How does heat travel through glass when it is thinned to the width of a single atom? A research team including Sai C. Yelishala, Yunxuan Zhu, and P. M. Martinez has measured the thermal conductance of atomic-scale junctions of amorphous silicon dioxide (silica) and found it reaches about 40% of the theoretical upper limit. Thermal conductance describes the heat flow across a junction when its two ends differ in temperature by 1 K (1°C). The representative value was 380 pW/K, about 40% of the 951 pW/K theoretical upper limit for three vibrational channels used as the comparison. The work was published on October 13, 2026 in Nature Nanotechnology as a peer-reviewed paper (DOI: 10.1038/s41565-026-02308-9), and was covered by the University of Colorado Boulder on November 10 and the Autonomous University of Madrid on November 12. The study clarifies heat transport through extremely thin glass junctions and presents a new way to detect electrically insulating atomic junctions using heat signals.
Detecting Electrically Insulating Atomic Junctions with Heat
The team used a 95 µm-long glass microbeam with an integrated heater and thermometer, and brought it into contact with a glass surface in ultra-high vacuum. When the microbeam was slowly pulled away from the contact, the junction connecting the two gradually thinned and eventually broke. The researchers continuously measured the heat flow passing through the junction during this process. According to the Autonomous University of Madrid, the pull-off operation was repeated about 2,000 times, and the thermal conductance most frequently observed just before breakage was determined. Note that the roughly 2,000 figure is the number of repeated measurement operations, not 2,000 independent samples.
In the experiment, the probe temperature was held at about 380 K, with a temperature difference of about 90 K from the surroundings. To detect tiny temperature changes, the team used niobium nitride, whose electrical resistance varies with temperature. When heat moves through the glass junction, the probe temperature changes, so reading that change reveals the formation and breaking of the junction. The 380 K here is the temperature of the heated probe, which differs from the 335 K used below to calculate the theoretical limit.
In past experiments on metallic atomic junctions and single-molecule junctions, the state of a junction was tracked by measuring the current flowing between conductive electrodes. Silica, however, is an electrical insulator, so that method cannot easily be applied directly. Silica is also used as an insulating layer in computer chips; even though it does not conduct electricity, it does conduct heat. The team exploited this property, using heat flow as a feedback signal so that atomic-scale junctions can be detected without relying on current. Details of the apparatus and detection method are in the paper's supplementary information.
What Does 40% of the Theoretical Limit Mean?
The measured thermal conductance of 380 pW/K corresponds to about 40% of the 951 pW/K theoretical upper limit, which applies if three vibrational channels transmit heat perfectly. Understanding this ratio requires distinguishing heat transport by atomic vibrations from its theoretical ceiling. In Note 13 of the supplementary information, the thermal conductance quantum, the theoretical reference for heat carried by a single vibrational channel, is calculated using the average probe–sample temperature of 335 K. This value is 317 pW/K, written as .
In an atomic-scale junction, one can consider three vibrational channels in total: one longitudinal vibration along the junction and two transverse vibrations perpendicular to it. Under ideal conditions in which these channels are not scattered and transmit all heat perfectly, the upper limit of thermal conductance is $3G_0$. At 335 K, this corresponds to 951 pW/K. The representative value obtained in this experiment, 380 pW/K, is about $1.2G_0$, or roughly 40% of the three-channel theoretical limit.
| Quantity compared | Value at 335 K | Category |
|---|---|---|
| Representative junction thermal conductance | 380 pW/K ($1.2G_0$) | Measured |
| Thermal conductance quantum for one channel | 317 pW/K () | Theoretical reference |
| Upper limit if three channels transmit perfectly | 951 pW/K ($3G_0$) | Theoretical limit |
The figures in the table are based on Note 13 of the paper's supplementary information. Dividing 380 pW/K by 951 pW/K gives about 0.40, yielding the result of roughly 40% of the theoretical limit.
Importantly, this 40% is not a performance improvement over conventional glass materials, but the ratio of the measured value to the theoretical limit under the same temperature conditions. Thermal conductance expresses how easily heat flows through an entire junction and is measured in W/K. It differs from thermal conductivity (W/(m K)), which expresses how readily a material itself conducts heat, so it does not mean that glass's thermal conductivity has improved by 40%. Also, although the measured value exceeds the single-channel thermal conductance quantum , it remains below the combined three-channel limit of $3G_0$, so it does not contradict theory.
