Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSO(8) Fermion Dynamical Symmetry and Strongly-Correlated Quantum Hall States in Monolayer Graphene
129
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
A formalism is presented for treating strongly-correlated graphene quantum Hall states in terms of an SO(8) fermion dynamical symmetry that includes pairing as well as particle--hole generators. The graphene SO(8) algebra is isomorphic to an SO(8) algebra that has found broad application in nuclear physics, albeit with physically very different generators, and exhibits a strong formal similarity to SU(4) symmetries that have been proposed to describe high-temperature superconductors. The well-known SU(4) symmetry of quantum Hall ferromagnetism for single-layer graphene is recovered as one subgroup of SO(8), but the dynamical symmetry structure associated with the full set of SO(8) subgroup chains extends quantum Hall ferromagnetism and allows analytical many-body solutions for a rich set of collective states exhibiting spontaneously-broken symmetry that may be important for the low-energy physics of graphene in strong magnetic fields. The SO(8) symmetry permits a natural definition of generalized coherent states that correspond to symmetry-constrained Hartree--Fock--Bogoliubov solutions, or equivalently a microscopically-derived Ginzburg--Landau formalism, exhibiting the interplay between competing spontaneously broken symmetries in determining the ground state.
rate research
Read More
Flat band moire superlattices have recently emerged as unique platforms for investigating the interplay between strong electronic correlations, nontrivial band topology, and multiple isospin flavor symmetries. Twisted monolayer-bilayer graphene (tMBG) is an especially rich system owing to its low crystal symmetry and the tunability of its bandwidth and topology with an external electric field. Here, we find that orbital magnetism is abundant within the correlated phase diagram of tMBG, giving rise to the anomalous Hall effect (AHE) in correlated metallic states nearby most odd integer fillings of the flat conduction band, as well as correlated Chern insulator states stabilized in an external magnetic field. The behavior of the states at zero field appears to be inconsistent with simple spin and valley polarization for the specific range of twist angles we investigate, and instead may plausibly result from an intervalley coherent (IVC) state with an order parameter that breaks time reversal symmetry. The application of a magnetic field further tunes the competition between correlated states, in some cases driving first-order topological phase transitions. Our results underscore the rich interplay between closely competing correlated ground states in tMBG, with possible implications for probing exotic IVC ordering.
Nonabelian anyons offer the prospect of storing quantum information in a topological qubit protected from decoherence, with the degree of protection determined by the energy gap separating the topological vacuum from its low lying excitations. Originally proposed to occur in quantum wells in high magnetic fields, experimental systems thought to harbor nonabelian anyons range from p-wave superfluids to superconducting systems with strong spin orbit coupling. However, all of these systems are characterized by small energy gaps, and despite several decades of experimental work, definitive evidence for nonabelian anyons remains elusive. Here, we report the observation of arobust, incompressible even-denominator fractional quantum Hall phase in a new generation of dual-gated, hexagonal boron nitride encapsulated bilayer graphene samples. Numerical simulations suggest that this state is in the Pfaffian phase and hosts nonabelian anyons, and the measured energy gaps are several times larger than those observed in other systems. Moreover, the unique electronic structure of bilayer graphene endows the electron system with two new control parameters. Magnetic field continuously tunes the effective electron interactions, changing the even-denominator gap non-monotonically and consistent with predictions that a transition between the Pfaffian phase and the composite Fermi liquid (CFL) occurs just beyond the experimentally explored magnetic field range. Electric field, meanwhile, tunes crossings between levels from different valleys. By directly measuring the valley polarization, we observe a continuous transition from an incompressible to a compressible phase at half-filling mediated by an unexpected incompressible, yet polarizable, intermediate phase. Valley conservation implies this phase is an electrical insulator with gapless neutral excitations.
Monolayer graphene placed with a twist on top of AB-stacked bilayer graphene hosts topological flat bands in a wide range of twist angles. The dispersion of these bands and gaps between them can be efficiently controlled by a perpendicular electric field, which induces topological transitions accompanied by changes of the Chern numbers. In the regime where the applied electric field induces gaps between the flat bands, we find a relatively uniform distribution of the Berry curvature. Consequently, interaction-induced valley- and/or spin-polarized states at integer filling factors are energetically favorable. In particular, we predict a quantum anomalous Hall state at filling factor $ u=1$ for a range of twist angles $1^circ<theta <1.4^circ$. Furthermore, to characterize the response of the system to magnetic field, we computed the Hofstadter butterfly and the Wannier plot, which can be used to probe the dispersion and topology of the flat bands in this material.
Strong spin-orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin-orbit and strong electron-electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a nontrivial state with a single point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behavior is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semi-metal, and quantum spin and anomalous Hall states.
The experimentally observed correlated insulating states and quantum anomalous Hall (QAH) effect in twisted bilayer graphene (TBG) have drawn significant attention. However, up to date, the specific mechanisms of these intriguing phenomena are still open questions. Using a fully unrestricted Hartree-Fock variational method, we have explained the correlated insulating states and QAH effects at various integer fillings of the flat bands in TBG. Our results indicate that states breaking flavor (valley and spin) symmetries are energetically favored at all integer fillings. In particular, the correlated insulating states at $pm 1/2$ filling and at the charge neutrality point are all valley polarized sates which break $C_{2z}$ and time-reversal ($mathcal{T}$) symmetries, but preserves $C_{2z}mathcal{T}$ symmetry. Such valley polarized states exhibit moire orbital antiferromagnetic ordering on an emergent honeycomb lattice with compensating circulating current pattern in the moire supercell. Within the same theoretical framework, our calculations indicate that the $C!=!mp 1$ QAH states at $pm 3/4$ fillings of the magic-angle TBG are spin and orbital ferromagnetic states, which emerge when a staggered sublattice potential is present. We find that the nonlocalness of the exchange interactions tend to enhance the bandwidth of the low-energy bands due to the exchange-hole effect, which reduces the gaps of the correlated insulator phases. The nonlocal exchange interactions also dramatically enhance the spin polarization of the system, which significantly stabilize the orbital and spin ferromagnetic QAH state at $3/4$ filling of TBG aligned with hexagonal boron nitride (hBN). We also predict that, by virtue of the orbital ferromagnetic nature, the QAH effects at electron and hole fillings of hBN-aligned TBG would exhibit hysteresis loops with opposite chiralities.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
