Abstract: What are the ground states of an interacting, low-density electron system? In the absence of disorder, it has long been expected that as the electron density is lowered, the exchange energy gained by aligning the electron spins should exceed the enhancement in the kinetic (Fermi) energy, leading to a (Bloch) ferromagnetic transition. At even lower densities, another transition to a (Wigner) solid, an ordered array of electrons, should occur. Experimental access to these regimes, however, has been limited because of the absence of a material platform that supports an electron system with very high quality (low disorder) and low density simultaneously. Here we explore the ground states of interacting electrons in an exceptionally clean, two-dimensional electron system confined to a modulation-doped AlAs quantum well. The large electron effective mass in this system allows us to reach very large values of the interaction parameter rs, defined as the ratio of the Coulomb to Fermi energies. As we lower the electron density via gate bias, we find a sequence of phases, qualitatively consistent with the above scenario: a paramagnetic phase at large densities, a spontaneous transition to a ferromagnetic state when rs surpasses 35, and then a phase with strongly nonlinear current-voltage characteristics, suggestive of a pinned Wigner solid, when rs exceeds ≃ 38. However, our sample makes a transition to an insulating state at rs ≃ 27, preceding the onset of the spontaneous ferromagnetism, implying that besides interaction, the role of disorder must also be taken into account in understanding the different phases of a realistic dilute electron system.

[Article] [arXiv]

Abstract: In 1929, Felix Bloch suggested that the paramagnetic Fermi sea of electrons should make a spontaneous transition to a fully magnetized state at very low densities, because the exchange energy gained by aligning the spins exceeds the enhancement in the kinetic energy. However, experimental realizations of this effect have been hard to implement. Here, we report the observation of an abrupt, interaction-driven transition to full magnetization, highly reminiscent of Bloch ferromagnetism. Our platform utilizes the two-dimensional Fermi sea of composite fermions near half-filling of the lowest Landau level. We measure the Fermi wave vector—which directly provides the spin polarization—and observe a sudden transition from a partially spin-polarized to a fully spin-polarized ground state as we lower the density of the composite fermions. Our theoretical calculations that take Landau level mixing into account provide a semi-quantitative account of this phenomenon.

[Article]

Abstract: A fundamental concept in physics is the Fermi surface, the constant-energy surface in momentum space encompassing all the occupied quantum states at absolute zero temperature. In 1960, Luttinger postulated that the area enclosed by the Fermi surface should remain unaffected even when electron-electron interaction is turned on, so long as the interaction does not cause a phase transition. Understanding what determines the Fermi surface size is a crucial and yet unsolved problem in strongly interacting systems such as high-T_c superconductors. Here we present a precise test of the Luttinger theorem for a two-dimensional Fermi liquid system where the exotic quasiparticles themselves emerge from the strong interaction, namely, for the Fermi sea of composite fermions (CFs). Via direct, geometric resonance measurements of the CFs’ Fermi wave vector down to very low electron densities, we show that the Luttinger theorem is obeyed over a significant range of interaction strengths, in the sense that the Fermi sea area is determined by the density of the minority carriers in the lowest Landau level. Our data also address the ongoing debates on whether or not CFs obey particle-hole symmetry, and if they are Dirac particles. We find that particle-hole symmetry is obeyed, but the measured Fermi sea area differs quantitatively from that predicted by the Dirac model for CFs.

[Article] [arXiv]

Abstract: Two-dimensional interacting electrons exposed to strong perpendicular magnetic fields generate emergent, exotic quasiparticles phenomenologically distinct from electrons. Specifically, electrons bind with an even number of flux quanta, and transform into composite fermions (CFs). Besides providing an intuitive explanation for the fractional quantum Hall states, CFs also possess Fermi-liquid-like properties, including a well-defined Fermi sea, at and near even-denominator Landau-level filling factors such as ν = 1/2 or 1/4. Here, we directly probe the Fermi sea of the rarely studied four-flux CFs near ν = 1/4 via geometric resonance experiments. The data reveal some unique characteristics. Unlike in the case of two-flux CFs, the magnetic field positions of the geometric resonance resistance minima for ν < 1/4 and ν > 1/4 are symmetric with respect to the position of ν=1/4. However, when an in-plane magnetic field is applied, the minima positions become asymmetric, implying a mysterious asymmetry in the CF Fermi sea anisotropy for ν < 1/4 and ν > 1/4. This asymmetry, which is in stark contrast to the two-flux CFs, suggests that the four-flux CFs on the two sides of ν = 1/4 have very different effective masses, possibly because of the proximity of the Wigner crystal formation at small ν.

[Article] [arXiv]

Abstract: The fractional quantum Hall state (FQHS) observed at a half-filled Landau level in an interacting two-dimensional electron system (2DES) is among the most exotic states of matter as its quasiparticles are expected to be Majorana excitations with non-Abelian statistics. We demonstrate here the unexpected presence of such a state in a novel 2DES with a strong band-mass anisotropy. The FQHS we observe has unusual characteristics. While its Hall resistance is well quantized at low temperatures, it exhibits highly anisotropic in-plane transport resembling compressible stripe or nematic charge-density-wave phases. More striking, the anisotropy sets in suddenly below a critical temperature, suggesting a finite-temperature phase transition. Our observations highlight how anisotropy modifies the many-body phases of a 2DES, and should further fuel the discussion surrounding the enigmatic even-denominator FQHS.

[Article] [arXiv]

My brief overview of this work [My blog post]

Abstract: The two-dimensional electron system in an InAs quantum well has emerged as a prime candidate for hosting exotic quasiparticles with non-Abelian statistics such as Majorana fermions and parafermions. To attain its full promise, however, the electron system has to be clean enough to exhibit electron-electron interaction phenomena. Here, we report the observation of the fractional quantum Hall effect in a very low disorder InAs quantum well with a well width of 24 nm, containing a two-dimensional electron system with a density n = 7.8×10¹¹ cm⁻² and low-temperature mobility 1.8×10⁶ cm²/Vs. At a temperature of ≃ 35 mK and B ≃ 24 T, we observe a deep minimum in the longitudinal resistance, accompanied by a nearly quantized Hall plateau at a Landau level filling factor ν = 4/3.

[Article] [arXiv]