nanoscale views: Thermometry at the mK scale, revisited
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Saturday, June 06, 2026
Thermometry at the mK scale, revisited
It's been almost a decade since I last wrote about this topic, and a preprint on the arXiv this week is a good jumping off point for more discussion.<br>Thermometers are devices that allow us to take some physical observable and infer temperature. I wrote about the nature of temperature 17 years ago (!!!) in a way that did not completely satisfy me or most of my readers, so maybe I should take another crack at it. Temperature is a statistically emergent quantity (it doesn't make sense to talk about the temperature of a single particle in isolation) that tells us whether there will be a net flow of energy when a system we care about is brought into contact (able to exchange energy via microscopic degrees of freedom that we aren't tracking, like jiggling of atoms bumping into each other or emission/absorption of radiated photons) with some other system. Temperature is closely related to the energy stored in the microscopic degrees of freedom of a system. Our definition of \(T\) is such that there will be a spontaneous, net, averaged flow of energy from hot (a high \(T\) system) to cold (a low \(T\) system). Two systems in contact at the same \(T\) will still exchange energy microscopically, but on average there will be no net flow, and in the absence of other complications, these systems are said to be in thermal equilibrium.<br>Measuring temperature is serious business with a fascinating history. The kelvin is, as of 2019 (see, told you it was time to revisit this), defined by using the fundamental definitions of the kilogram, the meter, and the second, and by declaring that Boltzmann's constant \(k_{\mathrm{B}}\) is exactly 1.380 649 ×10−23 J/K or equivalently kg m2/s2K. In practice, there are fixed, measurable reference points that help make sure temperatures are calibrated. For example, the triple point of water is a standard reference point at 273.16 K. In total, there are two internationally agreed temperature scales, ITS-90 (pdf) and PLTS-2000 (pdf), that include a total of 21 reference points spanning from 0.9 mK to 1357.77 K.<br>It's extremely helpful to have primary thermometers, where the physics involved in some measurable quantity are so well known that it is possible to analyze a measurement and directly pull out \(T\) based only on the data and known fundamental and numerical constants. The preprint linked at the top of this post does an extremely careful comparison of two nanostructure-based approaches.<br>Adapted from Fig. 1 from here.A Coulomb blockade thermometer consists of a series of tiny metal/insulator/metal junctions. The energy required to move a single electron across one such junction is proportional to \(e^2/C\), where \(C\) is the capacitance of the junction structure. When the temperature is low, that charging energy scale can exceed the thermal energy scale, \(k_{\mathrm{B}}T\), so that the conductance \(dI/dV\) of the junction near zero applied voltage is suppressed compared to its high voltage and high temperature value. Remarkably, the shape of \(dI/dV\) as a function of \(V\) is universal, independent of details, and for an array of \(N\) junctions in series, its width is \(5.44 N k_{\mathrm{B}}T/e\). (top panel of figure)
In a single tunnel junction, it is possible to measure Johnson-Nyquist noise, the current (voltage) fluctuations that take place across the device due to thermally driven motion of the electrons in equilibrium, and the charge shot noise, the fluctuations due to the statistical variations in the arrival times of the electrons. The theoretical expression for the noise as a function of bias voltage is known (Eq. (2) in the paper). (bottom panel of figure).<br>The authors find that the two thermometric approaches are quantitatively consistent to better than 2.5% between 20 mK and 235 mK, and the biggest uncertainty comes from knowing the effective bandwidth of the noise measurement. This is a characteristically careful, clean work from this Finnish group, who are world experts in the field.
Posted by<br>Douglas Natelson
at<br>2:51 PM
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Douglas Natelson
I am a physics professor at Rice University. My group uses nanoscale tools to address open questions in condensed matter physics, the study of the remarkable emergent properties of materials. Views expressed here are my own; they do not represent the views of my employer or any other entity.
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Thermometry at the mK scale, revisited
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