From the adiabatic theorem of quantum mechanics to topological states of matter

Budich, Jan Carl; Trauzettel, Björn

doi:10.1002/pssr.201206416

Cited by 78 publications

(78 citation statements)

References 98 publications

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“…To get a quick and broad overview of topological insulators, with citations for relevant research papers, we recommend the review papers [17,25,7]. For a more in-depth look, there are already a few textbooks on the subject (by Bernevig and Hughes [4], by Shen [30], and one edited by Franz and Molenkamp [10]).…”

Section: Literaturementioning

confidence: 99%

A Short Course on Topological Insulators

Asbóth

Oroszlány

Pályi

2016

Lecture Notes in Physics

914

881

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Section: Literaturementioning

confidence: 99%

A Short Course on Topological Insulators

Asbóth

Oroszlány

Pályi

2016

Lecture Notes in Physics

914

881

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“…In Ref. 34, it has been demonstrated that the propagator associated with the full non-Abelian Berry connection is nothing but the matrix representation of the…”

Section: This Conjugation Property Of the Kramers Bands Leads To The mentioning

confidence: 99%

Topological invariant for generic one-dimensional time-reversal-symmetric superconductors in class DIII

Budich

Ardonne

2013

Phys. Rev. B

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A one-dimensional time-reversal-symmetric topological superconductor (symmetry class DIII) features a single Kramers pair of Majorana bound states at each of its ends. These holographic quasiparticles are non-Abelian anyons that obey Ising-type braiding statistics. In the special case where an additional U (1) spin rotation symmetry is present, this state can be understood as two copies of a Majorana wire in symmetry class D, one copy for each spin block. We present a manifestly gauge invariant construction of the topological invariant for the generic case, i.e., in the absence of any additional symmetries like spin rotation symmetry. Furthermore, we show how the presence of inversion symmetry simplifies the calculation of the topological invariant. The proposed scheme is suitable for the classification of both interacting and disordered systems and allows for a straightforward numerical evaluation of the invariant since it does not rely on fixing a continuous phase relation between Bloch functions. Finally, we apply our method to compute the topological phase diagram of a Rashba wire with competing s-wave and p-wave superconducting pairing terms.

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“…Five experimental papers [1][2][3][4][5] overview the recent status and challenges of TI nanostructures [1], magnetotransport and induced superconductivity [2], chemistry of Bi-based TI materials [3], molecular beam epitaxial growth of TI thin films [4], and angle-resolved photoemission spectroscopy (ARPES) with circular dichroism [5]. On the other hand, five theoretical papers [6][7][8][9][10] report the progress from different perspectives: materials design by firstprinciples calculations [6,7], the relations between TIs and thermoelectric materials [8], Floquet TIs [9], and the classification of topological states [10].…”

Section: Topological Insulatorsfrom Materials Design To Realitymentioning

confidence: 99%

Topological Insulators – From Materials Design to Reality

Yan

Felser

Zhang³

2013

Physica Rapid Research Ltrs

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Topological insulators (TIs) are a new quantum state of matter discovered in recent years. They are beyond the spontaneous symmetry-breaking description by Landau and are instead characterized by topological invariants, and described by topological field theory. Their topological nature is similar to the quantum Hall effect, a major discovery of condensed-matter physics in the 1980s (Klaus von Klitzing, Nobel Prize in Physics, 1985). The manifestation of the topological effect is the existence of robust gapless surface states inside the bulk energy gap. The topological surface states exhibit Dirac-cone-like energy dispersion with strong spin-momentum locking. Potential future applications cover areas such as spintronics, thermoelectrics, quantum computing and beyond.It is remarkable that TIs have been realized in many common materials, without the requirement of extreme conditions such as high magnetic field and low temperature. The first TI was predicted in 2006 and experimentally realized in 2007 in HgTe quantum wells. Soon afterwards, three traditionally well-known binary chalcogenides, Bi 2 Se 3 , Bi 2 Te 3 and Sb 2 Te 3 , were predicted and observed to be TIs with a large bulk gap and a metallic surface state consisting of a single Dirac cone. The discovery of these topological materials opened up the exciting field of topological insulators. Extensive experimental and theoretical efforts are devoted to synthesizing and optimizing samples, characterizing the topological states by surface sensitive spectroscopy, transport measurements, device fabrications, and searching for new material candidates.The field of TIs is now expanding at a rapid pace in the communities of physics, chemistry and materials science. In this Focus Issue, we intend to present a highquality snapshot of the materials and applications aspect of this field.We present ten Review papers from both experiment and theory aspects. Five experimental papers [1][2][3][4][5] We present ten Letters that cover various aspects, ranging from ARPES, transport measurement and devices, thin film growth to first-principles simulations and fundamental theory. Letters on ARPES [11][12][13][14] [18] shows the dependence of edge state dispersion on edge geometry of graphene. Last but not the least, two papers on phenomenological models [19,20] report the maximally localized flat-band Hamiltonians and the spectra flow for Aharonov-Bohm rings, respectively.We hope that this Focus Issue will be helpful for your research and stimulate more activity in the exciting field of topological insulators.

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From the adiabatic theorem of quantum mechanics to topological states of matter

Cited by 78 publications

References 98 publications

A Short Course on Topological Insulators

A Short Course on Topological Insulators

Topological invariant for generic one-dimensional time-reversal-symmetric superconductors in class DIII

Topological Insulators – From Materials Design to Reality

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