Anomalous coupling between magnetic and nematic orders in quantum Hall systems (original) (raw)

The interplay between different orders is of fundamental importance in physics. The spontaneous, symmetry-breaking charge order, responsible for the stripe or the nematic phase, has been of great interest in many contexts where strong correlations are present, such as high-temperature super-conductivity and quantum Hall effect. In this article we show the unexpected result that in an interacting two-dimensional electron system, the robustness of the nematic phase, which represents an order in the charge degree of freedom, not only depends on the orbital index of the topmost, half-filled Landau level, but it is also strongly correlated with the magnetic order of the system. Intriguingly, when the system is fully magnetized, the nematic phase is particularly robust and persists to much higher temperatures compared to the nematic phases observed previously in quantum Hall systems. Our results give fundamental new insight into the role of magnetization in stabilizing the nematic phase, while also providing a new knob with which it can be effectively tuned. Besides the isotropic phases of nature such as the fractional quantum Hall and composite fermion liquids, interacting fermionic systems host a tantalizing nematic phase where the charges spontaneously organize into symmetry-breaking, stripe-like clusters [1, 2]. Its existence was first predicted for a two-dimensional electron system (2DES) subjected to a perpendicular magnetic field, where the electronic kinetic energy is quantized into a set of Landau levels (LLs). When a LL with high or-bital index is half filled, in the presence of long-range Coulomb interaction a spontaneous stripe-like charge ordering can emerge, manifesting periodic density (or LL filling-factor) oscillations along one spatial direction [3-5]. Quantum and thermal fluctuations, as well as disorder , affect the strictly periodic nature of these oscillations and induce a nematic order [1, 6]. Soon after the theoretical predictions, experimental signatures of the nematic phases were reported as strong anisotropies in the two in-plane transport directions (higher resistance along the direction of charge oscillations), in very high-mobility 2DESs [7, 8] and 2D hole systems [9] confined to GaAs quantum wells (QWs). These were followed by reports of nematic phases in a variety of bulk systems such as Sr 3 Ru 2 O 7 [10] and high-temperature superconductors [11-13]. Such ubiquity raises the question whether ne-matic ordering competes or is intertwined with magnetism , high-temperature superconductivity, quantum Hall effect, and quantum criticality. Although the existence of nematicity and some of its macroscopic properties have been scrutinized [1-29], understanding the interplay between the nematic and other intricate charge or magnetic orders remains a challenging problem in condensed matter physics [1, 30]. Here we unravel an unexpected coupling between magnetic and nematic orders at half-filled LLs in a novel 2DES confined to an AlAs QW that enables a complete tuning of magnetization. Thanks to the comparable magnitudes of the cyclotron and Zeeman energies in this 2DES, tilting the sample in the magnetic field allows us to tune the Fermi energy between LLs with different orbital (N) and spin (↑ and ↓) indices, and capture a complete evolution of the ground states as a function of N and the magnetization of the 2DES. For a half-filled LL with N = 0, there is no nematic phase, regardless of the mag-netization. For N > 0 LLs, when the magnetization of the topmost, half-filled LL is opposite to the magnetiza-tion of the underlying LLs, the nematic phase is absent, but when it is aligned a nematic phase is seen. If the half-filled and the underlying LLs are fully magnetized, the nematic phase is anomalously robust and persists at temperatures as high as 2 K. Our data provide a fresh outlook at the nematic phases in 2DESs as they highlight the importance of the spin degree of freedom, a factor that has been seldom accessible in previous experiments, and ignored in theoretical studies. The 2DES confined in our sample is confined to a very narrow (5.66-nm-thick) AlAs QW and occupies an out-of-plane conduction-band valley with an isotopic in-plane mass [31]. It exhibits fractional quantum Hall states (FQHSs) at high magnetic fields in the N = 0 LL, as seen in Fig. 1. The longitudinal resistivity (ρ xx) trace shows strong minima at ν = 5/3 and 4/3, accompanied by corresponding plateaus in the Hall resistivity (ρ xy). There are also weak ρ xx minima at ν = 8/5 and 7/5, hinting at developing FQHSs. Figure 1 traces provide evidence for the first observation of FQHSs in an AlAs QW with out-of-plane valley occupation, and attest to the sufficiently high quality of the sample to support many-body states. The 2DES has a relatively large effective Landé g-factor (g *)and effective mass (m *) [31]. These lead to a ratio of 0.63 for the Zeeman energy (E Z = g * µ B B) and cyclotron energy (E C = eB ⊥ /m *) in a purely perpendicular magnetic field, as the LL energy diagram in the right inset to Fig. 1 illustrates. The LL diagram implies that the energy gaps at odd LL fillings (ν) are larger than those at even ν, consistent with the stronger ρ xx minima