Quantum phase transition in the one-dimensional period-two and uniform compass model

Quantum phase transition in the one-dimensional period-two and uniform quantum compass model are studied by using the pseudo-spin transformation method and the trace map method. The exact solutions are presented, the fidelity, the nearest-neighbor pseudo-spin entanglement, spin and pseudo-spin correlation functions are then calculated. At the critical point, the fidelity and its susceptibility change substantially, the gap of pseudo-spin concurrence is observed, which scales as $1/N$ (N is system size). The spin correlation functions show smooth behavior around the critical point. In the period-two chain, the pseudo-spin correlation functions exhibit a oscillating behavior, which is absent in the unform chain. The divergent correlation length at the critical point is demonstrated in the general trend for both cases.Comment: 5 pages, 6 figure

Local Electrical Stress-Induced Doping and Formation of 2D Monolayer Graphene P-N Junction

We demonstrated doping in 2D monolayer graphene via local electrical stressing. The doping, confirmed by the resistance-voltage transfer characteristics of the graphene system, is observed to continuously tunable from N-type to P-type as the electrical stressing level (voltage) increases. Two major physical mechanisms are proposed to interpret the observed phenomena: modifications of surface chemistry for N-type doping (at low-level stressing) and thermally-activated charge transfer from graphene to SiO2 substrate for P-type doping (at high-level stressing). The formation of P-N junction on 2D graphene monolayer is demonstrated with complementary doping based on locally applied electrical stressing.Comment: 12 pages, 4 figure