Collective Edge Modes near the onset of a graphene quantum spin Hall state

Graphene subject to a strong, tilted magnetic field exhibits an insulator-metal transition tunable by tilt-angle, attributed to the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk state at filling factor zero. We develop a theoretical description for the spin and valley edge textures in the two phases, and the implied evolution in the nature of edge modes through the transition. In particular, we show that the CAF has gapless neutral modes in the bulk, but supports gapped charged edge modes. At the transition to the FM state the charged edge modes become gapless and are smoothly connected to the helical edge modes of the FM state. Possible experimental consequences are discussed.Comment: 5 pages, 2 figure

Collective Bulk and Edge Modes through the Quantum Phase Transition in Graphene at ν=0\nu=0

Undoped graphene in a strong, tilted magnetic field exhibits a radical change in conduction upon changing the tilt-angle, which can be attributed to a quantum phase transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk state at filling factor $\nu=0$. This behavior signifies a change in the nature of the collective ground state and excitations across the transition. Using the time-dependent Hartree-Fock approximation, we study the collective neutral (particle-hole) excitations in the two phases, both in the bulk and on the edge of the system. The CAF has gapless neutral modes in the bulk, whereas the FM state supports only gapped modes in its bulk. At the edge, however, only the FM state supports gapless charge-carrying states. Linear response functions are computed to elucidate their sensitivity to the various modes. The response functions demonstrate that the two phases can be distinguished by the evolution of a local charge pulse at the edge.Comment: 15 pages, 23 figure

Valley-kink in Bilayer Graphene at ν=0\nu=0: A Charge Density Signature for Quantum Hall Ferromagnetism

We investigate interaction-induced valley domain walls in bilayer graphene in the $\nu=0$ quantum Hall state, subject to a perpendicular electric field that is antisymmetric across a line in the sample. Such a state can be realized in a double-gated suspended sample, where the electric field changes sign across a line in the middle. The non-interacting energy spectrum of the ground state is characterized by a sharp domain wall between two valley-polarized regions. Using the Hartree-Fock approximation, we find that the Coulomb interaction opens a gap between the two lowest-lying states near the Fermi level, yielding a smooth domain wall with a kink configuration in the valley index. Our results suggest the possibility to visualize the domain wall via measuring the charge density difference between the two graphene layers, which we find exhibits a characteristic pattern. The width of the kink and the resulting pattern can be tuned by the interplay between the magnetic field and gate electric fields

Emergence of helical edge conduction in graphene at the \nu=0 quantum Hall state

The conductance of graphene subject to a strong, tilted magnetic field exhibits a dramatic change from insulating to conducting behavior with tilt-angle, regarded as evidence for the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) \nu=0 quantum Hall state. We develop a theory for the electric transport in this system based on the spin-charge connection, whereby the evolution in the nature of collective spin excitations is reflected in the charge-carrying modes. To this end, we derive an effective field theoretical description of the low-energy excitations, associated with quantum fluctuations of the spin-valley domain wall ground-state configuration which characterizes the two-dimensional (2D) system with an edge. This analysis yields a model describing a one-dimensional charged edge mode coupled to charge-neutral spin-wave excitations in the 2D bulk. Focusing particularly on the FM phase, naively expected to exhibit perfect conductance, we study a mechanism whereby the coupling to these bulk excitations assists in generating back-scattering. Our theory yields the conductance as a function of temperature and the Zeeman energy - the parameter that tunes the transition between the FM and CAF phases - with behavior in qualitative agreement with experiment.Comment: 16 pages, 1 figur

Spin-Valley Coherent Phases of the \u3cem\u3ev\u3c/em\u3e = 0 Quantum Hall State in Bilayer Graphene

Bilayer graphene (BLG) offers a rich platform for broken-symmetry states stabilized by interactions. In this work, we study the phase diagram of BLG in the quantum Hall regime at filling factor ν = 0 within the Hartree-Fock approximation. In the simplest noninteracting situation, this system has eight (nearly) degenerate Landau levels near the Fermi energy, characterized by spin, valley, and orbital quantum numbers. We incorporate in our study two effects not previously considered: (i) the nonperturbative effect of trigonal warping in the single-particle Hamiltonian, and (ii) short-range SU(4) symmetry-breaking interactions that distinguish the energetics of the orbitals. We find within this model a rich set of phases, including ferromagnetic, layer polarized, canted antiferromagnetic, Kekule, a “spin-valley entangled” state, and a “broken U(1) × U(1)” phase. This last phase involves independent spontaneous symmetry breaking in the layer and valley degrees of freedom, and has not been previously identified. We present phase diagrams as a function of interlayer bias D and perpendicular magnetic field B⊥ for various interaction and Zeeman couplings, and discuss which are likely to be relevant to BLG in recent measurements. Experimental properties of the various phases and transitions among them are also discussed

