Session B63: Quantum Hall and Low Dimensional Systems

Evolution between quantum Hall and conducting phases: simple models and some results

In this talk, we introduce and study a particularly simple model where kinetic energy, strong correlations, and band topology coexist.

We consider interacting quantum particles in two dimensions in a strong magnetic field such that the Hilbert space is restricted to the Lowest Landau Level (LLL). A periodic potential with a unit cell enclosing one flux quantum broadens the LLL into a dispersive Chern band. This enables an evolution from the familiar quantum Hall regime to large band width limit where a conducting state is expected.

This evolution is studied in detail for the specific case of bosons at filling factor ν=1. In the quantum Hall regime, the ground state at this filling is a gapped quantum hall state (the "bosonic Pfaffian") which may be viewed as descending from a (bosonic) composite Fermi liquid. At large bandwidth, the ground state is a bosonic superfluid.

We show how both phases and their evolution can be described within a single theoretical framework based on a LLL composite fermion construction. Building on our previous work on the bosonic composite Fermi liquid, we show that the evolution into the superfluid can be usefully described by a non-commutative quantum field theory in a periodic potential.   

Electrically Control of Two-Dimensional Electron-Hole Fluids in the Quantum Hall Regime

We study the influence of perpendicular magnetic fields on the ground state of electron-hole bilayers separated by opaque tunnel barriers. In the absence of a field, the ground state at low carrier densities is a condensate of s-wave excitons that has spontaneous interlayer phase coherence. We find that a series of phase transitions emerge at strong perpendicular fields between condensed and incompressible incoherent states with full electron and hole Landau levels. When the electron and hole densities are unequal, condensation can occur in higher angular momentum exciton states. We explain how this physics is expressed in the two-dimensional gate-voltage phase diagrams of dual-gated bilayers.    

Collective modes of partons in Jain sequence of quantum Hall states

I will discuss a parton construction of the effective field theory for Jain sequence at filling factor n/(2np+1). It will be explained how to derive previously suggested theories using parton starting point. I will aslo preset evidence that when p>1, partons are not simply a mathematical tool to construct topological effective theories of FQH groundstates, but are genuine quasiparticles that become observable at sufficiently high energies.   

Integrability and chaos of 1+1d chiral edge states with Abelian anyons

1+1d chiral edge states with marginal interactions, which may arise on the edge of 2+1d topological phases,  have rich quantum dynamics. In this talk, we first present a model consisting of $N$ interacting $SU(M)_1$ Wess-Zumino-Witten models hosting Abelian anyons, dubbed ``chiral Sachdev-Ye'' model. We analytically solve this model in two limits discovering behaviors from completely integrable to quantum chaos. We further extend our studies to the edge theory of a $\nu=4/3$ fractional quantum Hall state which show unusual integrability behavior.   

Representations of commutative electron operator algebras on MPS states for fractional quantum Hall systems

We study the action of several recently discussed second-quantized operator algebras satisfying Newton-Girard relations on matrix product state (MPS) trial wave functions for fractional quantum Hall systems. It is observed that this action generally preserves the MPS structure in a simple and well-defined manner, leading to insertion of bosonic modes into the MPS correlators. Various consequences of this direct translation between physical microscopic and virtual MPS degrees of freedom are discussed. On the one hand, it is intimately tied to the existence of frustration free parent Hamiltonians, notably in the Laughlin and Moore-Read case, but also in mixed-Landau-level situations such as unprojected Jain states. On the other hand, recent proposals for localized quasi-particle states by Bochniak et al. have straightforward MPS representations. Natural, spatially extended bases for such quasi-particle states are discussed.   

Complete Population Inversion between Ying-Ying flat bands

Using exact diagonalization methodology, we solve a many-body problem of electrons and holes in the flat conduction and valence band respectively of opposite chirality, namely the Ying-Yang flat bands, as hosted in a diatomic Kagome lattice. We first benchmark the results of single exciton formation with those obtained using DFT-GW methodology [Sethi, et. al., PRL 126, 196403], and then solve the many-exciton problem for the possibility of complete population inversion between the Ying-Yang flat bands. Our calculations show that the completely population inverted pair of flat bands can be stabilized by direct and exchange Coulomb interactions between electrons and holes, which are significantly enhanced by their vanishing kinetic energy. Our findings offer new insights on the nature of flat-band-enabled exciton-exciton interactions, leading to exotic quantum phenomenon, such as excited quantum Hall effects, excitonic insulator state, and topological flat-band laser.   

