The goal of this project is to find the topological phases of matter in AlAs quantum wells where other than spin, there is an additional degree of freedom, the valley degree of freedom.

In the first phase of our quest, we found the nematic order in the half-filled Landau levels, a charge order that is related to high-temperature superconductivity and the quantum Hall effect. We observed an unexpected interplay between the nematic order and the spin of the system and found that the ferromagnetism stabilizes the nematic order. This finding is very fundamental and offers a way to control the charge ordering via controlling the spin. [Link to the article]

In the second stage, we provided evidence for a valley tunable topological phase of matter that can be of potential use in topological quantum computation. Just by tuning the valley occupancy, the topological properties can be switched on/off. Strikingly, such a phase was theoretically predicted to be very unstable. Our measurements, however, proved otherwise. [Link to the article]

Finally, we add another degree of freedom to the topological phase in AlAs. This additional degree of freedom is the width of the charge distribution. By tuning the charge distribution, we can turn on and off the topological phase of matter that we observe. Thus, we achieve unprecedented control over the topological phase that we can tune independently by in-plane strain (that controls the valley) and in-plane magnetic field (that controls the charge distribution).

The enigmatic even-denominator fractional quantum Hall state at ν = 5/2 in the first-excited Landau level has been of enormous interest recently thanks to the possibility that it can host Majorana quasi-particles with non-Abelian statistics, and therefore be of use for topological quantum computation. This state is commonly explained theoretically in a paired, fully-spin-polarized composite fermion (CF) picture. There is, however, no direct and conclusive experimental evidence for the existence of CFs near ν = 5/2 or for an underlying fully-spin-polarized Fermi sea.

In this work, we address precisely these two very fundamental questions regarding the origin of the 5/2 state: Are CFs present near ν = 5/2, and are they fully spin polarized? Our geometric resonance measurements, which directly probe the Fermi sea and wavevector of CFs, provide unambiguous and conclusive positive answers to these questions. We emphasize that our technique is simple, and yet most direct and quantitative. Moreover, our measurements are minimally invasive as they do not involve, e.g., exposure of the sample to illumination/radiation, or to in-plane magnetic fields that might alter the ground state of the electron system. Also, they do not rely on any fitting schemes or parameters. [Link to the article]

My brief overview of this work [My blog post]

Two-dimensional electron systems exposed to high magnetic fields generate emergent quasiparticles, the so-called composite fermions (CFs), whose physics is fundamentally different from electrons. They are intimately linked to different many-body phases, the most intriguing of which is the metallic phase in the half- or quarter-filled Landau levels (LLs). In our work, we unveil remarkable properties of four-flux CFs (4CFs) at the quarter-filled LL (ν = ¼) via direct measurements of the Fermi wavevector. While the theory of the two-flux CFs (2CFs) is an ongoing topic of intense debate and controversy, particularly in the context of particle-hole symmetry and a newly proposed Dirac CF theory, very little is known about the four-flux 4CFs. Via our geometric resonance experiments, we find that the 4CFs are very different from the 2CFs, namely, 4CFs show no particle-hole asymmetry (in zero parallel magnetic field). Strikingly, however, in the presence of a parallel magnetic field, a mysterious asymmetry appears in their Femi sea anisotropy and effective mass between ν > ¼ and ν < ¼. In particular, our data suggest different effective masses on the two sides of ν = ¼ with the high-field side having a much larger mass. These results hint intricate, unexplored emergent symmetries around ν = ¼. [Link to the article]

Two-dimensional electron systems confined to InAs quantum wells have been widely studied for its amazing prospects in topological quantum computation. However, in order to realize such prospects, observation of the fractional quantum Hall effect, which is the signature of a topological phase of matter, is one of the prerequisites. Even though the InAs material system has been around for a long time, search for fractional quantum Hall effect has not been successful before our study. Here, we report the first observation of such fractional quantum Hall effect and conclude the search.

Our observation places InAs material platform in an elite list of a very few material systems (for example, GaAs, AlAs, Graphene, Si/Ge) where fractional quantum Hall states have been observed. [Link to the article]

[Article] [arXiv]

Here we studied the subtle competition between different many-body phases at a Landau level filling ν= 3/2 in tilted magnetic fields. At large tilt angles (θ), a nematic phase replaces the isotropic compressible Fermi sea at ν = 3/2 if the quantum well has a symmetric charge distribution. When the charge distribution is made asymmetric, instead of the stripe phase, an even-denominator fractional quantum state appears at ν = 3/2 in a range of large θ, and reverts back to a compressible state at even higher θ. This evolution results from the significant mixing of the excited and ground-state Landau levels of 2D hole systems in tilted fields.

[Link to the article]