Discussion on Anæsthesia in Operations on the Thyroid Gland.

Low, Harold T.

doi:10.1177/003591572001301407

Cited by 7 publications

(8 citation statements)

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“…A building block of the topological phases of matter is the Berry phase − a geometric phase acquired by the eigenstates in an adiabatic cycle in the parameter space such as time, position, or momentum. [144,145] One way to grasp an intuitive understanding of the Berry phase is to compare it with the Peierls phase (p) acquired by a charged particle (e) under the application of a vector potential A as p = e A(r) · dr. [146] The Peierls phase becomes quantized in a periodic boundary condition, which is called the Aharonov-Bohm phase. [147] Similarly, the Berry phase acquired by the adiabatic evolution can be casted into a geometrical 'vector potential' A(k), called the Berry connection.…”

Section: Brief Review On Topological Invariants In Hermitian Hamimentioning

confidence: 99%

New topological invariants in non-Hermitian systems

Ghatak

Das

2019

J. Phys.: Condens. Matter

364

295

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Both theoretical and experimental studies of topological phases in non-Hermitian systems have made a remarkable progress in the last few years of research. In this article, we review the key concepts pertaining to topological phases in non-Hermitian Hamiltonians with relevant examples and realistic model setups. Discussions are devoted to both the adaptations of topological invariants from Hermitian to non-Hermitian systems, as well as origins of new topological invariants in the latter setup. Unique properties such as exceptional points and complex energy landscapes lead to new topological invariants including winding number/vorticity defined solely in the complex energy plane, and half-integer winding/Chern numbers. New forms of Kramers degeneracy appear here rendering distinct topological invariants. Modifications of adiabatic theory, time-evolution operator, biorthogonal bulk-boundary correspondence lead to unique features such as topological displacement of particles, 'skin-effect', and edge-selective attenuated and amplified topological polarizations without chiral symmetry. Extension and realization of topological ideas in photonic systems are mentioned. We conclude with discussions on relevant future directions, and highlight potential applications of some of these unique topological features of the non-Hermitian Hamiltonians.

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Section: Brief Review On Topological Invariants In Hermitian Hamimentioning

confidence: 99%

New topological invariants in non-Hermitian systems

Ghatak

Das

2019

J. Phys.: Condens. Matter

364

295

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“…The butterfly graph as a whole describes all possible phases of a two-dimensional electron gas that arise as one varies the electron density and the magnetic field where each phase is characterized by an integer. These integers have their origin in topological properties described within the framework of geometric phases known as Berry phases [5]. The relative smoothness of colored channels in Fig.…”

Section: Introductionmentioning

confidence: 99%

A tale of two fractals: The Hofstadter butterfly and the integral Apollonian gaskets

Satija

2016

Eur. Phys. J. Spec. Top.

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Abstract. This paper unveils a mapping between a quantum fractal that describes a physical phenomena, and an abstract geometrical fractal. The quantum fractal is the Hofstadter butterfly discovered in 1976 in an iconic condensed matter problem of electrons moving in a twodimensional lattice in a transverse magnetic field. The geometric fractal is the integer Apollonian gasket characterized in terms of a 300BC problem of mutually tangent circles. Both of these fractals are made up of integers. In the Hofstadter butterfly, these integers encode the topological quantum numbers of quantum Hall conductivity. In the Apollonian gaskets an infinite number of mutually tangent circles are nested inside each other, where each circle has integer curvature. The mapping between these two fractals reveals a hidden D3 symmetry embedded in the kaleidoscopic images that describe the asymptotic scaling properties of the butterfly. This paper also serves as a mini review of these fractals, emphasizing their hierarchical aspects in terms of Farey fractions.

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“…Topological charge. Conventionally, a nodal line can be regarded as an infinitely thin "solenoid" with fixed "magnetic flux" in momentum space, such that an electron circling around it along a closed path C picks up a Berry phase similar to the Aharonov-Bohm effect [32]:…”

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confidence: 99%

Quadratic and cubic nodal lines stabilized by crystalline symmetry

Sheng

et al. 2019

Phys. Rev. B

122

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In electronic band structures, nodal lines may arise when two (or more) bands contact and form a one-dimensional manifold of degeneracy in the Brillouin zone. Around a nodal line, the dispersion for the energy difference between the bands is typically linear in any plane transverse to the line. Here, we perform an exhaustive search over all 230 space groups for nodal lines with higher-order dispersions that can be stabilized by crystalline symmetry in solid state systems with spin-orbit coupling and time reversal symmetry. We find that besides conventional linear nodal lines, only lines with quadratic or cubic dispersions are possible, for which the allowed degeneracy cannot be larger than two. We derive effective Hamiltonians to characterize the novel low-energy fermionic excitations for the quadratic and cubic nodal lines, and explicitly construct minimal lattice models to further demonstrate their existence. Their signatures can manifest in a variety of physical properties such as the (joint) density of states, magneto-response, transport behavior, and topological surface states. Using ab-initio calculations, we also identify possible material candidates that realize these exotic nodal lines. * Z.-M. Yu and W. Wu contributed equally to this work. †

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Discussion on Anæsthesia in Operations on the Thyroid Gland.

Cited by 7 publications

References 0 publications

New topological invariants in non-Hermitian systems

New topological invariants in non-Hermitian systems

A tale of two fractals: The Hofstadter butterfly and the integral Apollonian gaskets

Quadratic and cubic nodal lines stabilized by crystalline symmetry

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