Credit: Wikipedia
Credit: Wikipedia

 

 

 

 

Oscillators are necessary for many technologies, most notably, to send information wirelessly. Current technology has broken through to the THz regime (1012 oscillations per second), and there is always a drive to push the limit further. As our grasp over quantum phenomena becomes more realizable in the laboratory, novel devices are being introduced regularly. An exciting branch of materials being studied today are topological insulators. Research performed by Brian Casas and the Xia group here at UCI have created an oscillator out of a topological insulator. The particular crystal being studied is SmB6.

Topological insulators are a type of crystal that conduct electricity only on the surface while the bulk remains highly resistive. The oscillator designed here oscillates in and out of conductive surface states. As an electron flows through a crystal, many mechanisms can cause this electron to scatter from its original path: a defect in the crystal, a lattice vibration (phonon), even a small magnetic impurity can scatter an electron. The more scattering that exists in the crystal, the higher the electrical resistance. The surface states of topological insulators can only hold electrons with certain features, in the case of SmB6, a specific spin moving in a certain direction. Since these states must be occupied by an electron with these characteristics, it is difficult to scatter the electron in or out of its state. The scattering mechanisms are strongly suppressed, and the states are “topologically protected”. In SmB6, the bulks’ resistance is dominated by a magnetic interaction called the Kondo effect, a particular scattering mechanism related to the electrons’ spin. This phenomenon occurs only at low temperatures for this material.

At low temperatures (~4 K) where the resistance of the bulk is very high, surface conduction dominates. Above this temperature, the surface becomes much more resistive, and most of the conduction will occur through the bulk of the crystal. As electrical current passes through the surface, the exterior of the crystal will heat up due to Joule heating. This continues until the surface heats above a certain threshold temperature, after which the current will then pass primarily through the bulk. This gives the surface a chance to cool off. Once the surface temperature falls below that threshold again, conduction will move back to the surface. This oscillation of heating and cooling will yield a voltage oscillation due to Ohm’s law (δV=IδR). Driving the crystal with a constant current, the surface’s resistance will change due to self-heating while it is in its conducting state, and cooling while it is in its resistive state. While these voltage oscillations are not a new measurement, the thermal oscillations are. This is a necessary measurement to confirm the validity of the theory governing this type of crystal. Diagrams of the device and sample data are shown below (figure 1).

 

 

 

 

 

 

 

 

 

 

 

Figure 1. a) shows a cartoon representation of the device b) shows a zoom-in of the thermometry element c) shows a circuit diagram of the measurement. The right-hand side shows sample temperature and voltage measurements of this device.

The novelty in this article is the struggle in obtaining the temperature measurement itself. The difficulty lies in the ability to measure a trustworthy temperature quick enough. Especially with low temperatures, it is easy to alter the system just by measuring it. Very low temperatures require special thermometers, which are typically made by passing current through a known metal and measuring the resistance (which is a known function of temperature). However, the energy dissipated in the resistor causes self-heating of the sample. Great care must be taken in choosing a thermometer. Two important factors in the reliability of a temperature measurement are the heat capacity and the thermal conductivity of the thermometer. A thermometer with a large heat capacity has a long settling time to equilibrate with its environment. Similarly, a thermometer attached to the system with a low thermal conductivity will take a long time to equilibrate as well. The thermometer needs to be relatively small compared to the sample, and it needs to respond quick enough to measure any kind of oscillation.

Additionally, in order to observe this phenomenon in the simplest case, the sample needs to be a single crystal. Scientists can make entire careers out of the ability to grow single crystals; this is not a simple task. The single crystal grown and used is about 2 mm3. The thermometer needs to be relatively small compared to the sample crystal, and it needs to be mounted in a way to ensure good thermal conductivity.

Even the voltage produced by the oscillation is low, in the microvolt range. In order to measure periodic potentials this low, a lock-in amplifier is needed. This amplifier “locks-in” to a certain frequency and amplifies signals only with that frequency. This dramatically reduces background noise (external sources of noise can couple into the system at many different frequencies). Locking-in to the frequency of the potential across the crystal, temperature oscillations are measured and shown to be in-phase with the potential. The frequency scales with the surface area of the sample, “This is one fact we observed that pushed us to expect the surface conduction contributed substantially to the observed effect,” says Casas regarding previous experiments (figure 2).

Figure 2. Samples of different surface area are measured and plotted against the response frequency. Figure from Alex Stern, Dmitry K. Efimkin, Victor Galitski, Zachary Fisk, and Jing Xia. Phys. Rev. Lett. 116, 166603

 

 

 

 

 

 

 

 

 

Once the data was acquired, further refinement was still needed. The signal is periodic, so one can average over many periods to further average out the noise. Some of the post-processing data is seen below (Figure 3). The signal is seen despite the background noise after averaging over two periods. Collecting data for hours reveals an easily analyzable signal. “My favorite part of this project was developing our lab’s ability to perform temporally resolved thermal measurements. This work included performing resistance measurements on the surface thermometer nearly 5000 times per minute. Then I created a customized signal processing script to extract our signal from beneath the noise level of the measurement,” said Casas regarding his work.

Figure 3. a) shows the raw data averaged over 2, 20, 200, and 2000 periods of oscillation. b) shows the voltage and temperature measurement to be in-phase.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

More research of course still needs to be done for this to become a realizable technology, but this is an excellent proof of concept, and solidifies the theory governing this type of material. Brian intends to apply for postdoctoral research positions at a national lab before pursuing a career in academia. The publication can be found here, “Direct observation of surface-state thermal oscillations in SmB6 oscillators,” Phys. Rev. B. 97, 035121 (2018).

Post by Mackenzie Turvey, graduate student working on his PhD in Condensed Matter Experiment at UCI.