Topology of critical chiral phases: Multiband insulators and superconductors

Balabanov, Oleksandr; Erkensten, Daniel; Johannesson, Henrik

doi:10.1103/physrevresearch.3.043048

“…The critical exponents of the curvature function at criticality near the multicritical points can be obtained from equation (35). The Ornstein-Zernike form of the curvature function in the vicinity of the multicritical points allows one to extract the exponent values numerically using the fitting equation…”

Section: Curvature Function and Critical Exponentsmentioning

confidence: 99%

“…Recently, this conventional understanding has been re-investigated and the edge modes are observed to be localized and stable even at certain critical points [28][29][30][31][32][33][34][35][36][37][38][39][40]. Therefore, similar to the gapped topological phases, certain critical phases also possess localized stable edge modes.…”

Section: Introductionmentioning

confidence: 99%

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

Kumar

¹

,

Kartik

²

,

Sarkar

³

2023

New J. Phys.

6

0

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The interplay between topology and criticality has been a recent interest of study in condensed matter physics. A unique topological transition between certain critical phases has been observed as a consequence of the edge modes living at criticalities. In this work, we generalize this phenomenon by investigating possible transitions between critical phases which are non-high symmetry in nature. We find the triviality and non-triviality of these critical phases in terms of the decay length of the edge modes and also characterize them using the winding numbers. The distinct non-high symmetry critical phases are separated by multicritical points with linear dispersion at which the winding number exhibits the quantized jump, indicating a change in the topology (number of edge modes) at the critical phases. Moreover, we reframe the scaling theory based on the curvature function, i.e. curvature function renormalization group method to efficiently address the non-high symmetry criticalities and multicriticalities. Using this we identify the conventional topological transition between gapped phases through non-high symmetry critical points, and also the unique topological transition between critical phases through multicritical points. The renormalization group flow, critical exponents and correlation function of Wannier states enable the characterization of non-high symmetry criticalities along with multicriticalities.

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“…The change from a gapless to a gapped regime will possibly facilitate the emergence and analysis of possible topological nontrivial states. In a gapless regime, edge states are usually not found, even though exceptions have been identified in gapless critical systems 22,23 . In a gapped regime edge states may appear, and one may wonder if signals of their presence will be felt on spin transport.…”

Section: Introductionmentioning

confidence: 99%

Topological states in chiral electronic chains

Sacramento

¹

,

Madeira²

2022

Phys. Rev. B

0

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We consider the influence of topological phases, or their vicinity, on the spin density and spin polarization through a chiral chain. We show the quantization of the Berry phase in a one-dimensional polarization helix structure, under the presence of an external magnetic field, and show its influence on the spin density. The polar angle of the momentum space spin density becomes quantized in the regime that the Berry phase is quantized, as a result of the combined effect of the induced spin-orbit coupling and the external transverse magnetic field, while the edge states do not show the polar angle quantization, in contrast with the bulk states. Under appropriate conditions, the model can be generalized to have similarities with a chain with non-homogeneous Rashba spin-orbit couplings, with zero or low energy edge states. Due to the breaking of time-reversal symmetry, we recover the effect of chiral induced spin polarization and spin transport across the chiral chain, when coupling to external leads. Some consequences of the quantized spin polarization and low energy states on the spin transport are discussed.

show abstract

“…Recently, this conventional understanding has been reinvestigated and the edge modes are observed to be local-ized and stable even at certain critical points [28][29][30][31][32][33][34][35][36][37][38][39][40] . Therefore, similar to the gapped topological phases, certain critical phases also possess localized stable edge modes.…”

Section: Introductionmentioning

confidence: 99%

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

Kumar¹,

Kartik²,

Sarkar³

2022

Preprint

0

View full text Add to dashboard Cite

The interplay between topology and criticality has been a recent interest of study in condensed matter physics. A unique topological transition between certain critical phases has been observed as a consequence of the edge modes living at criticalities. In this work, we generalize this phenomenon by investigating possible transitions between critical phases which are non-high symmetry in nature. We find the triviality and non-triviality of these critical phases in terms of the decay length of the edge modes and also characterize them using the winding numbers. The distinct non-high symmetry critical phases are separated by multicritical points with linear dispersion at which the winding number exhibits the quantized jump, indicating a change in the topology (number of edge modes) at the critical phases. Moreover, we reframe the scaling theory based on the curvature function, i.e. curvature function renormalization group method to efficiently address the non-high symmetry criticalities and multicriticalities. Using this we identify the conventional topological transition between gapped phases through non-high symmetry critical points, and also the unique topological transition between critical phases through multicritical points. The renormalization group flow, critical exponents and correlation function of Wannier states enable the characterization of non-high symmetry criticalities along with multicriticalities.

show abstract

Topology of critical chiral phases: Multiband insulators and superconductors

Cited by 14 publications

References 43 publications

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

Topological states in chiral electronic chains

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

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