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Very few topological systems with long-range couplings have been considered so far due to our lack of analytic approaches. Here we extend the Kitaev chain, a 1D quantum liquid, to infinite-range couplings and study its topological properties. We demonstrate that, even though topological phases are intimately linked to the notion of locality, the infinite-range couplings give rise to topological zero and non-zero energy Majorana end modes depending on the boundary conditions of the system. We show that the analytically derived properties are to a large degree stable against modifications to decaying long-range couplings. Our work opens new frontiers for topological states of matter that are relevant to current experiments where suitable interactions can be designed.
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We establish the appearance of a qualitatively new type of spin liquid with emergent exceptional points when coupling to the environment. We consider an open system of the Kitaev honeycomb model generically coupled to an external environment. In extended parameter regimes, the Dirac points of the emergent Majorana fermions from the original model are split into exceptional points with Fermi arcs connecting them. In glaring contrast to the original gapless phase of the honeycomb model which requires time-reversal symmetry, this new phase is stable against all perturbations. The system also displays a large sensitivity to boundary conditions resulting from the non-Hermitian skin effect with telltale experimental consequences. Our results point to the emergence of new classes of spin liquids in open systems which might be generically realized due to unavoidable couplings with the environment.
Motivated by recent transport measurements in high-$T_c$ cuprate superconductors in a magnetic field, we study the thermal Hall conductivity in materials with topological order, focusing on the contribution from neutral spinons. Specifically, different Schwinger boson mean-field ans{a}tze for the Heisenberg antiferromagnet on the square lattice are analyzed. We allow for both Dzyaloshinskii-Moriya interactions, and additional terms associated with scalar spin chiralities that break time-reversal and reflection symmetries, but preserve their product. It is shown that these scalar spin chiralities, which can either arise spontaneously or are induced by the orbital coupling of the magnetic field, can lead to spinon bands with nontrivial Chern numbers and significantly enhanced thermal Hall conductivity. Associated states with zero-temperature magnetic order, which is thermally fluctuating at any $T>0$, also show a similarly enhanced thermal Hall conductivity.
The electron-phonon interaction is of central importance for the electrical and thermal properties of solids, and its influence on superconductivity, colossal magnetoresistance, and other many-body phenomena in correlated-electron materials is currently the subject of intense research. However, the non-local nature of the interactions between valence electrons and lattice ions, often compounded by a plethora of vibrational modes, present formidable challenges for attempts to experimentally control and theoretically describe the physical properties of complex materials. Here we report a Raman scattering study of the lattice dynamics in superlattices of the high-temperature superconductor $bf YBa_2 Cu_3 O_7$ and the colossal-magnetoresistance compound $bf La_{2/3}Ca_{1/3}MnO_{3}$ that suggests a new approach to this problem. We find that a rotational mode of the MnO$_6$ octahedra in $bf La_{2/3}Ca_{1/3}MnO_{3}$ experiences pronounced superconductivity-induced lineshape anomalies, which scale linearly with the thickness of the $bf YBa_2 Cu_3 O_7$ layers over a remarkably long range of several tens of nanometers. The transfer of the electron-phonon coupling between superlattice layers can be understood as a consequence of long-range Coulomb forces in conjunction with an orbital reconstruction at the interface. The superlattice geometry thus provides new opportunities for controlled modification of the electron-phonon interaction in complex materials.
We study charge transport through a floating mesoscopic superconductor coupled to counterpropagating fractional quantum Hall edges at filling fraction $ u=2/3$. We consider a superconducting island with finite charging energy and investigate its effect on transport through the device. We calculate conductance through such a system as a function of temperature and gate voltage applied to the superconducting island. We show that transport is strongly affected by the presence of parafermionic zero modes, leading at zero temperature to a zero-bias conductance quantized in units of $ u e^2/h$ independent of the applied gate voltage.
We study the spin excitation spectra and the dynamical exchange coupling between iron adatoms on a Bi bilayer nanoribbon. We show that the topological character of the edge states is preserved in the presence of the magnetic adatoms. Nevertheless, they couple significantly to the edge spin currents, as witnessed by the large and long-ranged dynamical coupling we obtain in our calcula- tions. The large effective magnetocrystalline anisotropy of the magnetic adatoms combined with the transport properties of the topologically protected edge states make this system a strong candidate for implementation of spintronics devices and quantum information and/or computation protocols.
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