Imaginary-Disorder-Induced Topological Phase Transitions
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Abstract:
We demonstrate non-Hermitian topological phase transitions induced solely by imaginary disorder. Starting from the trivial phase in the well-known Benalcazar, Bernevig, and Hughes model, we find that adding sufficient imaginary disorder to the trivial bulk can lead to a higher-order topological insulator supporting topological corner-localized states. In experiments, we elaborately design a two-dimensional reconfigurable acoustic lattice with a loss configuration that can be randomly set. By increasing the strength of lossy disorder, we observe the transitions from a trivial to a higher-order topological phase and subsequently to a gapless phase. To further show that imaginary disorder offers an alternative degree of freedom for controlling topological phases, we propose a non-Hermitian topological disclination state induced by imaginary disorder. Our work demonstrates an example of a non-Hermitian higher-order topological Anderson insulator and offers a reconfigurable platform to study the interplay between non-Hermitian disorder and topological phases.Keywords:
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A workable model for describing dislocation lines introduced into a three-dimensional topological insulator is proposed. We show how fragile surface Dirac cones of a weak topological insulator evolve into protected gapless helical modes confined to the vicinity of a dislocation line. It is demonstrated that surface Dirac cones of a topological insulator (either strong or weak) acquire a finite-size energy gap when the surface is deformed into a cylinder penetrating the otherwise surfaceless system. We show that, when a dislocation with a nontrivial Burgers vector is introduced, the finite-size energy gap plays the role of stabilizing the one-dimensional gapless states.
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Topological insulators are nonmagnetic insulators in the bulk, but have gapless edge/surface states characterized by Z2 topological numbers. In this paper we review basic properties of topological insulators. We then focus on the two-dimensional topological insulators, and describe various properties of the edge states.
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The quantum spin Hall (QSH) effect is the property of a new state of matter which preserves time-reversal, has an energy gap in the bulk, but has topologically robust gapless states at the edge. Recently, it has been shown that HgTe quantum wells realize this novel effect. In this work, we start from realistic tight-binding models and demonstrate the existence of the helical edge states in HgTe quantum wells and calculate their physical properties. We also show that 3d HgTe is a topological insulator under uniaxial strain, and show that the surface states are described by single-component massless relativistic Dirac fermions in 2+1 dimensions. Experimental predictions are made based on the quantitative results obtained from realistic calculations.
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The Dirac cone on a surface of a topological insulator shows linear dispersion analogous to optics and its velocity depends on materials. We consider a junction of two topological insulators with different velocities, and calculate the reflectance and transmittance. We find that they reflect the backscattering-free nature of the helical surface states. When the two velocities have opposite signs, both transmission and reflection are prohibited for normal incidence, when a mirror symmetry normal to the junction is preserved. In this case we show that there necessarily exist gapless states at the interface between the two topological insulators. Their existence is protected by mirror symmetry, and they have characteristic dispersions depending on the symmetry of the system.
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Topological insulators in the ${\text{Bi}}_{2}{\text{Se}}_{3}$ family have an energy gap in the bulk and a gapless surface state consisting of a single Dirac cone. Low-frequency optical absorption due to the surface state is universally determined by the fine-structure constant. When the thickness of these three-dimensional topological insulators is reduced, they become quasi-two-dimensional insulators with enhanced absorbance. The two-dimensional insulators can be topologically trivial or nontrivial depending on the thickness, and we predict that the optical absorption is larger for topological nontrivial case compared with the trivial case. Since the three-dimensional topological insulator surface state is intrinsically gapless, we propose its potential application in wide bandwidth, high-performance photodetection covering a broad spectrum ranging from terahertz to infrared. The performance of photodetection can be dramatically enhanced when the thickness is reduced to several quintuple layers with a widely tunable band gap depending on the thickness.
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Topological insulators in the ${\text{Bi}}_{2}{\text{Se}}_{3}$ family have an energy gap in the bulk and a gapless surface state consisting of a single Dirac cone. Low-frequency optical absorption due to the surface state is universally determined by the fine-structure constant. When the thickness of these three-dimensional topological insulators is reduced, they become quasi-two-dimensional insulators with enhanced absorbance. The two-dimensional insulators can be topologically trivial or nontrivial depending on the thickness, and we predict that the optical absorption is larger for topological nontrivial case compared with the trivial case. Since the three-dimensional topological insulator surface state is intrinsically gapless, we propose its potential application in wide bandwidth, high-performance photodetection covering a broad spectrum ranging from terahertz to infrared. The performance of photodetection can be dramatically enhanced when the thickness is reduced to several quintuple layers with a widely tunable band gap depending on the thickness.
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Topological insulators are new class of quantum materials, which have insulating energy gaps in bulk, but exhibit gapless edge states or surface states that are protected by time-reversal symmetry at boundary. It was theoretically predicted and experimentally confirmed that the binary tetradymites Bi2Te3, Bi2Se3, and Sb2Te3 are three-dimensional topological insulators. In this work, we demonstrate by first-principles approach that the ignored Sb2Se3, although with relatively smaller spin-orbital coupling strength, can also exhibit topologically protected surface states with a bulk gap of 0.19 eV, as long as the van der Waals interaction is explicitly included in the calculations. Detailed analysis of the band structures of Sb2Se3 thin films indicates that the non-trivial surface state appears at a critical thickness of six quintuple layers.
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Topological insulators (quantum spin Hall systems) are insulating in the bulk but have gapless edge/surface states, which remain gapless even when nonmagnetic disorder or interaction is present. This robustness stems from the topological nature characterized by the Z2 topological number, and this offers us various kinds of new novel properties. We review prominent advances in theories and in experiments on topological insulators since their theoretical proposal in 2005.
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