Phase diagram of a disordered higher-order topological insulator: A machine learning study

Araki, Hiromu; Mizoguchi, Tsuyoshi; Hatsugai, Yasuhiro

doi:10.1103/physrevb.99.085406

Cited by 86 publications

(57 citation statements)

References 58 publications

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“…Following the currently growing interest in machine learning technology, the design of topological systems by machine learning has been suggested [235][236][237][238][239][240] . A design methodology, which was originally based on researchers' intuition and trial-and-error, was developed by training neural networks to estimate topological invariants or find topological band gaps.…”

Section: Topological Photonics Towards Applicationsmentioning

confidence: 99%

Recent advances in 2D, 3D and higher-order topological photonics

2020

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Over the past decade, topology has emerged as a major branch in broad areas of physics, from atomic lattices to condensed matter. In particular, topology has received significant attention in photonics because light waves can serve as a platform to investigate nontrivial bulk and edge physics with the aid of carefully engineered photonic crystals and metamaterials. Simultaneously, photonics provides enriched physics that arises from spin-1 vectorial electromagnetic fields. Here, we review recent progress in the growing field of topological photonics in three parts. The first part is dedicated to the basics of topological band theory and introduces various two-dimensional topological phases. The second part reviews three-dimensional topological phases and numerous approaches to achieve them in photonics. Last, we present recently emerging fields in topological photonics that have not yet been reviewed. This part includes topological degeneracies in nonzero dimensions, unidirectional Maxwellian spin waves, higher-order photonic topological phases, and stacking of photonic crystals to attain layer pseudospin. In addition to the various approaches for realizing photonic topological phases, we also discuss the interaction between light and topological matter and the efforts towards practical applications of topological photonics.

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Section: Topological Photonics Towards Applicationsmentioning

confidence: 99%

Recent advances in 2D, 3D and higher-order topological photonics

2020

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“…The second-order topological insulators, characterized by in-gap topological states in the (d − 2)dimensional boundary, are the current focus in the field because of its experimental realizations in phononics [9][10][11], photonics [14], and circuitry [31]. So far, most of the works are on the constructions of second-order topological insulators in crystals with well-defined crystalline symmetries, the fate of such a phase under disorder has been less studied [32][33][34][35]. Thus, it should be very interesting to find out how the hinge states in 3DSOTIs are modified by disorders.…”

Section: Introductionmentioning

confidence: 99%

Disorder-induced quantum phase transitions in three-dimensional second-order topological insulators

Wang

2020

Phys. Rev. Research

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Disorder effects on three-dimensional second-order topological insulators (3DSOTIs) are investigated numerically and analytically. The study is based on a tight-binding Hamiltonian for noninteracting electrons on a cubic lattice with a reflection symmetry that supports a 3DSOTI in the absence of disorder. Interestingly, unlike the disorder effects on a topological trivial system that can only be either a diffusive metal (DM) or an Anderson insulator (AI), disorders can sequentially induce four phases of 3DSOTIs, three-dimensional first-order topological insulators (3DFOTIs), DMs, and AIs. At a weak disorder when the on-site random potential of strength W is below a low critical value W c1 at which the gap of surface states closes while the bulk sates are still gapped, the system is a disordered 3DSOTI characterized by a constant density of states and a quantized integer conductance of e 2 /h through its chiral hinge states. The gap of the bulk states closes at a higher critical disorder W c2 , and the system is a disordered 3DFOTI in a lower intermediate disorder between W c1 and W c2 in which electron conduction is through the topological surface states. The system becomes a DM in a higher intermediate disorder between W c2 and W c3 above which the states at the Fermi level are localized. It undergoes a normal three-dimensional metal-to-insulator transition at W c3 and becomes the conventional AI for W > W c3. The self-consistent Born approximation allows one to see how the density of bulk states and the Dirac mass are modified by the on-site disorders.

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“…Along with the above significant progress of correlated topological phases, new classes of topological insulators/superconductors have been proposed which are referred to as higher-order topological insulators/superconductors [41][42][43][44][45][46][47]. These phases exhibit the characteristic bulk-boundary correspondence; topological properties in the d-dimensional bulk predict gapless charge excitations around d − 2-or d − 3-dimensional boundaries, while gapless charge excitations are absent around d − 1-dimensional boundaries.…”

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confidence: 99%

Higher-Order Topological Mott Insulators

2019

Self Cite

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We propose a new correlated topological state which we call a higher-order topological Mott insulator (HOTMI). This state exhibits a striking bulk-boundary correspondence due to electron correlations. Namely, the topological properties in the bulk, characterized by the Z3 spin-Berry phase, result in gapless corner modes emerging only in spin excitations (i.e., the single-particle excitations remain gapped around the corner). We demonstrate the emergence of the HOTMI in a Hubbard model on the kagome lattice, and elucidate how strong correlations change gapless corner modes at the noninteracting case.e R r L W M c W t p H m 7 m W c 4 R w X U o 8 0 J y 1 K S 8 1 S K R Z p x v A j p L U v 0 i i Q Q Q = = < / l a t e x i t > 0.05 < l a t e x i t s h a 1 _ b a s e 6 4 = " J 0 P A z R S z 1 o 8 A e V G E q s V O C / Z d q m 4 = " > A A d E t N e q Q 7 e q b 3 X 3 v V w h 6 B l 2 P O a k s r n I O h 0 7 H s 2 7 8 q k 7 O P 8 q f q T 8 8 + i l g O v e r s 3 Q m Z 4 B V a S 1 8 9 O W 9 m V z L J 2 h R d 0 w v 7 v 6 I G P f A L r O q r d r M l M p d / + F H Z S 5 3 H I 3 8 f x k + w M 5 u S 5 1 K 0 N Z 9 Y W 4 8 G 1 Y 1 x T G K a p 7 G E N W w i j R x 3 L + M M 5 7 i Q u q Q Z a V 5 a b J V K s U g z i i 8 h r X 4 A 2 q C Q R Q = = < / l a t e x i t > 0.1 < l a t e x i t s h a 1 _ b a s e 6 4 = " w Y j U U b Q H z J 0 q L U H E w a n A 1 x r T v O Y = " > A A A C h H i c h V G 7 S g N B F D 2 u r x h f U R v B J h g i F h L u + k C x k K C N Z R 5 G A x r C 7 j r G x c 3 u s r s J x J A f E G x N Y a V g I f b + g I 0 / Y J F P E M s I N h b e b B Z E R b 3 D z J w 5 c 8 + d M 1 z V N n T X I 2 r 1 S L 1 9 / Q O D o a H w 8 M j o 2 H h k Y n L X t S q O J n K a Z V h O X l V c Y e i m y H m 6 Z 4 i 8 7 Q i l r B p i T z 3 Z 6 t z v V Y X j 6 p a 5 4 9 V s U S g r J

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Phase diagram of a disordered higher-order topological insulator: A machine learning study

Cited by 86 publications

References 58 publications

Recent advances in 2D, 3D and higher-order topological photonics

Recent advances in 2D, 3D and higher-order topological photonics

Disorder-induced quantum phase transitions in three-dimensional second-order topological insulators

Higher-Order Topological Mott Insulators

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