The measurements also carry uncertainty. Including errors from measurement and calibration, the representative thermal conductance is 380 ± 43 pW/K, or in units of the thermal conductance quantum. When effects of estimating the distribution peak and the contribution of near-field radiation are conservatively considered, the total uncertainty widens to . Meanwhile, the standard deviation, which expresses the junction-to-junction spread in measured values, is about $0.22G_0$, a separate metric from the estimation error of the representative value. These figures are not presented as 95% confidence intervals, and the scatter of the measured values itself must be evaluated separately from how accurately the representative value can be estimated.
Why Heat Passes Through Glass With Disordered Atoms
What stands out in this study is that even amorphous silica, whose atoms lack regular arrangement, showed relatively large thermal conductance in a junction one atom wide. Combining experiments with atomic-level simulations, the team interprets this as showing that, in such extremely thin junctions, atomic disorder does not necessarily strongly limit heat transport. The key concept here is the Debye frequency, which characterizes the upper limit of atomic vibration frequencies. The silicon and oxygen that make up silica are lighter than gold and can vibrate at higher frequencies, a property thought to be relevant to heat transport in atomic-scale junctions.
To investigate this mechanism, the team built atomic models using molecular dynamics simulations. First, a 30 × 30 × 20 nm model was melted and rapidly cooled to create an amorphous structure, from which a probe with a tip radius of 10 nm and a substrate 4 nm thick were extracted. The model before contact analysis contained 132,258 atoms; this is the scale of the model used in the calculation, not the number of samples examined experimentally.
In non-equilibrium molecular dynamics simulations, two thermal baths set at 380 K and 290 K were used, applying the same 90 K temperature difference as in the experiment. The heat flow through four cross-sections within the junction was then analyzed by frequency, and the results from each cross-section agreed within numerical noise. The team interprets this as supporting ballistic transport, in which atomic vibrations travel through the junction with almost no scattering. The paper describes this as coherent transport, in which the phase of the vibrations is preserved, and cites the agreement of heat flow across the four cross-sections as one piece of evidence. The calculations also considered not only a single atomic junction but cases in which two or three junctions are connected in parallel.
However, it was the simulations that examined the atomic structure and the heat flow through each cross-section inside the junction in detail; atomic vibrations were not directly imaged in the experiment. The study explains the measured thermal conductance through a transport mechanism derived from atomic models. Because no experiment varied atomic disorder independently or tested its effect across various materials and dimensions, the interpretation cannot be applied to all amorphous materials. What has been shown so far is the possibility that atomic vibrations carry heat efficiently in the atomic-scale silica junctions examined here.
A New Experimental Platform for Heat Transport in Insulators
To confirm the reproducibility of the results, the team also ran additional experiments using a different microdevice and probe. In about 500 pull-off measurements, the peak of the thermal conductance distribution was , consistent with the $1.2G_0$ found in the first experiment. The Autonomous University of Madrid also explains that it confirmed the results using a different probe and sample. Furthermore, unsupervised classification that did not include breakage values or manually assigned labels as input also identified peaks or shoulders near $1.2G_0$ in multiple groups of measurement records. These results support the conclusion that the observed thermal conductance does not originate only from a few exceptional measurement records.
However, these checks confirm reproducibility within the same research team and must be distinguished from replication by independent groups. Whether similar results can be obtained with different instruments and experimental conditions remains a subject for future verification.
The significance of the new method also lies in widening the range of materials whose atomic-scale heat transport can be studied. When different materials are joined, such as a metal electrode and a molecule, differences in their vibrational properties affect how heat is transmitted. By contrast, if the junction and both sides are made of the same silica, heat transport can be studied under conditions that avoid the vibrational mismatch that arises at boundaries between dissimilar materials. The technique of detecting atomic junctions with heat signals rather than current becomes a new foundation for studying atomic-scale heat transport in insulators, which has been difficult to measure.
In a November 10, 2026 release from the University of Colorado Boulder, Longji Cui pointed out that thermal management inside electronic devices is extremely important and stressed the need to understand how heat flows in nanoscale devices. The team also hopes the results could eventually lead to research on devices that control heat flow, such as thermal diodes and thermal transistors. However, what has been demonstrated here is a technique for measuring the thermal conductance of atomic junctions; no device that directs heat flow in one direction or switches it externally has been realized. If independent replications and measurements with other materials and junction structures advance, and reveal under what conditions heat transport by atomic vibrations can be controlled, it could lead to the design of new heat-control devices using insulators.