Collective Bulk and Edge Modes Through the Quantum Phase Transition in Graphene at \u3cem\u3eν\u3c/em\u3e = 0

Undoped graphene in a strong, tilted magnetic field exhibits a radical change in conduction upon changing the tilt angle, which can be attributed to a quantum phase transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk state at filling factor ν = 0. This behavior signifies a change in the nature of the collective ground state and excitations across the transition. Using the time-dependent Hartree-Fock approximation, we study the collective neutral (particle-hole) excitations in the two phases, both in the bulk and on the edge of the system. The CAF has gapless neutral modes in the bulk, whereas the FM state supports only gapped modes in its bulk. At the edge, however, only the FM state supports gapless charge-carrying states. Linear response functions are computed to elucidate their sensitivity to the various modes. The response functions demonstrate that the two phases can be distinguished by the evolution of a local charge pulse at the edge

Geographic max-flow and min-cut under a circular disk failure model

Failures in fiber-optic networks may be caused by natural disasters, such as floods or earthquakes, as well as other events, such as an Electromagnetic Pulse (EMP) attack. These events occur in specific geographical locations, therefore the geography of the network determines the effect of failure events on the network's connectivity and capacity. In this paper we consider a generalization of the min-cut and max-flow problems under a geographic failure model. Specifically, we consider the problem of finding the minimum number of failures, modeled as circular disks, to disconnect a pair of nodes and the maximum number of failure disjoint paths between pairs of nodes. This model applies to the scenario where an adversary is attacking the network multiple times with intention to reduce its connectivity. We present a polynomial time algorithm to solve the geographic min-cut problem and develop an ILP formulation, an exact algorithm, and a heuristic algorithm for the geographic max-flow problem.National Science Foundation (U.S.) (Grant CNS-0830961)National Science Foundation (U.S.) (Grant CNS-1017714)National Science Foundation (U.S.) (Grant CNS-1017800)National Science Foundation (U.S.) (CAREER Grant 0348000)United States. Defense Threat Reduction Agency (Grant HDTRA1-07-1-0004)United States. Defense Threat Reduction Agency (Grant HDTRA-09-1-005

Emergence of Helical Edge Conduction in Graphene at the \u3cem\u3eν\u3c/em\u3e = 0 Quantum Hall State

The conductance of graphene subject to a strong, tilted magnetic field exhibits a dramatic change from insulating to conducting behavior with tilt angle, regarded as evidence for the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) ν = 0 quantum Hall state. We develop a theory for the electric transport in this system based on the spin-charge connection, whereby the evolution in the nature of collective spin excitations is reflected in the charge-carrying modes. To this end, we derive an effective field-theoretical description of the low-energy excitations, associated with quantum fluctuations of the spin-valley domain-wall ground-state configuration which characterizes the two-dimensional (2D) system with an edge. This analysis yields a model describing a one-dimensional charged edge mode coupled to charge-neutral spin-wave excitations in the 2D bulk. Focusing particularly on the FM phase, naively expected to exhibit perfect conductance, we study a mechanism whereby the coupling to these bulk excitations assists in generating backscattering. Our theory yields the conductance as a function of temperature and the Zeeman energy—the parameter that tunes the transition between the FM and CAF phases—with behavior in qualitative agreement with experiment

Quarter-Filled Honeycomb Lattice with a Quantized Hall Conductance

We study a generic two-dimensional hopping model on a honeycomb lattice with strong spin-orbit coupling, without the requirement that the half-filled lattice be a Topological Insulator. For quarter-(or three-quarter) filling, we show that a state with a quantized Hall conductance generically arises in the presence of a Zeeman field of sufficient strength. We discuss the influence of Hubbard interactions and argue that spontaneous ferromagnetism (which breaks time-reversal) will occur, leading to a quantized anomalous Hall effect.Comment: 4 pages, 3 figure

Topological characteristics of oil and gas reservoirs and their applications

We demonstrate applications of topological characteristics of oil and gas reservoirs considered as three-dimensional bodies to geological modeling.Comment: 12 page