The quantum Hall system can be used to study many-body physics owing to its multiple internal electronic degrees of freedom and tunability. While quantum phase transitions have been studied intensively, research on the temperature-induced phase transitions of this system is limited. We measured the pure bulk conductivity of a quantum Hall antiferromagnetic state in bilayer graphene over a wide range of temperatures and revealed the two-step phase transition associated with the breaking of the long-range order, i.e., the Kosterlitz-Thouless transition, and short-range antiferromagnetic order. Our findings are fundamental to understanding electron correlation in quantum Hall systems.
The quantum Hall system can be used to study many-body physics owing to its multiple internal electronic degrees of freedom and tunability. While quantum phase transitions have been studied intensively, research on the temperature-induced phase transitions of this system is limited. We measured the pure bulk conductivity of a quantum Hall antiferromagnetic state in bilayer graphene over a wide range of temperatures and revealed the two-step phase transition associated with the breaking of the long-range order, i.e., the Kosterlitz-Thouless transition, and short-range antiferromagnetic order. Our findings are fundamental to understanding electron correlation in quantum Hall systems.
Motivated by recent experimental studies that have found signatures of a correlated insulator phase and tuning superconductivity in twisted bilayer graphene, we study the temperature-dependent conductivity, the spin correlation and the superconducting pairing correlation within a two-orbital Hubbard model on an emergent honeycomb lattice. Evaluation of the temperature dependence of the conductivity demonstrates that there is a metal-insulator transition, and the Mott phase at strong coupling is accompanied by antiferromagnetic order. The electronic correlation drives a d+id superconducting pairing to be dominant over a wide filling region. All of the dc conductivity, the spin correlation and the superconductivity are suppressed as the interlayer coupling strength increases, and the critical Uc for metal-insulator transition is also reduced. Our intensive numerical results reveal that the TBG should be a uniquely tunable platform for exploring correlated states.
Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.
Abstract Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.
Motivated by recent experimental studies that have found signatures of a correlated insulator phase and tuning superconductivity in twisted bilayer graphene, we study the temperature-dependent conductivity, the spin correlation, and the superconducting pairing correlation within a two-orbital Hubbard model on an emergent honeycomb lattice. The evaluation of the temperature dependence of the conductivity demonstrates that there is a metal-insulator transition and the Mott phase at strong coupling is accompanied by antiferromagnetic order. The electronic correlation drives a d+id superconducting pairing to be dominant over a wide filling region. All of the dc conductivity, the spin correlation, and the superconductivity are suppressed as the interlayer coupling strength increases, and the critical Uc for the metal-insulator transition is also reduced. Our intensive numerical results reveal that twisted bilayer graphene should be a uniquely tunable platform for exploring strongly correlated phenomena.
We study a number of quantum phase transitions, which are exotic in their nature and separates non-trivial phases of matter. Since quantum fluctuations, which drive these phase transitions, are stronger in low-dimensions, we concentrate on low-dimensional systems. We consider two different two-dimensional systems in this thesis and study their phase transition. \n\nFirst, we investigate a phase transition in graphene, one of the most famous two-dimensional systems in condensed matter. For a suspended bilayer graphene in ν = 0 quantum Hall regime, the conductivity data and mean-field analysis suggests a phase transition from an antiferromagnetic (AF) state to a valence bond solid (VBS) state, when perpendicular electric field is increased. This AF to VBS phase transition is reminiscent of deconfined criticality, which is a novel phase transition that cannot be explained by Landau’s theory of symmetry breaking. We show that in the strong coupling regime of bilayer graphene, the AF state is destabilized by the transverse electric field, likely resulting in a VBS state. We also consider monolayer and bilayer graphene in the large cyclotron gap limit and show that the effective action for the AF and VBS order parameters have a topological Wess-Zumino-Witten term, supporting that the phase transition observed in experiments is in the deconfined criticality class. \n\nSecond, we study the model systems of cuprate superconductor, which is effectively a two-dimensionalal system in the CuO_2 plane. The proposal that the pseudogap metal is a fractionalized Fermi liquid described by a quantum dimer model is extended using the density matrix renormalization group. Measuring the Friedel oscillations in the open boundaries reveals that the fermionic dimers have dispersion minima near (π/2,π/2), which is compatible with the Fermi arcs in photoemission. Moreover, investigating the entanglement entropy suggests that the dimer model with low fermion density is similar to the free fermion system above the Lifshitz transition. We also study the phase transition from a metal with SU(2) spin symmetry to an AF metal. By applying the functional renormalization group to the two-band spin-fermion model, we establish the existence of a strongly coupled fixed point and calculate critical exponents of the fixed point.
The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands.An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight-binding models, and the long-ranged Coulomb interactions.While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit.Here, we present unbiased Monte Carlo simulations of realistic models of magic-angle TBG at charge neutrality.We establish the absence of a sign problem for this model in a momentumspace approach and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion.Our results include (i) the emergence of an insulating Kramers intervalley coherent ground state in competition with a correlated semimetal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions that reveal a "pseudogap" regime, in which gap features are established at a higher temperature than the onset of order, and (iii) predictions for electronic tunneling spectra and their evolution with temperature.Our results pave the way towards uncovering the physics of magic-angle graphene through exact simulations of over a hundred electrons across a wide temperature range.