We devise a model to explain why twisted bilayer graphene exhibits insulating behavior when ν = 2 or 3 charges occupy a unit moiré cell, a feature attributed to Mottness per previous work but not for ν = 1, clearly inconsistent with Mott insulation. We compute r = E/ E, where E and E are the potential and kinetic energies, respectively, and show that (i) the Mott criterion lies at a density larger than experimental values by a factor of 10 and (ii) a transition to a series of Wigner crystalline states exists as a function of ν. We find that, for ν = 1, r fails to cross the threshold ( r = 37) for the triangular lattice, and metallic transport ensues. However, for ν = 2 and ν = 3, the thresholds r = 22 and r = 17, respectively, are satisfied for a transition to Wigner crystals (WCs) with a honeycomb (ν = 2) and a kagome (ν = 3) structure. We posit that such crystalline states form the correct starting point for analyzing superconductivity.
We study an anisotropic holographic bottom-up model displaying a quantum phase transition (QPT) between a topologically trivial insulator and a non-trivial Weyl semimetal phase. We analyze the properties of quantum chaos in the quantum critical region. We do not find any universal property of the Butterfly velocity across the QPT. In particular it turns out to be either maximized or minimized at the quantum critical point depending on the direction of propagation. We observe that instead of the butterfly velocity, it is the dimensionless information screening length that is always maximized at a quantum critical point. We argue that the null-energy condition (NEC) is the underlying reason for the upper bound, which now is just a simple combination of the number of spatial dimensions and the anisotropic scaling parameter.
Recent experiments on twisted bilayer graphene (TBLG) have observed insulating states for two and three unit charges per moiré supercell, whereas the quarter-filling state (QFS) remained metallic. Subsequent experiments show that under hydrostatic pressure the QFS turns insulating for a certain window of pressure. In fact, the resistivity of the 1/2-filling and 3/4-filling states are also enhanced in the same pressure-window. Using pressure-dependent band structure calculations we compute the ratio of the potential to the kinetic energy, rs. We find a window of pressure for which rs crosses the threshold for a triangular Wigner crystal, thereby corroborating our previous work that the insulating states in TBLG are driven by Wigner physics, A key prediction of this work is that the window for the onset of the hierarchy of Wigner states that obtains at commensurate fillings conforms to a dome shape under pressure. We also predict the optimal condition for Wigner crystallization to be around 1.5 GPa. Consequently, TBLG provides a new platform for the exploration of Wigner physics and its relationship with superconductivity.
We study the spin orbit coupled ultra cold Bose-Einstein condensate placed in a single mode Fabry-Pérot cavity. The cavity introduces a quantum optical lattice potential which dynamically couples with the atomic degrees of freedom and realizes a generalized extended Bose Hubbard model whose zero temperature phase diagram can be controlled by tuning the cavity parameters.In the non-interacting limit, where the atom-atom interaction is set to zero, the resulting atomic dispersion shows interesting features such as bosonic analogue of Dirac points, cavity controlled Hofstadter spectrum which bears the hallmark of pseudo-spin-1/2 bosons in presence of Abelian and non-Abelian gauge field ( the later due to spin-orbit coupling) in a cavity induced optical lattice potential. In the presence of atom-atom interaction, using a mapping to a generalized Bose Hubbard model of spin-orbit coupled bosons in classical optical lattice, we show that the system realizes a host of quantum magnetic phases whose magnetic order can be be detected from the cavity transmission. This provides an alternative approach for detecting quantum magnetism in ultra cold atoms. We discuss the effect of cavity induced optical bistability on this phases and their experimental consequences.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.