Time-reversal-invariant topological superconductivity in one and two dimensions

We review theoretical and experimental highlights in transport in two-dimensional materials focussing on key developments over the last five years. Topological insulators are finding applications in magnetic devices, while Hall transport in doped samples and the general issue of topological protection remain controversial. In transition metal dichalcogenides valley-dependent electrical and optical phenomena continue to stimulate state-of-the-art experiments. In Weyl semimetals the properties of Fermi arcs are being actively investigated. A new field, expected to grow in the near future, focuses on the non-linear electrical and optical responses of topological materials, where fundamental questions are once more being asked about the intertwining roles of the Berry curvature and disorder scattering. In topological superconductors the quest for chiral superconductivity, Majorana fermions and topological quantum computing is continuing apace. :1907.10058v1 [cond-mat.mes-hall] arXiv

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“…[355,356,357]). Their properties have been a subject of several review articles [358,359,360,361,362,363,364,365].…”

Section: Chiral Superconductivity Majorana Edge Modes and Related Phmentioning

confidence: 99%

Transport in two-dimensional topological materials: recent developments in experiment and theory

et al. 2020

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“…Clearly P left |G 0 = −|G 0 . It has been proved that P left anticommutes with the time reversal operator K. [13][14][15] In the present case, this is proved using Eqs. (5) and (6).…”

Section: Discussion On the "Time-reversal Anomaly"mentioning

confidence: 54%

“…The explicit construction of the many-body eigenstates allows us to discuss in detail the arguments involved in the so called "time-reversal anomaly." [13][14][15] Following for example Ref. 13, we can identify an independent zeromode operator at the left side (a in the notation of Ref.…”

Section: Discussion On the "Time-reversal Anomaly"mentioning

confidence: 99%

“…This might be solved if both ends are included in the argument. 15 Our results in which the many-body states are constructed explicitly shed light on the underlying physics (see Section III B 3).…”

Section: Introductionmentioning

confidence: 90%

“…Specifically for the left and right ends S z left , S z right = ±1/4. The first argument to show this fractional spin 14,15 was based on the so called "time-reversal anomaly", first proposed for two-and three-dimensional TRITOPS. 13 The argument can be summarized as follows.…”

Section: Introductionmentioning

confidence: 99%

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Exact analytical solution of a time-reversal-invariant topological superconducting wire

Aligia

Camjayi

2019

Phys. Rev. B

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We consider a model proposed before for a time-reversal-invariant topological superconductor (TRITOPS) which contains a hopping term t, a chemical potential µ, an extended s-wave pairing ∆ and spin-orbit coupling λ. We show that for |∆| = |λ|, µ = t = 0, the model can be solved exactly defining new fermion operators involving nearest-neighbor sites. The many-body ground state is four-fold degenerate due to the existence of two zero-energy modes localized exactly at the first and the last site of the chain. These four states show entanglement in the sense that creating or annihilating a zero-energy mode at the first site is proportional to a similar operation at the last site. By continuity, this property should persist for general parameters. Using these results we correct some statements related with the so called "time-reversal anomaly". Addition of a small hopping term for a chain with an even number of sites breaks the degeneracy and the ground state becomes unique with an even number of particles. We also consider a small magnetic field applied to one end of the chain. We compare the many-body excitation energies and spin projection along the spin-orbit direction for both ends of the chains with numerical results obtaining good agreement.

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Double Nanowires for Hybrid Quantum Devices

Kanne

Olsteins

Marnauza

et al. 2021

Adv Funct Materials

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Parallel 1D semiconductor channels connected by a superconducting strip constitute the core platform in several recent quantum device proposals that rely, for example, on Andreev processes or topological effects. In order to realize these proposals, the actual material systems must have high crystalline purity, and the coupling between the different elements should be controllable in terms of their interfaces and geometry. A strategy for synthesizing double InAs nanowires by the vapor‐liquid‐solid mechanism using III‐V molecular beam epitaxy is presented. A superconducting layer is deposited onto nanowires without breaking the vacuum, ensuring pristine interfaces between the superconductor and the two semiconductor nanowires. The method allows for a high yield of merged as well as separate parallel nanowires with full or half‐shell superconductor coatings. Their utility in complex quantum devices by electron transport measurements is demonstrated.

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Time-reversal-invariant topological superconductivity in one and two dimensions

Cited by 87 publications

References 191 publications

Transport in two-dimensional topological materials: recent developments in experiment and theory

Transport in two-dimensional topological materials: recent developments in experiment and theory

Exact analytical solution of a time-reversal-invariant topological superconducting wire

Double Nanowires for Hybrid Quantum Devices

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