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 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][...