Tidal surface states as fingerprints of non-Hermitian nodal knot metals

Zhang, Xiao; Li, Guangjie; Liu, Yuhan; Tai, Tommy; Thomale, Ronny; Lee, Ching Hua

doi:10.1038/s42005-021-00535-1

Cited by 57 publications

(27 citation statements)

References 81 publications

(106 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, in two dimensions, an exceptional point has a nontrivial topological charge associated with eigenvalue braiding on a small circle enclosing it [36]. In three dimensions, the exceptional locus is generically one-dimensional, for example forming exceptional rings, lines, or even knots and links [37][38][39][40]. In addition to these topologically charged exceptional objects, braid-group valued invariants can be associated to non-contractible cycles in the Brillouin zone torus [25].…”

mentioning

confidence: 99%

Eigenvalue topology of non-Hermitian band structures in two and three dimensions

Wojcik,

Wang,

Dutt

et al. 2021

Preprint

View full text Add to dashboard Cite

In the band theory for non-Hermitian systems, the energy eigenvalues, which are complex, can exhibit non-trivial topology which is not present in Hermitian systems. In one dimension, it was recently noted theoretically and demonstrated experimentally that the eigenvalue topology is classified by the braid group. The classification of eigenvalue topology in higher dimensions, however, remained an open question. Here, we give a complete description of eigenvalue topology in two and three dimensional systems, including the gapped and gapless cases. We reduce the topological classification problem to a purely computational problem in algebraic topology. In two dimensions, the Brillouin zone torus is punctured by exceptional points, and each nontrivial loop in the punctured torus acquires a braid group invariant. These braids satisfy the constraint that the composite of the braids around the exceptional points is equal to the commutator of the braids on the fundamental cycles of the torus. In three dimensions, there are exceptional knots and links, and the classification depends on how they are embedded in the Brillouin zone three-torus. When the exceptional link is contained in a contractible ball, the classification can be expressed in terms of the knot group of the link. Our results provide a comprehensive understanding of non-Hermitian eigenvalue topology in higher dimensional systems, and should be important for the further explorations of topologically robust open quantum and classical systems.

show abstract

mentioning

confidence: 99%

Eigenvalue topology of non-Hermitian band structures in two and three dimensions

Wojcik,

Wang,

Dutt

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Here we use the so-called generalized Brillouin zone (GBZ) method to elaborate why ν ( E r ) can be captured by the complex spectral evolution. According to the non-Bloch band theory, the OBC spectrum can be described by the PBC one in a GBZ, using a complex deformation of the quasi-momentum k → k + i κ OBC ( k ) 9 , 12 , 32 , 62 , 63 . The PBC-OBC spectral evolution can then be effectively described by k → k + i κ ( k ) with κ ( k ) varying from 0 to κ OBC ( k ), with κ OBC ( k ) having the minimal magnitude to yield the OBC spectrum 12 , 63 .…”

Section: Methodsmentioning

confidence: 99%

Quantized classical response from spectral winding topology

Lee

et al. 2021

Nat Commun

Self Cite

View full text Add to dashboard Cite

Topologically quantized response is one of the focal points of contemporary condensed matter physics. While it directly results in quantized response coefficients in quantum systems, there has been no notion of quantized response in classical systems thus far. This is because quantized response has always been connected to topology via linear response theory that assumes a quantum mechanical ground state. Yet, classical systems can carry arbitrarily amounts of energy in each mode, even while possessing the same number of measurable edge states as their topological winding. In this work, we discover the totally new paradigm of quantized classical response, which is based on the spectral winding number in the complex spectral plane, rather than the winding of eigenstates in momentum space. Such quantized response is classical insofar as it applies to phenomenological non-Hermitian setting, arises from fundamental mathematical properties of the Green’s function, and shows up in steady-state response, without invoking a conventional linear response theory. Specifically, the ratio of the change in one quantity depicting signal amplification to the variation in one imaginary flux-like parameter is found to display fascinating plateaus, with their quantized values given by the spectral winding numbers as the topological invariants.

show abstract

“…To understand how, note that the complex deformation k → p(k) can be understood geometrically [Fig. 1c]: While the PBC spectrum (solid loop) traces out a loop E(k), k ∈ [0, 2π) in the complex E plane, the OBC spectrum (line of crests within the loop) is obtained by the ramping up |Im(p)| such that the PBC loop "shrinks" into its interior until it overlaps with itself i.e is degenerate everywhere [6,12,38,39]. In this OBC limit, the spectrum Ē traces out lines or curve segments connected to each other at branch points.…”

Section: A Unbalanced Couplings Real Spectra and Their Electrostatics...mentioning

confidence: 99%

Designing non-Hermitian real spectra through electrostatics

Yang¹,

Tan²,

Tai³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

Non-hermiticity presents a vast newly opened territory that harbors new physics and applications such as lasing and sensing. However, only non-Hermitian systems with real eigenenergies are stable, and great efforts have been devoted in designing them through enforcing parity-time (PT) symmetry. In this work, we exploit a lesser-known dynamical mechanism for enforcing real-spectra, and develop a comprehensive and versatile approach for designing new classes of parent Hamiltonians with real spectra. Our design approach is based on a novel electrostatics analogy for modified non-Hermitian bulk-boundary correspondence, where electrostatic charge corresponds to density of states and electric fields correspond to complex spectral flow. As such, Hamiltonians of any desired spectra and state localization profile can be reverse-engineered, particularly those without any guiding symmetry principles. By recasting the diagonalization of non-Hermitian Hamiltonians as a Poisson boundary value problem, our electrostatics analogy also transcends the gain/loss-induced compounding of floating-point errors in traditional numerical methods, thereby allowing access to far larger system sizes.

show abstract

Tidal surface states as fingerprints of non-Hermitian nodal knot metals

Cited by 57 publications

References 81 publications

Eigenvalue topology of non-Hermitian band structures in two and three dimensions

Eigenvalue topology of non-Hermitian band structures in two and three dimensions

Quantized classical response from spectral winding topology

Designing non-Hermitian real spectra through electrostatics

Contact Info

Product

Resources

About