Papers

Spin Hall effect is one of the primary sources of pure spin current in spintronic devices, observed in spin-orbit coupled materials. In this work, we investigate linear and non-linear pure spin currents in the hexagonally warped surface states of topological insulators like $\rm Bi_2Te_3$, using the formalism of conserved spin transport. The hexagonal warping effect enables the application of this formalism by providing a well-defined Berry curvature without breaking the time-reversal symmetry. The absence of in-plane spin currents in the linear response motivates the extension of the formalism to the non-linear regime, by combining the perturbation of Bloch states with the Boltzmann transport equation. The second-order response exhibits both intrinsic and extrinsic in-plane spin currents induced by the spin-weighted Berry curvature, Berry connection polarizability (BCP) dipole and Berry curvature dipole (BCD) respectively. The band anisotropy due to the $C_{3v}$ symmetry of the material ($\rm Bi_2Te_3$) propagates through the spin textures and the band geometric quantities, resulting in the selection of certain components of the spin conductivity tensors.

Achieving high-lying vibrational states is essential for actively controlling molecular reactions. We demonstrate vibrational ladder climbing of CO adsorbed on Pt(111) within the plasmonic tip-substrate nanogap formed in a scanning tunneling microscope, detected via tip-enhanced sum-frequency generation (TE-SFG). As the infrared pulse energy increases, hot-band peaks appear sequentially up to the 3-4 transition, indicating the stepwise population of higher vibrational states. Numerical analysis using the optical Bloch equations captures the observed energy dependence of these features. These results demonstrate the capability of TE-SFG to probe vibrational ladder climbing in surface molecular systems and suggest a promising route toward accessing high-lying vibrational states and controlling vibrational excitation at the nanoscale.

Topological $K$-theory supplies the decisive stable classification principle for gapped free-fermion phases in Euclidean crystals once symmetry and stabilization are fixed. In hyperbolic band theory, by contrast, it is less decisive for the full band problem: generalized momentum sectors vary through moduli spaces, but passing to ordinary $K$-classes collapses their geometric and holomorphic variation. We distinguish kinematical holomorphy, in which complex geometry organizes the sector spaces, from dynamical holomorphy, in which that geometry informs a Hamiltonian or projector, and formulate the resulting loss as an observable-factorization problem. For a compact hyperbolic surface $X$, we prove nonfactorization in three settings: fibrewise $K^0(X)$, occupied-state $K^0(B)$, and operator-algebraic $K$-theory. The affected quantities include spectra and Higgs spectral curves, the Berry holonomy and the quantum metric, the partially filled Hall response, and the Fermi surface and nodal geometries. We also identify the quantized pairings and local charges retained by topology. Up to an explicit area factor, the Kotani–Sunada bottom-band Hessian is the Hodge inner product on $H^1(X;\mathbb R)$. Together with the integral intersection form, it recovers the homology-marked principally polarized Jacobian and hence, by Torelli and uniformization, the underlying complex and hyperbolic surface, though not a full Teichmüller marking. We also separate finite-rank sectors from the thermodynamic bulk. Locally faithful covers reproduce polynomial traces exactly and control continuous spectral observables. In arithmetic congruence towers, analytic observables converge as $O(|G_n|^{-\eta})$ for some $\eta>0$, and $C^s$ observables as $O((\log |G_n|)^{-s})$, while established coherent large-rank limits recover bulk density-of-states moments.

Transition metal dichalcogenide moiré heterobilayers with type-II band alignment provide a versatile platform for layer-polarized generalized Wigner crystals, in which strong Coulomb interactions drive charge ordering at fractional lattice fillings. With a finite interlayer band offset, an out-of-plane electric field can tune layer-resolved moiré bands through resonance and enable controllable interlayer hybridization. Although hybridized Mott insulators have been previously demonstrated, whether fractional charge-ordered states can survive such hybridization remains elusive. Here we drive an H-stacked MoSe2/WS2 moiré heterobilayer through a type-I-to-type-II band-alignment transition and realize layer-hybridized Mott insulator and generalized Wigner crystals. For fillings below one electron per moiré cell, tunneling delocalizes electrons and modifies Wigner crystallization. However, above one electron per cell, Coulomb repulsion overcomes tunneling and favors layer-separated occupation, stabilizing stronger charge-ordered states. These results establish electrically tunable hybridized moiré heterobilayers as a powerful platform for engineering correlated charge order and exploring fractional Chern phases and emergent magnetism.