Inter-valley coherent order and fluctuation-mediated superconductivity in rhombohedral trilayer graphene

Symmetry-broken correlated metals and superconductivity have recently been observed in rhombohedral trilayer graphene. Interestingly, superconductivity always occurs on the cusp of isospin symmetry breaking, indicating that the pairing glue may be provided by order parameter fluctuations. I will argue that the relevant symmetry broken state is inter-valley coherent (IVC), and that IVC fluctuations can lead to unconventional superconductivity which is chiral when the fluctuations are strong. Along the way, I will clarify the role of the inter-valley Hund's coupling in choosing the spin-structure of both the IVC phase and the superconductor, and find a natural explanation of an apparently puzzling feature in the experiments — the occurrence of spin-singlet superconductivity in close proximity of a spin-polarized metal.   

Memristive Behavior in Epitaxial Cu2-xSe Thin Films

Materials with memristor properties are of much current interest because of their applications in neuromorphic circuitry and resistive switching devices. In these applications, low leakage current and high on-to-off current ratios are essential for efficient devices.  Non-stoichiometric copper selenide is a promising material that exhibits the above behavior, where the resistive switching is believed to be attributed to the ionic conductivity of copper ions [1]. We will present the memory resistive behavior of epitaxially grown Cu_2-xSe on Al₂O₃ using Molecular Beam Epitaxy (MBE).  The films were characterized using Reflection High Energy Electron Diffraction (RHEED), X-Ray Diffraction (XRD), and Atomic Force Microscopy (AFM). Pt interdigitated contacts were used to perform current-voltage (I-V) measurements. The (I-V) measurements showed resistive switching of  Cu_2-xSe at room temperature with over five orders of magnitude of on-off current ratios.

 

Tuning electronic correlation in atomic chains with fractional nuclear charge

In recent years, the 1D hydrogen chain H_∞ has been studied extensively as a platform for understanding phase transitions in correlated materials using many-body ground state computational methods.^1,2 The 1D fractional nuclear charge (FNC) hydrogen-like chain (H₂^FNC)_∞ is an extension of H_∞ that consists of 2 nuclei per unit cell and allows individual nuclear charges to be rational while restricting the total charge to +2e. Left-right symmetry breaking within the cell enables the competition between strong correlation and charge transfer,³ resulting in an exotic metallic phase transition at large nuclear separation. Here, we study the effects of dimerization on the electronic properties of (H₂^FNC)_∞ for various magnetic configurations. Additionally, potential topological properties will be examined by calculating the Zak phase in relevant parameter regimes.

References:

¹M. Motta, C. Genovese, F. Ma, Z. Cui, R. Sawaya et al., Phys. Rev. X 10, 031058 (2020).

²M. Motta et al., Phys. Rev. X 7, 031059 (2017).

³J. Furness, R. Zhang, and J. Sun, arXiv:2103.03178 (2021).   

"Low temperature energy relaxation in a two-dimensional carrier system"

We discuss mechanisms and available predictions for carrier thermalization in a two-dimensional quantum well, with the eye towards understanding regimes in which carrier interactions are prominent. Of primary interest to us is the value of the exponent u that controls the thermal power flow P between the 2-dimensional charged layer at a temperature T_e  and the environment  at a temperature T according to the frequently used form P~ T_e^u - T^u. We will review theory for the P(T) functions in the cases of piezoelectric and deformation electron-photon coupling, the effects of disorder on the exponent and the predictions for the so-called hydrodynamic regime  and compare these to energy relaxation measurements obtained in studies of transport in GaAs/AlGaAs quantum wells with a high interaction parameter r_s>20.   

Observing separate spin and charge Fermi seas in a strongly correlated one-dimensional conductor

An electron is usually considered to have only one type of kinetic energy, but could it have more, for its spin and charge, or by exciting other electrons? In one-dimension (1D), the physics of interacting electrons is captured well at low energies by the linear Tomonaga-Luttinger liquid model. Recent theoretical work has focused on extending the theory to deal with curved dispersions, yet little has been observed experimentally in the nonlinear regime. Here, we report on measurements of many-body modes in gated 1D wires using a momentum-resolved tunnelling spectroscopy technique. We map their dispersion both in and out of equilibrium, observing the formation of two separate Fermi seas at high energies, associated with spin and charge excitations, which cannot be accounted for by the noninteracting model. The effective interaction strength in the wires is varied from the non-interacting limit g=1 all the way down to g=0.5, by changing the amount of 1D inter-subband screening by over 50%. Our spectroscopy technique offers an important tool to explore nonlinear spinful regimes.    

