Multiple odd-frequency superconducting states in buckled quantum spin Hall insulators with time-reversal symmetry

Kuzmanovski, Dushko; Black‐Schaffer, Annica M.

doi:10.1103/physrevb.96.174509

Cited by 34 publications

(59 citation statements)

References 42 publications

(50 reference statements)

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“…Such an asymmetry between the sublattices has been shown to directly lead to odd‐ω pairing in these materials, in complete analogy with the results in Section 2.1. Another interesting aspect of buckled honeycomb materials is that a sublattice asymmetry has also been shown to appear in finite‐width nanoribbons due to the presence of sample edges …”

Section: Examples Of Multiband Odd‐frequency Pairingmentioning

confidence: 99%

“…More specifically, in ref. [], the authors start by describing the normal state of a buckled honeycomb system with possibly finite spin‐orbit coupling, using the Kane–Mele Hamiltonian in real space:

H_{0} = t \sum_{⟨ i, j ⟩, σ} c_{i σ}^{†} c_{j σ} + \frac{i λ_{SO}}{3 \sqrt{3}} \sum_{⟨ ⟨ i, j ⟩ ⟩, σ} ν_{i j} {({\overset{σ}{true}}_{3})}_{σ σ^{'}} c_{i σ}^{†} c_{j σ^{'}} - \sum_{i, σ} μ_{i} c_{i σ}^{†} c_{i σ}

where

c_{i σ}^{†}

(

c_{i σ}

) creates (annihilates) a fermionic quasiparticle at site i with spin σ,

⟨ i, j ⟩

sums over nearest‐neighbor (NN) sites,

i, j

, of the honeycomb lattice,

⟨ ⟨ i, j ⟩ ⟩

sums over next‐nearest‐neighbor (NNN) sites. Here, t represents the NN hopping parameter and

λ_{SO}

is the spin‐orbit coupling due to NNN hopping, where

ν_{i j} = \pm 1

depending on whether the vector from site i to j is oriented clockwise or counterclockwise around the hexagonal plaquette .…”

Section: Examples Of Multiband Odd‐frequency Pairingmentioning

confidence: 99%

“…Ref. [] also studied this phase by considering nanoribbons with both zigzag (ZZ) and armchair (AC) terminations in the low doping region. In this case, superconductivity vanishes throughout the bulk, but a finite

Δ_{i}

was obtained using a self‐consistent algorithm for each site along the edges .…”

Section: Examples Of Multiband Odd‐frequency Pairingmentioning

confidence: 99%

“…[] also studied this phase by considering nanoribbons with both zigzag (ZZ) and armchair (AC) terminations in the low doping region. In this case, superconductivity vanishes throughout the bulk, but a finite

Δ_{i}

was obtained using a self‐consistent algorithm for each site along the edges . However, in contrast to the translation‐invariant case, the magnitudes of all pair amplitudes in these cases are largest in the absence of

λ_{V}

.…”

Section: Examples Of Multiband Odd‐frequency Pairingmentioning

confidence: 99%

“…For example, in the case of UPt 3 , the hybridization term,

ε_{k}

, induces odd‐ω pair amplitudes; however, from the Hamiltonian in Equation no avoided crossings emerge due to

ε_{k}

, because, in the absence of spin‐orbit coupling (

g = 0

) the bands are degenerate for

ε_{boldk} = 0

. Furthermore, it can also be shown that neither Sr 2 RuO 4 nor the buckled honeycomb lattice possesses these hybridization gaps for similar reasons. Thus, it is necessary to also study alternative experimental signatures of odd‐ω pairing in multiband superconductors.…”

Section: Experimental Signaturesmentioning

confidence: 99%

See 4 more Smart Citations

The Role of Odd‐Frequency Pairing in Multiband Superconductors

2020

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Recent progress in the understanding of multiband superconductivity and its relationship to odd‐frequency pairing are reviewed herein. The discussion begins by reviewing the emergence of odd‐frequency pairing in a simple two‐band model, providing a brief pedagogical overview of the formalism. Several examples of multiband superconducting systems are examined, in each case describing both the origin of the band degree of freedom and the nature of the odd‐frequency pairing. Throughout, it is attempted to convey a unified picture of how odd‐frequency pairing emerges in these materials and propose that similar mechanisms are responsible for odd‐frequency pairing in several analogous systems: layered 2D heterostructures, double quantum dots, double nanowires, Josephson junctions, and systems described by isolated valleys in momentum space. In addition, experimental probes of odd‐frequency pairing in multiband systems are reviewed, focusing on hybridization gaps in the electronic density of states, paramagnetic Meissner effect, and Kerr effect.

