Session EE01: V: The Integer and Fractional Quantum Hall Effects

Re-entrant Anomalous Quantum Hall Phase of 5/2 State

Recent thermal Hall conductivity [1] and shot noise [2] measurements have revealed the true topological nature of the enigmatic 5/2 state to be the particle-hole symmetric Pfaffian (PH-Pf) order, which contradicts most theoretical predictions of Pfaffian or anti-Pfaffian orders. In an intermediate range of Landau level mixing strength, we find [3] a re-entrant anomalous phase (A-phase) which is topologically different from all the above topological orders. This A-phase has a unique topology that is adiabatically connected to all the Pfaffian, anti-Pfaffian, and PH-Pf flux shifts (not to be confused with topological orders) as the corresponding entanglement spectra appear to be similar. We propose a wave function for this A-phase, having the same flux shift of PH-Pf order but without particle-hole symmetry. In the A-phase this wave function has extremely high overlap with the exact ground state for the PH-Pf shift and non-ignorable overlaps with the exact ground states for Pfaffian and Anti-Pfaffian shifts, and further shows a high degree of matching of low-lying entanglement spectra with the same for the exact state. Analyzing the topological properties of the proposed wave function, we find the thermal Hall conductance of 5/2 unit, in agreement to experiment [1].

[1] M. Banerjee et al. Nature 559, 205–210 (2018)

[2] B. Dutta et al. Science 375, 193 (2022)

[3] S. Das, S. Das, and S. S. Mandal, arXiv: 2206.04419   

Cavity Modification of the Quantum Hall Effects

Cavity modification of materials is a novel research field motivated by the advances in strong light-matter interactions. In this talk we present how the strong coupling of Landau levels (in a two-dimensional electron gas) to the cavity field leads to the emergence of quasiparticles between the Landau levels and the photons, known as Landau polaritons [1]. The Landau polaritons have direct implications for the transport properties of the electron gas [3,4]. Further, we will present how our theory predicts that the cavity field can alter the fundamental quantization of the Hall conductance in the integer regime [4], as it has been also recently observed experimentally [3]. Connections of our theoretical prediction to these experiments will be discussed. Finally, in the case where the electron gas is replaced by a 2D periodic material we show that our theory predicts the emergence of polaritonic fractal energy spectra as a function of the cavity coupling strength [4]. The polaritonic fractal spectra are a polaritonic extension of the well-known Hofstadter butterfly [5]. 

[1] V. Rokaj, M. Penz, M. A. Sentef, M. Ruggenthaler, and A. Rubio, Phys. Rev. Lett. 123, 047202 (2019)

[2] G. L. Paravicini-Bagliani et al., Nat. Phys. 15, 186-190 (2019)

[3] F. Appugliese et al., Science 375 (6584), 1030-1034 (2022)

[4] V. Rokaj, M. Penz, M.A. Sentef, M. Ruggenthaler, A. Rubio, Phys. Rev. B 105, 205424 (2022)

[5] D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976)   

Complete phase diagram of charge-neutral graphene in the Quantum Hall regime

Monolayer graphene at charge neutrality in a quantizing magnetic field is a quantum Hall ferromagnet. Due to the spin and valley (near) degeneracies, there is a plethora of possible ground states. Based on a stringent assumption on symmetry-allowed interactions, previous theoretical work predicts a phase diagram with distinct regions of spin-polarized, canted antiferromagnetic, inter-valley coherent, and charge density wave order. While early experiments suggested that the system was in the canted antiferromagnetic phase at a perpendicular field, recent scanning tunnelling studies universally find Kekule bond order, and sometimes also charge density wave order. Recently, it was found that if one relaxes the stringent assumption mentioned above, a phase with coexisting canted antiferromagnetic and Kekule order exists in the region of the phase diagram believed to correspond to real samples. In this work we present the complete phase diagram of ν=0 graphene in the Hartree-Fock approximation, using generic symmetry-allowed interactions, assuming translation invariant ground states up to an intervalley coherence. Allowing for a sublattice potential (valley Zeeman coupling) in accordance with spin Zeeman coupling, we find numerous phases with different types of coexisting order. We conclude with a discussion of the physical signatures of the various states.   