Transitions from Abelian composite fermion to non-Abelian parton states in the zeroth Landau level of bilayer graphene

The electron-electron interaction in the Landau levels of bilayer graphene is markedly different from that of conventional semiconductors such as GaAs. We show that in the zeroth Landau level of bilayer graphene, in the orbital which is dominated by the non-relativistic second Landau level wave function, by tuning the magnetic field a topological quantum phase transition from an Abelian composite fermion state to a non-Abelian parton state can be induced at filling factors ν=1/2,  2/5 and 3/7. The parton states host exotic anyons that could potentially form building blocks of a fault-tolerant topological quantum computer. Intriguingly, some of these transitions may have been observed in a recent experiment [Huang et al. arXiv:2105.07058].   

Bosonisation of quasiholes and transmutation of braiding statistics in fractional quantum Hall states

We investigate the robustness of fractional braiding statistics of quasiholes in fractional quantum Hall (FQH) states. On the one hand, it is commonly believed that the quasiholes of FQH state at 1/m filling exhibit a braiding phase of 2π/3. On the other hand, there exist a one-to-one mapping between the Hilbert space of a model FQH state and the Hilbert space of bosons. This “bosonisation” scheme[1] implies that it is possible to construct an FQH state whose quasihole exhibit bosonic statistics. We show very high overlaps between the bosonic and anyonic states when the particle separation is large, indicating their energy difference can be very small. We emphasize that since the braiding statistics is a result of fluctuations in the electron density profile, the braiding phase measured in experiments is very sensitive to the exact shape of the quasihole packet, rather than a robust quantity as previously thought. Our analysis also suggests that it may be possible to observe fractional statistics in the (relatively) simple bosonic systems in a single Landau level. We propose an experimental scheme to realize these anyonic few-particle states.

References

[1] Bo Yang, Phys. Rev. Lett. 127, 126406 (2021).   

Phase Transitions and the Nature of the Ground State in Triangular Artificial Graphene Quantum Dots

We present theoretical results based on mean-field and exact many-body approaches showing that in artificial triangular graphene quantum dots with zigzag edges (ATGQD), the ground state transitions from a metallic to an antiferromagnetic by changing the distance between sites. The electronic states of these triangular dots in a metallic state have a macroscopically degenerate shell at the fermi level but no such shell exists in a AF state. We determine the effects of electron-electron interactions on the ground state, the total spin, and the excitation spectrum as a function of filling of the ATGQD with electrons. We find that the half-filled charge neutral shell leads to a partially spin polarized state in the metallic state but also in AF state in accordance with Lieb's theorem. In both regimes a relatively large gap separates the spin polarized ground state to the first excited many-body state at half filling of the degenerate shell, but by adding or removing an electron, this gap collapses, and alternate total spin states emerge with energies nearly degenerate to a spin polarized ground state.   

Magic thickness of 25 Å alternately makes metal-insulator transitions

Interesting physical properties, e.g., high-temperature superconductivity, topological properties, and charge/spin density waves, are observed in low-dimensional conductive materials. It is also possible to artificially create low-dimensional systems by fabricating ultrathin films, quantum wires, or quantum dots with flat interfaces. We develop the 2-dimensional electronic systems to grow ultrathin films on CaRuO₃. We have succeeded in fabrication of high-crystalline CaRuO₃ ultrathin films, whose surface roughness is controlled at 199 pico-meters, by molecular beam epitaxy. We observe that magnitude of resistivity oscillates with a ‘magic’ thickness of 25 Å, and changes by 3 and 9 orders at 300 K and at 4.2 K, respectively. These changes are much larger than conventional size effects accompanied with quantum well. We also confirm the same periodicity to perform photoelectron spectroscopy by etching the ultrathin film. Considering the large excitation energy, periodicity of 25 Å, and crystal anisotropy, we will discuss that the oscillating transitions originate from the commensurability of Mott insulation triggered by Peierls instability arising from a dual restriction on the dimensions in wavenumber space and real space.