Using a block of three separated solid elements, a thermal source and drain together with a gate made of an insulator-metal transition material exchanging near-field thermal radiation, we introduce a nanoscale analog of a field-effect transistor that is able to control the flow of heat exchanged by evanescent thermal photons between two bodies. By changing the gate temperature around its critical value, the heat flux exchanged between the hot body (source) and the cold body (drain) can be reversibly switched, amplified, and modulated by a tiny action on the gate. Such a device could find important applications in the domain of nanoscale thermal management and it opens up new perspectives concerning the development of contactless thermal circuits intended for information processing using the photon current rather than the electric current.

We present measurements of the near-field heat transfer between the tip of a thermal profiler and planar material surfaces under ultrahigh vacuum conditions. For tip-sample distances below 10 −8 m our results differ markedly from the prediction of fluctuating electrodynamics. We argue that these differences are due to the existence of a material-dependent small length scale below which the macroscopic description of the dielectric properties fails, and discuss a corresponding model which yields fair agreement with the available data. These results are of importance for the quantitative interpretation of signals obtained by scanning thermal microscopes capable of detecting local temperature variations on surfaces.PACS numbers: 44.40.+a, 03.50.De, 78.20.Ci Radiative heat transfer between macroscopic bodies increases strongly when their spacing is made smaller than the dominant wavelength λ th of thermal radiation. This effect, caused by evanescent electromagnetic fields existing close to the surface of the bodies, has been studied theoretically already in 1971 by Polder and van Hove for the model of two infinitely extended, planar surfaces separated by a vacuum gap [1], and re-investigated later by Loomis and Maris [2] and Volokitin and Persson [3,4]. While early pioneering measurements with flat chromium bodies had to remain restricted to gap widths above 1 µm [5], and later studies employing an indium needle in close proximity to a planar thermocouple remained inconclusive [6], an unambiguous demonstration of near-field heat transfer under ultrahigh vacuum conditions and, thus, in the absence of disturbing moisture films covering the surfaces, could be given in Ref. [7].The theoretical treatment of radiative near-field heat transfer is based on fluctuating electrodynamics [8]. Within this framework, the macroscopic Maxwell equations are augmented by fluctuating currents inside each body, constituting stochastic sources of the electric and magnetic fields E and H. The individual frequency components j(r, ω) of these currents are considered as Gaussian stochastic variables. According to the fluctuationdissipation theorem, their correlation function reads [9]where E(ω, β) = ω/ exp(β ω) − 1 , with the usual inverse temperature variable β = 1/(k B T ); the angular brackets indicate an ensemble average. Moreover, ǫ ′′ (ω) denotes the imaginary part of the complex dielectric function ǫ(ω) = ǫ ′ (ω) + iǫ ′′ (ω). It describes the dissipative properties of the material under consideration, which is assumed to be homogeneous and non-magnetic. Thus, Eq. (1) contains the idealization that stochastic sources residing at different points r, r ′ are uncorrelated, no matter how small their distance may be. Applied to a material occupying the half-space z < 0, facing the vacuum in the complementary half-space z > 0, these propositions can be evaluated to yield the electromagnetic energy density in the distance z above the surface, giving [10]dκ ρ E (ω, κ, β, z) + ρ H (ω, κ, β, z)

We study the near-field heat exchange between hyperbolic materials and demonstrate that these media are able to support broadband frustrated modes which transport heat by photon tunnelling with a high efficiency close to the theoretical limit. We predict that hyperbolic materials can be designed to be perfect thermal emitters at nanoscale and derive the near-field analog of the blackbody limit.PACS numbers: 44.40.+a;81.05.Xj A black body is usually defined by its property of having a maximum absorptivity and therefore also a maximum emissivity by virtue of Kirchhoff's law [1]. The energy transmission between two black bodies having different temperatures obey the well-known Stefan-Boltzmann law. This law sets an upper limit for the power which can be transmitted by real materials, but it is itself a limit for the far-field only, since it takes only propagating modes into account. In terms of the energy transmission between two bodies the black body case corresponds to maximum transmission for all allowed frequencies ω and all wave vectors smaller than ω/c, where c is the vacuum light velocity. This means that all the propagating modes are perfectly transmitted across the separation gap.In the near-field regime, i.e., for distances smaller than the thermal wavelength λ th = c/k B T (2π is Planck's constant, k B is Boltzmann's constant, and T is the temperature) the radiative heat flux is not due to the propagating modes, but it is dominated by evanescent waves [2-4] and especially surface polaritons as confirmed by recent experiments [5][6][7][8][9][10][11]. The common paradigm is that the largest heat flux can be achieved when the materials support surface polaritons which will give a resonant energy transfer restricted to a small frequency band around the surface mode resonance frequency [3,4,12,13]. Many researchers have tried to find materials enhancing the nanoscale heat flux due to the contribution of the coupled surface modes by using layered materials [14,15] In the present work the aim is twofold: (i) We show, that materials supporting a broad band of evanescent frustrated modes can outperform the heat flux due to surface modes. This provides new possibilies for designing materials giving large nanoscale heat fluxes which could be used for thermal management at the nanoscale for instance. (ii) We derive a general limit for the heat flux carried by the frustrated modes and show that it is, in fact, the near-field analog of the usual black body limit. For the evanescent modes a near field analog of a black body can be defined in the sense that the energy transmission coefficient must be equal to one for all frequencies and all wave vectors larger than ω/c. With today's nanofabrication techniques it is possible to manufacture artificial materials such as photonic band gap materials and metamaterials which exhibit very unusual material properties like negative refraction [23]. Due to such properties they are considered as good candidates for perfect lensing [24,25], for repulsive Casimir forces [26][27][28][...

