## 1 Introduction  
In the field of frequency metrology, a paradigmatic shift has occurred with the invention of optical Frequency Combs [1; 2; 3] (optical FCs), whose emission is a superposition of a series of quasi-monochromatic electromagnetic waves (the FC modes) that can be fully controlled via two parameters, i.e., repetition rate and offset frequency. To this purpose, a necessary and non-trivial requirement is the existence of a fixed (i.e., constant over time) phase relation among all the modes, defining the overall coherence of the source. In this way, the modes of such lasers can be used as a precise ruler in the visible and near-infrared (IR) domain, providing a direct link between optical and microwave/radio frequencies [4]. Thanks to these outstanding features, FCs are nowadays key tools in many fields of fundamental and applied research [5]. Moreover, in recent years, FCs' application possibilities have been migrated to less common spectral regions (mid- and far-IR, ultraviolet), while vigorous efforts have been spent trying to miniaturize these sources, achieving the most interesting results with mainly three different technologies: Microresonators [6; 7], interband cascade lasers [8], and quantum cascade lasers frequency combs (QCL-FCs) [9]. However, among these, only QCL-FCs are able to access the THz portion of the electromagnetic spectrum [10; 11]. This THz (or far-infrared) window, ranging from 0.1 to 10 THz, is a largely under-exploited section of the electromagnetic spectrum, and it has been historically referred to as \"THz gap\". However, in the latest years, high-precision molecular spectroscopy in this region has attracted a lot of attention from the scientific community, as many intriguing molecules present characteristic rotational and ro-vibrational THz transitions that, as a consequence, build up a novel fingerprint region [12]. For this reason, in order to be suitable for metrological-grade THz spectroscopic applications, a quest for high performance laser sources has been initiated [13]. These lasers sources should be ideally spectrally pure, broadband, or widely tunable, traceable against a primary frequency standard, emitting high-power, and--last but not least--compact and easy to operate for in situ or field operation. In this respect, single-frequency THz QCLs might be ideal candidates. In fact, these current-driven semiconductor lasers rely on inter-sub-band transitions in quantum wells, and therefore their emission frequency can be quantum engineered. Moreover, they show relatively high optical power [14; 15; 16; 17; 18; 19] and very high spectral purity [20; 21; 22]. These features have been exploited for high precision THz molecular spectroscopy [23; 24] by phase referencing a QCL to a THz FC [25; 26]. Unfortunately, this approach still shows two main limitations: Firstly, the limited mode-hop-free tunability range of the single device (few hundred MHz) is not suited for broadband spectroscopy; secondly, the need for cryogenic cooling has profoundly hampered QCLs' widespread use. In fact, despite the extreme miniaturization of the sources, the need of a liquid helium cryostat, of the corresponding liquid helium dewar, or (alternatively) the need of expensive low mechanical noise pulse tube refrigerators, make the experimental setup bulky, unfriendly to operate, and unfit for field deployment, even if first attempts have been recently pioneered [17; 27; 28]. The first problem can be efficiently solved by replacing QCL single frequency devices with QCL-FCs based on broadband Fabry-Perot (FP) devices with low group velocity dispersion [9; 10]. In fact, thanks to degenerate and non-degenerate four wave mixing non-linear processes inside the device active region, the cavity longitudinal modes can be injection-locked, resulting in a coherent FC emission.