S. -R. Eric Yang
Intrinsically topologically ordered phases can host anyons. Here, we take the view that entanglement between anyons can give rise to an emergent geometry resembling Anti-de Sitter (AdS) space. We analyze the entanglement structure of…
Our numerical study of the disordered Hubbard model with nearest-neighbor hopping shows that a two-leg electron ladder has a finite topological entanglement entropy in the regime where the density of states exhibits an exponentially…
The Coulomb impurity problem of graphene, in the absence of a magnetic field, displays discrete scale invariance. Applying a magnetic field introduces a new magnetic length scale $\ell$ and breaks discrete scale invariance. Moreover, a…
We computed the phase diagram of the zigzag graphene nanoribbons as a function of on-site repulsion, doping, and disorder strength. The topologically ordered phase undergoes topological phase transitions into crossover phases, which are new…
We explore the edge properties of rectangular graphene nanoribbons featuring two zigzag edges and two armchair edges. Although the self-consistent Hartree-Fock fields break chiral symmetry, our work demonstrates that graphene nanoribbons…
Graphene zigzag nanoribbons, initially in a topologically ordered state, undergo a topological phase transition into crossover phases distinguished by quasi-topological order. We computed mutual information for both the topologically…
We investigate interacting disordered zigzag nanoribbons at low doping, using the Hubbard model to treat electron interactions within the density matrix renormalization group and Hartree-Fock method. Extra electrons that are inserted into…
Interacting disordered zigzag graphene nanoribbons have fractional charges, are quasi-one-dimensional, and display an exponentially small gap. Our numerical computations showed that the topological entanglement entropy of these systems has…
We numerically compute the density of states (DOS) of interacting disordered zigzag graphene nanoribbon (ZGNR) having midgap states showing $e/2$ fractional edge charges. The computed Hartree-Fock DOS is linear at the critical disorder…
An introductory overview of current research developments regarding solitons and fractional boundary charges in graphene nanoribbons is presented. Graphene nanoribbons and polyacetylene have chiral symmetry and share numerous similar…
We examine the long wave length limit of the self-consistent Hartree-Fock approximation irreducible static density-density response function by evaluating the charge induced by an external charge. Our results are consistent with the…
We investigate the properties of the gap-edge states of half-filled interacting disordered zigzag graphene nanoribbons. We find that the midgap states can display the quantized fractional charge of 1/2. These gap-edge states can be…
We investigate edge properties of a gapful rectangular graphene quantum dot in a staggered potential. In such a system gap states with discrete and closely spaced energy levels exist that are spatially located on the left or right zigzag…
We consider the end states of a half-filled rectangular armchair graphene ribbon (RAGR) in a staggered potential. Taking electron-electron interactions into account we find that, as the strength of the staggered potential varies, three…
A matrix Berry phase can be generated and detected by {\it all electric means} in II-VI or III-V n-type semiconductor quantum dots by changing the shape of the confinement potential. This follows from general symmetry considerations in the…
Two one-dimensional Luttinger liquid systems coupled by Hund's coupling are studied by the renormalization group and the non-abelian bosonization methods. It is found that the Hund's coupling is always relevant irrespective of the repulsive…
A graphene nanoribbon is a good candidate for a $(1+1)$ Chern-Simons topological insulator since it obeys particle-hole symmetry. We show that in a finite semiconducting armchair ribbon, which has two zigzag edges and two armchair edges, a…
In this article we discuss the ground state of a parabolically confined quantum dots in the limit of very strong magnetic fields where the electron system is completely spin-polarized and all electrons are in the lowest Landau level.…
We have investigated, using effective mass approach (EMA), magnetic properties of a one-dimensional electron gas in graphene armchair ribbons when the electrons of occupy only the lowest conduction subband. We find that magnetic properties…
We report on transport measurement performed on a room-temperature-operating ultra-small Coulomb blockade devices with a silicon island of sub-5nm. The charge stability at 300K exhibits a substantial change in slopes and diagonal size of…