In this Letter a N -body theory for the radiative heat exchange in thermally non equilibrated discrete systems of finite size objects is presented. We report strong exaltation effects of heat flux which can be explained only by taking into account the presence of many body interactions. Our theory extends the standard Polder and van Hove stochastic formalism used to evaluate heat exchanges between two objects isolated from their environment to a collection of objects in mutual interaction. It gives a natural theoretical framework to investigate the photon heat transport properties of complex systems at mesoscopic scale.PACS numbers: 44.40.+a, 03.50.De The photon heat tunneling between two bodies has attracted much attention in the last decades since it has been predicted that the heat flux (HF) can exceed, at nanoscale, the far field limit set by Planck's black body law by several orders of magnitude [1,2]. This discovery has opened the way to promising technologies for energy conversion and data storage as for example the near-field thermophotovoltaics [3,4] and the plasmon assisted nanophotolitography [5]. This dramatic increase is generally speaking due to the contribution of evanescent modes, which are not accounted for in the StefanBoltzmann law and become only important if the distance between the objects is smaller than the thermal wavelength [6]. The detailed mechanisms which lead to such an enhancement are nowadays for a number of geometries and materials well understood [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and recent experiments [23][24][25][26][27] have confirmed all theoretical predictions both qualitatively and quantitatively.However, some questions of fundamental importance remain unsolved in complex mesoscopic systems. Indeed, so far, only the HF between two objects [6-9] out of equillibrium has been considered, but how does the heat transport for a collection of individual objects in mutual interaction look like? The collective effects in such many particle systems has not been explored yet, although it is of prime importance for understanding the different heat propagation regimes in disordered systems, determining the thermal percolation tresholds in random nanocomposites structures and studying thermal effects due to the presence of localized modes in such systems.Inside a discrete system of bodies maintained at different temperatures the local thermal fluctuations give rise to oscillations of partial charges which, in turn, radiate their own time dependent electric field in the surrounding medium. These thermally generated fields interact with the nearby bodies and modify through different cross interactions all these primary fields to generate secondary fields which in turn affect the radiated fields and so on. Generally speaking, this problem belongs to the vast category of many-body problems which constitute the theoretical framework of numerous branches of physics (celestial mechanics,condensed matter physics, atomic physics, quantum chemistry). A general th...

