Scientists / Open questions

Charles L. Kane

Condensed matter theory; topological insulators

16 questions

Generalized index theorem and interaction-robust invariants for topological defects in insulators and superconductors beyond the adiabatic free-fermion classification
Microscopic and exactly-solvable realization of the symmetry-respecting topologically ordered surface phase of the three-dimensional electron topological insulator, and the minimal such surface order
Coupled-wire constructions of non-Abelian quantum Hall states: generality, microscopic quasiparticle braiding, and realization beyond the anisotropic limit
Complete characterization of the pinch-off quantum critical point of a point contact in a quantum spin Hall insulator: boundary conformal field theory, universal scaling, fixed-point classification, and experimental signatures
Self-consistent surface potentials and a mirror-chirality-correct tight-binding model for the Bi $_{1-x}$ Sb $_x$ (111) surface spectrum
Weyl lines in three-dimensional Maxwell lattices: experimental detection and systematic classification
Open ends of thermal transport in a Luttinger liquid: interaction-modified Lorenz numbers, microscopic weak-link parameters, and their experimental test
Generalized index theorem and classification for topological Maxwell lattices with topologically protected gapless bulk spectra, and the mechanical-frustrated-magnet correspondence
Open questions for three-dimensional double Dirac semimetals: an interaction-driven symmetry-preserving insulator in space group 135 and materials realization of the double Dirac point
Gauging time-reversal symmetry in three dimensions and a bulk diagnostic for bosonic SPT phases protected by time reversal alone
Stability of sliding Luttinger liquid phases against the complete set of multiwire, marginal, and disorder perturbations
Nonsymmorphic two-dimensional Dirac semimetals: experimental realization at $4n+2$ filling, correlated gapped phases, and disorder-induced localization
Open quantitative tests of the twiston mechanism for the temperature-dependent resistivity of single-wall carbon nanotubes: the low-temperature upturn, the rope-slope discrepancy, single-tube high-temperature transport, and the inter-tube coupling parameters
Rigorous nonperturbative fate of a single weak link in the one-channel Luttinger liquid: the Kane–Fisher impurity renormalization-group flow
Nonperturbative strong-coupling structure of the replica-limit nonlinear sigma model for the two-dimensional symplectic Anderson transition
Facet-dependent chiral edge and corner states in uniformly magnetized three-dimensional topological insulators: experimental realization, detection, and quantitative characterization of the exchange and hybridization parameters

Back to open problems

Generalized index theorem and interaction-robust invariants for topological defects in insulators and superconductors beyond the adiabatic free-fermion classification

Microscopic and exactly-solvable realization of the symmetry-respecting topologically ordered surface phase of the three-dimensional electron topological insulator, and the minimal such surface order

Coupled-wire constructions of non-Abelian quantum Hall states: generality, microscopic quasiparticle braiding, and realization beyond the anisotropic limit

Complete characterization of the pinch-off quantum critical point of a point contact in a quantum spin Hall insulator: boundary conformal field theory, universal scaling, fixed-point classification, and experimental signatures

Self-consistent surface potentials and a mirror-chirality-correct tight-binding model for the Bi1−x_{1-x}1−x​Sbx_xx​ (111) surface spectrum

Weyl lines in three-dimensional Maxwell lattices: experimental detection and systematic classification

Open ends of thermal transport in a Luttinger liquid: interaction-modified Lorenz numbers, microscopic weak-link parameters, and their experimental test

Generalized index theorem and classification for topological Maxwell lattices with topologically protected gapless bulk spectra, and the mechanical-frustrated-magnet correspondence

Open questions for three-dimensional double Dirac semimetals: an interaction-driven symmetry-preserving insulator in space group 135 and materials realization of the double Dirac point

Gauging time-reversal symmetry in three dimensions and a bulk diagnostic for bosonic SPT phases protected by time reversal alone

Stability of sliding Luttinger liquid phases against the complete set of multiwire, marginal, and disorder perturbations

Nonsymmorphic two-dimensional Dirac semimetals: experimental realization at 4n+24n+24n+2 filling, correlated gapped phases, and disorder-induced localization

Open quantitative tests of the twiston mechanism for the temperature-dependent resistivity of single-wall carbon nanotubes: the low-temperature upturn, the rope-slope discrepancy, single-tube high-temperature transport, and the inter-tube coupling parameters

Rigorous nonperturbative fate of a single weak link in the one-channel Luttinger liquid: the Kane–Fisher impurity renormalization-group flow

Nonperturbative strong-coupling structure of the replica-limit nonlinear sigma model for the two-dimensional symplectic Anderson transition

Facet-dependent chiral edge and corner states in uniformly magnetized three-dimensional topological insulators: experimental realization, detection, and quantitative characterization of the exchange and hybridization parameters

Self-consistent surface potentials and a mirror-chirality-correct tight-binding model for the Bi $_{1-x}$ Sb $_x$ (111) surface spectrum

Nonsymmorphic two-dimensional Dirac semimetals: experimental realization at $4n+2$ filling, correlated gapped phases, and disorder-induced localization