monolayer graphene (MLG) p-n junction devices. At the p-n interface, the photothermoelectric (PTE) effect dominates the photocurrent generation [2-4] and exhibits a nonmonotonic temperature dependence. We demonstrate that both the magnitude and spatial extent of the photoresponse are highly enhanced at an intermediate temperature T Ã , indicating the coexistence of momentum-conserving NC cooling and disorder-assisted SC mechanisms. NC (SC) cooling dominates below (above) T Ã , which can be tuned by varying the charge and impurity densities. In addition, we observed that the photoresponse at the graphene-metal (G-M) interface is also dominated by the PTE effect with a similar temperature-de...

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Interaction of massless Dirac electrons with acoustic phonons in graphene at low temperatures

Cited by 140 publications

References 36 publications

Ambipolar Surface State Thermoelectric Power of Topological Insulator Bi₂Se₃

Ambipolar Surface State Thermoelectric Power of Topological Insulator Bi₂Se₃

Weak localization scattering lengths in epitaxial, and CVD graphene

Competing Channels for Hot-Electron Cooling in Graphene

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Interaction of massless Dirac electrons with acoustic phonons in graphene at low temperatures

Cited by 140 publications

References 36 publications

Ambipolar Surface State Thermoelectric Power of Topological Insulator Bi2Se3

Ambipolar Surface State Thermoelectric Power of Topological Insulator Bi2Se3

Weak localization scattering lengths in epitaxial, and CVD graphene

Competing Channels for Hot-Electron Cooling in Graphene

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Ambipolar Surface State Thermoelectric Power of Topological Insulator Bi₂Se₃

Ambipolar Surface State Thermoelectric Power of Topological Insulator Bi₂Se₃