The Curious Behavior of Topological Insulators

IQIM hosts a Summer Research Institute that invites high school Physics teachers to work directly with staff, students, and researchers in the lab.  Last summer I worked with Marcus Teague, a highly intelligent and very patient Caltech Staff Scientist in the Yeh Group, to help set up an experiment for studying exotic material samples under circularly polarized light.  I had researched, ordered, and assembled parts for the optics and vacuum chamber.  As I returned to Caltech this summer, I was eager to learn how the Yeh Group had proceeded with the study.

Yeh group (2017): I am the one on the front-left of the picture, next to Dr. Yeh and in front of Kyle Chen. Benjamin Fackrell, another physics teacher interning at the Yeh lab, is all the way to the right.

The optics equipment I had researched, ordered, and helped to set up last summer is being used currently to study topological insulator (TI) samples that Kyle Chien-Chang Chen, a doctoral candidate, has worked on in the Yeh Lab.  Yes, a high school Physics teacher played a small role in their real research! It is exciting and humbling to have a connection to real-time research.

Quartz quarter-wave plates are important elements in many experiments involving light. They convert linearly polarized light to circularly polarized light.

Kyle receives a variety of TI samples from UCLA; the current sample up for review is Bismuth Antimony Telluride $\mathrm{(BiSb)}_2\mathrm{Te}_3$.  Depending on the particular sample and the type of testing, Kyle has a variety of procedures to prep the samples for study.  And this summer, Kyle has help from visiting Canadian student Adrian Llanos. Below are figures of some of the monolayer and bilayer structures for topological insulators studied in the lab.

Pictures of samples from UCLA

Under normal conditions, a topological insulator (TI) is only conductive on the surface. The center of a TI sample is an insulator. But when the surface states open an energy gap, the surface of the TI becomes insulating. The energy gap is the amount of energy necessary to remove an electron from the top valence band to become free to move about.  This gap is the result of the interaction between the conduction band and valence band surface states from the opposing surfaces of a thin film. The resistance of the conducting surface actually increases. The Yeh group is hoping that the circularly polarized light can help align the spin of the Chromium electrons, part of the bilayer of the TI.  At the same time, light has other effects, like photo-doping, which excites more electrons into the conduction bands and thus reduces the resistance. The conductivity of the surface of the TI changes as the preferentially chosen spin up or spin down is manipulated by the circularly polarized light or by the changing magnetic field.

A physical property measurement system.

This interesting experiment on TI samples is taking place within a device called a Physical Property Measurement System (PPMS).  The PPMS is able to house the TI sample and the optics equipment to generate circularly polarized light, while allowing the researchers to vary the temperature and magnetic field.  The Yeh Group is able to artificially turn up the magnetic field or the circularly polarized light in order to control the resistance and current signal within the sample.  The properties of surface conductivity are studied up to 8 Tesla (over one-hundred thousand times the Earth’s magnetic field), and from room temperature (just under 300 Kelvin) to just below 2 Kelvin (colder than outer space).

Right-Hand-Rule used to determine the direction of the magnetic (Lorentz) force.

In the presence of a magnetic field, when a current is applied to a conductor, the electrons will experience a force at a right angle to the magnetic field, following the right-hand rule (or the Physics gang sign, as we affectionately call it in my classroom).  This causes the electrons to curve perpendicular to their original path and perpendicular to the magnetic field. The build up of electrons on one end of the conductor creates a potential difference. This potential difference perpendicular to the original current is known as the ordinary Hall Effect.  The ratio of the induced voltage to the applied current is known as the Hall Resistance.

Under very low temperatures, the Quantum Hall Effect is observed. As the magnetic field is changed, the Hall Voltage increases in set quantum amounts, as opposed to gradually. Likewise, the Hall Resistance is quantized.  It is a such an interesting phenomenon!

For a transport measurement of the TI samples, Kyle usually uses a Hall Bar Geometry in order to measure the Hall Effect accurately. Since the sample is sufficiently large, he can simply solder it for measurement.

Transport Measurements of TI Samples follow the same setup as Quantum Hall measurements on graphene: Current runs through electrodes attached to the North/South ends of the sample, while electron flow is measured longitudinally, as well as along the East/West ends (Hall conductance).

What is really curious is that the Bismuth Antimony Telluride samples are exhibiting the Hall Effect even when no external magnetic field is applied!  When the sample is measured, there is a Hall Resistance despite no external magnetic field. Hence the sample itself must be magnetic.  This phenomenon is called the Anomalous Hall Effect.

According to Kyle, there is no fancy way to measure the magnetization directly; it is only a matter of measuring a sample’s Hall Resistance. The Hall Resistance should be zero when there is no Anomalous Hall Effect, and when there is ferromagnetism (spins want to align in the direction of their neighbors), you see a non-zero value.  What is really interesting is that they assume ferromagnetism would break the time-reversal symmetry and thus open a gap at the surface states.  A very strange behavior that is also observed is that the longitudinal resistance increases gradually.

Running PPMS

Typically the quantum Hall Resistance increases in quantum increments.  Even if the surface gap is open, the sample is not insulating because the gap is small (<0.3 eV); hence, under these conditions this TI is behaving much more like a semiconductor!

Next, the group will examine these samples using the Scanning Tunneling Microscope (STM).  The STM will be able to provide local topological information by examining 1 micron by 1 micron areas.  In comparison, the PPMS research with these samples is telling the story of the global behavior of the sample.  The combination of information from the PPMS and STM research will provide a more holistic story of the behavior of these unique samples.

I am thrilled to see how the group has used what we started with last summer to find interesting new results.  I am fascinated to see what they learn in the coming months with the different samples and STM testing. And I am quite excited to share these applications with my students in the upcoming new school year.  Another summer packed with learning!