quantum transport in topological matter

*Jorrit de Boer is a PhD student in the research group Interfaces and Correlated Electrons. His supervisor is prof.dr.ir. A. Brinkman from the Faculty of Science and Technology.*

Solids have always been a powerful platform for the study of interesting phenomena due to the periodicities that allow for the use of simple models in describing the governing physics. Now that topology has been added as an extra dimension to the modeling toolkit, new ways of characterizing materials opened up. In this thesis, I used magnetotransport, nonlocal transport and conductance spectroscopy to characterize strongly correlated and topological materials.

We started off by studying the electronic band structure of the LaAlO_{3}/SrTiO_{3} interface using magnetotransport measurements and analysis. Using a Drude two-band fit, we were able to identify the character of the charge carriers and to find that their top-gate voltage dependencies show highly unusual behavior; the d_{xy} carrier density appears to decrease with increasing top-gate voltage. We modelled the band structure of the interface using a self-consistent Schrödinger-Poisson solver. Only when electron-electron interactions are included, which cause a redistribution of the charge carriers as soon as the d_{xz,yz} band becomes populated, can we accurately reproduce the unusual gate-voltage dependence of the carrier density. Because the band structure itself is dependent on the charge carrier distribution, it becomes clear that the band structure is gate-tunable. This highlights the influence of electron-electron interactions on the electronic structure of the LaAlO_{3}/SrTiO_{3} interface.

Another material with interesting electronic properties, is the 3D dirac semimetal BiSb_{3%}. In this work, I performed magnetotransport measurements, Shubnikov-de Haas analysis, extracted surface carrier densities from angle-resolved photoemission spectroscopy data and combined the results with a Drude multiband fit to unravel the electronic structure of BiSb_{3%}. Through this analysis it becomes clear that the 3D Dirac electron pockets are occupied by high-mobility electrons, with the Fermi level close to the Dirac point. These Dirac electrons are shunted by a high-mobility bulk hole pocket and by low-mobility surface electron and hole states. Nevertheless, we found that the Dirac electrons contribute significantly to electronic transport.

In order to study the detailed effects of magnetic fields on topological materials, we focus on the effects of adding a Zeeman term to the model Hamiltonian. To this end, I re-evaluated some simplifications made in the derivations of the Drude model and pinpointed the scattering time and Fermi velocity as Zeeman-term dependent factors in the conductivity tensor. The driving mechanisms here are the alignment of spins, which allows for backscattering, and a significant change to the Fermi velocity by the opening of a hybridization gap. After considering 2D and 3D Dirac states, as well as 2D Rashba surface states and the quasi-2D bulk states of 3D topological insulators, I found that only the 2D Dirac states on the surfaces of 3D topological insulators produce considerable magnetoresistance effects to be noticable in experiments. As this effect is only pronounced at energies (with respect to the Dirac point) comparable to the Zeeman energy, this effect may be used as an indication of the Fermi level being in the vicinity of the Dirac point.

A tell-tale sign of topological Dirac semimetals is the chiral magnetic effect (CME), which shows up as negative magnetoresistance in parallel electric and magnetic fields. In this work, we measured negative longitudinal magnetoresistance (LMR) in BiSb_{3%} in a local measurement setup. This negative LMR may originate from the CME, but also from other effects such as current jetting. To provide conclusive evidence for the topological nature of BiSb_{3%}, we measured the CME nonlocally in nanostructured exfoliated flakes. In the setup, we locally applied parallel electric and magnetic fields to one side of the structure, where we chirally polarized the material, and measured the diffused chiral polarization at multiple distances from the source channel, where it coupled to the parallel magnetic field to build up a measurable potential difference. From the dependence of the CME strength on the distance from the source channel, we extracted a chiral charge diffusion length of 1.07 μm. The temperature dependence of this chiral charge diffusion length indicates that chiral charge relaxation mainly occurs through inelastic processes, as is expected for a Dirac semimetal with Dirac cones widely separated in momentum space, such as BiSb_{3%}.

Next, we combined the 3D Dirac semimetallic nature of BiSb_{3%} with induced superconductivity to artificially establish topological superconductivity in a Josephson junction. First, we followed a straighforward procedure of matching wavefunctions at the interfaces to model the Josephson junction and showed that 4π-periodic Andreev bound states are expected to arise as a signal of topological superconductivity. Then, through the inverse AC-Josephson effect, we measured a distinct Shapiro-step pattern with a missing first step, which is a consequence of the presence of 4π-periodic bound states. The junction critical current, subjected to a magnetic field parallel to the current, shows oscillating behavior with varying magnetic field strength, associated with finite momentum pairing. The Zeeman shift in momentum space corresponds to a large g-factor of 800, confirming that a large part of the supercurrent is carried by Dirac electrons. In addition, we showed that the unusually large 4π-periodic component that we observe in the supercurrent, can be understood by considering Fabry-Perot type resonances that allow 4π-periodic modes non-perpendicular to the interface, in combination with a finite temperature that provides a cut-off energy for the observability of an opened spectral gap.

While artificially induced topological superconductivity may be stable enough to be harnessed as the functional part of qubits, there is no law of physics that prevents materials from hosting intrinsic topological superconductivity. Here we investigated PdTe_{2}, a 3D Dirac semimetal that becomes superconducting below T_{C} ≈ 1.6 K, by means of in-plane conductance spectroscopy on normal metal - insulator - superconductor nanostructures to look for possible signs of topological *p*-wave superconductivity. Devices of varying resistance were measured and some datasets were tempting to wrongfully interpret as signs of *p*-wave superconductivity. Here, the culprit was current biasing low-resistance devices that likely contain pinholes or weak spots in the barrier, which showed up as critical current effects, mimicking *p*-wave like conductance spectra. Taking this into account and focusing on the devices with larger barrier resistances, the overall trend in the measured conductance spectra pointed towards *s*-wave superconductivity being the dominant pairing mechanism in PdTe_{2}.

Based on all these results, several conclusions come to light. First of all, while the LaAlO_{3}/SrTiO_{3 }system may not be used as the functional part of future electronics, the results of this thesis demonstrate that the material is undoubtedly highly interesting and serves as an interesting platform for fundamental research into the interplay of intriguing phenomena. The use of nanometer-scale exfoliated DSM flakes can be viewed in a similar way: while flakes may not be suitable for use in functional applications, they are indispensable for fundamental research. This is because of the high quality materials that can be obtained with relative ease. To make the transition from fundamental proof-of-principle applications (such as described in this work) to functional electronics, as seen from an engineering perspective, high quality thin films are required.