Quantum valley Hall effect with quantized conductance in bilayer graphene kink states

Ballistic edge states arising from the bulk-edge correspondence of a topological insulator are interesting one-dimension systems with potential applications in quantum electronics. Helical edge states hosted by the quantum spin Hall effect and quantum valley Hall effect preserve the time reversal symmetry and enable the construction of novel state of matter such as topological superconductivity. Previous work has demonstrated the existence of quantum valley Hall kink states at the electrically created line junction of two oppositely biased bilayer graphene regions and the operations of a valley valve, waveguide and tunable beam splitter [1][2]. However, the resistance of the kink states was not quantized to the expected value of h/4e² at zero magnetic field. By improving device quality, here we show the attainment of very flat resistance plateaus to within 50omega of the expected value. The quantization is robust in a wide range of temperatures (20mK-10 K), Fermi energies, and dc biases. The gate-defined nature of the kink states enables in situ electrical operations. We demonstrate the on/off switching of the kink states with the speed of a few ms and an on/off ratio of greater than 100.

[1] Li. et al., Nat. Nano. 11, 1060 (2016), [2] Li et al., Science 362, 1149 (2018)

    

Optical probing of lowest Landau level neutral collective excitations in fractional quantum Hall fluids

Low-lying collective neutral excitations of fractional quantum Hall (FQH) fluids would provide key examinations of strongly correlated electronic phases, which could be detected by precise optical methods (e. g. photoluminescence (PL) and resonant inelastic light scattering (RILS)) at milli-Kelvins. Here, we report initial experimental results of probing the long-wavelength gap excitations and roton modes around filling factor v=1/3 in a single GaAs quantum well with ultra-high electron mobility, through circular polarized RILS. Excitations involving spin degree of freedom as an indicator of the interactions and polarization of FQH fluids are found to be subject to multiple resonances. We discuss that they correspond to an unexpected large number of transitions in PL. Selective enhancement of collective excitations at resonance would enrich the insights on incompressible quantum liquids in the regime of the FQH effect.   

Anomalous hysteretic behavior induced by Landau level pinning

We studied two-dimensional electron systems confined in asymmetric wide GaAs quantum wells at high magnetic field with capacitance measurement method. Because of the interlayer Coulomb interaction, Landau levels from different subbands will be pinned together when they cross at Fermi energy, leading to a charge instability. Our capacitance measurement reveals hysteretic behavior and two split minima around q/3 states related to this phenomenon.

    

Capacitive Response of Wigner Crystals

Here, we report our capacitance measurement of Wigner crystal near $ u$ = 1/5. We observe an anomalously large capacitance when the crystal forms, which is likely caused by the polarization charge. Our thorough study reveals several interesting new features, and shine light on the study of the dynamic response of this electron solid phase.   

Universal features of single particle and collective localization along the ν=1 integer quantum Hall plateau

Integer quantum Hall plateaus in low disorder two-dimensional electron gases exhibit both single particle and collective localization. The former is associated with an Anderson insulator, while the latter with a Wigner solid called the integer quantum Hall Wigner solid. We find that in two samples of different densities the layout of the phase stability diagram is similar, highlighting therefore density-independent universal properties of the two insulating phases. Furthermore, the two insulating phases develop at different magnetic fields and different quasiparticle densities, but at similar ranges of filling factors. These properties are inconsistent with a classical electron solid and underline therefore the quantum nature of the integer quantum Hall Wigner solid. The transition or crossover from the Anderson insulator to the integer quantum Hall Wigner solid remains poorly understood.

 

    

Magneto-optic Kerr effect measurement of 2D electron system at mK-temperature

We study high mobility 2D electron system using a high-resolution magneto-optic Kerr effect measurement at mK-temperature. With only 1uW probing light, we achieve 0.5urad Kerr angle resolution and 15um spatial resolution. We observe SdH-like quantum oscillation in our result.