Morphing of 2D Hole Systems at ν =3/2 in Parallel Magnetic Fields: Compressible, Stripe, and Fractional Quantum Hall Phases Yang Liu, M. A. Mueed, Md. Shafayat Hossain, S. Hasdermir, L.N. Pfeiffer, K.W. West, K.W. Baldwin, and M. Shayegan Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544 (Dated: October 17, 2018) 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 elec- tron system (2DES) quantizes the electron kinetic energy into a set of highly-degenerate Landau levels (LLs). The dominating Coulomb interaction then gives rise to nu- merous, 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 fill- ing 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 elec- trons 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 pres- sure 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 dif- ferent 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 preva- lent as the filling deviates from ν =1/2 and 3/2, qual- itatively 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 con- fined 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 suf- ficiently 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 interme- diate 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 phe- nomena 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 par- allel 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 lon- gitudinal 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- arXiv:1607.03956v1 [cond-mat.mes-hall] 13 Jul 2016