We present a formulation of the nanoscale radiative heat transfer (RHT) using concepts of mesoscopic physics. We introduce the analog of the Sharvin conductance using the quantum of thermal conductance. The formalism provides a convenient framework to analyse the physics of RHT at the nanoscale. Finally, we propose a RHT experiment in the regime of quantized conductance.PACS numbers: 44.40.+a;73.23.-b It has been discovered in the late sixties that the RHT between two metallic parallel plates can be larger than predicted using the blackbody radiation form [1][2][3]. It is now known that this anomalous RHT is due to the contribution of evanescent waves and becomes significant when the distance separating the interfaces becomes smaller than the thermal wavelength λ th = c kBT where is Planck's constant, k B is Boltzmann's constant, c is the light velocity and T is the temperature. Using the framework of fluctuational electrodynamics [4], Polder and van Hove (PvH) were able to derive a general form of the RHT accounting for the optical properties of the media [5]. Since this seminal contribution, several reports have been published in the literature [6][7][8][9][10][11]. A quantum-mechanical derivation [12] has confirmed these results obtained within the framework of fluctuational electrodynamics. While the first papers considered metals, it has been realized that the RHT at the nanoscale can be further enhanced for dielectrics due to the contribution of surface phonon polaritons [13,14]. Recent reviews can be found in Refs. [15][16][17][18].The first attempts to measure a heat flux between metallic surfaces at room temperature and micrometric distances have proved to be inconclusive [19,20]. Experiments in the nanometric regime have clearly demonstrated the transfer enhancement [21,22]. Yet the lack of good control of the tip geometry did not allow quantitative comparison with theory. More recent experiments [23,24] are performed using silica taking advantage of the flux enhancement due to the resonant contribution of surface phonon polaritons. A good agreement between PvH theory and experiments has been reported [24].The purpose of this paper is to establish a link between the PvH form of the radiative heat flux and the formalism of transport in mesoscopic physics. It will help to develop a more physical understanding of the RHT at the nanoscale, which also clarifies how losses and non-local effects determine the maximal achievable heat flux [10]. Finally, we will show that this reformulation raises the prospect of observing quantized conductance for systems with sizes on the order of the thermal wavelength λ th .We start our discussion with the PvH form of the RHT. We consider a vacuum gap with width d separating two homogeneous half spaces labeled medium 1 and 2 [see Fig. 1 a)]. Then, the heat flux is [5,16] ( 1) where κ = (k x , k y ) and γ = k 2 0 − κ 2 are the parallel and normal wave vector, Θ(ω,is the mean energy of a harmonic oscillator, k 0 = ω/c, r 1,2 j are the usual Fresnel factors for s-or p-polar...

Heat is transferred by radiation between two well-separated bodies at temperatures of finite difference in vacuum. At large distances the heat transfer can be described by black body radiation, at shorter distances evanescent modes start to contribute, and at separations comparable to inter-atomic spacing the transition to heat conduction should take place. We report on quantitative measurements of the near-field mediated heat flux between a gold coated near-field scanning thermal microscope tip and a planar gold sample at nanometre distances of 0.2–7 nm. We find an extraordinary large heat flux which is more than five orders of magnitude larger than black body radiation and four orders of magnitude larger than the values predicted by conventional theory of fluctuational electrodynamics. Different theories of phonon tunnelling are not able to describe the observations in a satisfactory way. The findings demand modified or even new models of heat transfer across vacuum gaps at nanometre distances.

A thermal diode transports heat mainly in one preferential direction rather than in the opposite direction. This behavior is generally due to the non-linear dependence of certain physical properties with respect to the temperature. Here we introduce a radiative thermal diode which rectifies heat transport thanks to the phase transitions of materials. Rectification coefficients greater than 70% and up to 90% are shown, even for small temperature differences. This result could have important applications in the development of futur contactless thermal circuits or in the conception of radiative coatings for thermal management.PACS numbers: 44.05.+e, 12.20.-m, 44.40.+a, 78.67.-n Asymmetry of heat transport with respect to the sign of the temperature gradient between two points is the basic definition of thermal rectification [1,2] which is at the heart of a variety of applications as for example in thermal regulation, thermal modulation, and heat engines. This unusual thermal behavior has opened the way to new concepts for manipulating the heat flow similarly to the electric current in electronic devices. Usually this manipulation finds its origin in the non-linear behavior of materials with respect to the temperature, which, for the thermal rectification, breaks the symmetry of transfer when the temperature gradient is reversed. The effectiveness of the thermal rectification can be measured by means of the rectification coefficient η =where Φ F and Φ R denote the heat flux in the forward and reverse operating mode, respectively. Different solidstate thermal diodes have been conceived during the last decade from various mechanisms (see [3] for a review on phononic rectification), including nonlinear atomic vibrations [4], nonlinearity of the electron gas dispersion relation in metals [5], direction dependent Kapitza resistances [6] or dependence of the superconducting density of states and phase dependence of heat currents flowing through Josephson junctions [7].More Recently, photon-mediated thermal rectifiers [8,9] have been proposed to tune near-field heat exchange using materials with thermally dependent optical resonances. Since then, numerous mechanisms have been introduced to manipulate the non-radiative heat exchanges [10][11][12][13] between two bodies. Recently a far-field thermal rectifier has been proposed on the basis of spectrally selective micro or nanostructured thermal emitters [14] as previously developed to design coherent thermal sources [15] and to enhance the near-field thermal emission of composite structures [16]. However, so far only relatively weak radiative and non-radiative thermal rectifications have been highlighted with these mecha-

A general fluctuational-electrodynamic theory is developed to investigate radiative heat exchanges between objects which are assumed small compared with their thermal wavelength (dipolar approximation) in N -body systems immersed in a thermal bath. This theoretical framework is applied to study the dynamic of heating/cooling of three-body systems. We show that many-body interactions allow to tailor the temperature field distribution and to drastically change the time scale of thermal relaxation processes.