Morphing of 2D Hole Systems at ν = 3/2 in Parallel Magnetic Fields: Compressible, Stripe, and Fractional Quantum Hall Phases (original) (raw)

A transport study of two-dimensional (2D) holes confined to wide GaAs quantum wells provides a glimpse of a subtle competition between different many-body phases at Landau level filling ν = 3/2 in tilted magnetic fields. At large tilt angles (θ), an anisotropic, stripe (or 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. We attribute this remarkable evolution to the significant mixing of the excited and ground-state Landau levels of 2D hole systems in tilted fields. A strong magnetic field perpendicular to a 2D electron system (2DES) quantizes the electron kinetic energy into a set of highly-degenerate Landau levels (LLs). The dominating Coulomb interaction then gives rise to numerous , exotic quantum many-body phases [1, 2]. When the Fermi energy (E F) lies in an N = 0 LL, there is a compressible Fermi sea of composite fermions at LL filling factors ν = 1/2 and 3/2 while numerous fractional quantum Hall states (FQHSs) are observed at nearby odd-denominator ν [1-5]. In N ≥ 2 LLs, FQHSs are typically absent and anisotropic phases dominate at half-filled LLs, e.g., at ν = 9/2 and 11/2 as the system breaks the rotational symmetry and forms unidirectional charge density waves-the so-called stripe (or nematic) phases [6-8]. The intermediate N = 1 LL is special. The electrons exhibit FQHSs not only at odd-denominator ν but also at the even-denominator fillings ν = 5/2 and 7/2 [1, 2, 9]. The latter are believed to be the Moore-Read Pfaffian state [10], obey non-Abelian statistics, and be of potential use in topological quantum computing [11]. The application of parallel magnetic field (B ||) or pressure can break the rotational symmetry and introduce LL mixing, leading to the destruction of the ν = 5/2 FQHS and stabilization of the stripe phase in the N = 1 LL [12-16]. In GaAs two-dimensional hole systems (2DHSs), the spin-orbit coupling mixes harmonic oscillators with different Landau and spin indices and leads to a complex set of LLs [17]. Nevertheless, in narrow quantum wells (QWs), the 2DHS is compressible at ν = 1/2 and 3/2 and numerous odd-denominator FQHSs are still prevalent as the filling deviates from ν = 1/2 and 3/2, qualitatively similar to those in 2DESs. However, the even-denominator FQHSs at ν = 5/2 and 7/2 are very weak [18, 19], and instead stripe phases are typically observed at these fillings, particularly at low densities [19-21]. Here, we report transport measurements in 2DHSs confined in wide GaAs QWs and subjected to strong B ||. We observe a remarkable metamorphosis of the ground state at ν = 3/2. The compressible Fermi sea seen at ν = 3/2 turns into a stripe phase when we apply a sufficiently large B || to a symmetric QW. The stripe phase can be destabilized in asymmetric QWs and, strikingly, an even-denominator FQHS forms at ν = 3/2 at intermediate B ||. At larger B || , the ν = 3/2 FQHS disappears and the 2DHS reverts back to becoming compressible. Our results highlight the rich and subtle many-body phenomena manifested by high-quality 2DHSs. Our samples were grown by molecular beam epitaxy, and each consists of a GaAs QW (well widths W = 35 or 30 nm) which is bounded on either side by undoped Al 0.3 Ga 0.7 As spacer layers and C δ-doped layers. They have as grown densities p 1 to 1.5 × 10 11 cm −2 and high mobility µ 100 m 2 /Vs. Each sample has a van der Pauw geometry, with alloyed InZn contacts at the four corners of a 4 × 4 mm 2 piece. We carefully control the density and the charge distribution symmetry in the QW by applying voltage biases to the back-and front-gates [22, 23]. For the low-temperature measurements, we use a dilution refrigerator with a sample platform which can be rotated in-situ in the magnetic field to induce a parallel field component B || along the x-direction (see Fig. 1(c)). We use θ to express the angle between the field and the normal to the sample plane, and denote the longitudinal resistances measured along and perpendicular to the direction of B || as R xx and R yy , respectively (Fig. 1(c)). Although the main focus of our study is the state of the 2DHS near ν = 3/2 in tilted magnetic fields, the data at θ = 0 are also very intriguing. Figure 2 shows R xx measured from a symmetric 35-nm-QW 2DHS at θ = 0 • and different densities. Strong odd-denominator FQHSs are seen as vertical, low-resistance (blue) stripes at ν = 5/3, 8/5, 7/5, and 4/3. With increasing density, R xx steeply increases above a boundary marked by the white solid line. This sharp transition is a signature of a LL crossing near ν = 3/2. We indeed expect such a crossing from the typical LL diagram (see Fig. 1(a)) for our wide-QW 2DHSs [24]. As depicted in Fig. 1(a), the light-hole-like β-level (blue) crosses the heavy-hole