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Section: Examples Of Multiband Odd‐frequency Pairingmentioning

confidence: 99%

H_{0} = t \sum_{⟨ i, j ⟩, σ} c_{i σ}^{†} c_{j σ} + \frac{i λ_{SO}}{3 \sqrt{3}} \sum_{⟨ ⟨ i, j ⟩ ⟩, σ} ν_{i j} {({\overset{σ}{true}}_{3})}_{σ σ^{'}} c_{i σ}^{†} c_{j σ^{'}} - \sum_{i, σ} μ_{i} c_{i σ}^{†} c_{i σ}

where

c_{i σ}^{†}

(

c_{i σ}

) creates (annihilates) a fermionic quasiparticle at site i with spin σ,

⟨ i, j ⟩

sums over nearest‐neighbor (NN) sites,

i, j

, of the honeycomb lattice,

⟨ ⟨ i, j ⟩ ⟩

sums over next‐nearest‐neighbor (NNN) sites. Here, t represents the NN hopping parameter and

λ_{SO}

is the spin‐orbit coupling due to NNN hopping, where

ν_{i j} = \pm 1

depending on whether the vector from site i to j is oriented clockwise or counterclockwise around the hexagonal plaquette .…”

Section: Examples Of Multiband Odd‐frequency Pairingmentioning

confidence: 99%

Δ_{i}

was obtained using a self‐consistent algorithm for each site along the edges .…”

Section: Examples Of Multiband Odd‐frequency Pairingmentioning

confidence: 99%

Δ_{i}

λ_{V}

.…”

Section: Examples Of Multiband Odd‐frequency Pairingmentioning

confidence: 99%

“…For example, in the case of UPt 3 , the hybridization term,

ε_{k}

, induces odd‐ω pair amplitudes; however, from the Hamiltonian in Equation no avoided crossings emerge due to

ε_{k}

, because, in the absence of spin‐orbit coupling (

g = 0

) the bands are degenerate for

ε_{boldk} = 0

Section: Experimental Signaturesmentioning

confidence: 99%

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The Role of Odd‐Frequency Pairing in Multiband Superconductors

2020

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Van Der Waals Heterostructures with Spin‐Orbit Coupling

Rossi

Triola

2019

Annalen der Physik

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Herein, recent work on van der Waals (vdW) systems in which at least one of the components has strong spin‐orbit coupling is reviewed, focussing on a selection of vdW heterostructures to exemplify the type of interesting electronic properties that can arise in these systems. First a general effective model to describe the low energy electronic degrees of freedom in these systems is presented. The model is then applied to study the case of (vdW) systems formed by a graphene sheet and a topological insulator. The electronic transport properties of such systems are discussed and it is shown how they exhibit much stronger spin‐dependent transport effects than isolated topological insulators. Then, vdW systems are considered in which the layer with strong spin‐orbit coupling is a monolayer transition metal dichalcogenide (TMD) and graphene‐TMD systems are briefly discussed. In the second part of the article, a case is discussed in which the vdW system includes a superconducting layer in addition to the layer with strong spin‐orbit coupling. It is shown in detail how these systems can be designed to realize odd‐frequency superconducting pair correlations. Finally, twisted graphene‐NbSe2 bilayer systems are discussed as an example in which the strength of the proximity‐induced superconducting pairing in the normal layer, and its Ising character, can be tuned via the relative twist angle between the two layers forming the heterostructure.

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Surface Andreev Bound States and Odd-Frequency Pairing in Topological Superconductor Junctions

Tanaka

Tamura

2018

J Low Temp Phys

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Multiple odd-frequency superconducting states in buckled quantum spin Hall insulators with time-reversal symmetry

Cited by 34 publications

References 42 publications

The Role of Odd‐Frequency Pairing in Multiband Superconductors

The Role of Odd‐Frequency Pairing in Multiband Superconductors

Van Der Waals Heterostructures with Spin‐Orbit Coupling

Surface Andreev Bound States and Odd-Frequency Pairing in Topological Superconductor Junctions

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