publications

2021

1. PhysRevB

   Interacting stochastic topology and Mott transition from light response

   Klein, Philipp W., Grushin, Adolfo G., and Le Hur, Karyn

   Physical Review B Jan 2021

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   We develop a stochastic description of the topological properties in an interacting Chern insulator. We confirm the Mott transition’s first-order nature in the interacting Haldane model on the honeycomb geometry, from a mean-field variational approach, supported by density matrix renormalization group results and Ginzburg-Landau arguments. From the Bloch sphere, we make predictions for circular dichroism of light related to the quantum Hall conductivity on the lattice and in the presence of interactions. This analysis shows that the topological number can be measured from the light response at the Dirac points. Electron-electron interactions can also produce a substantial number of particle-hole pairs above the band gap, which leads us to propose a "stochastic Chern number" as an interacting measure of the topology. The stochastic Chern number can describe disordered situations with a fluctuating staggered potential and we build an analogy between interaction-induced particle-hole pairs and temperature effects. Our stochastic approach is physically intuitive, easy to implement and leads the way to further studies of interaction effects.

2. PhysRevB

   Analytical approach for the Mott transition in the Kane-Mele-Hubbard model

   Hutchinson, Joel, Klein, Philipp W., and Le Hur, Karyn

   Physical Review B Aug 2021

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   The description of interactions in strongly-correlated topological phases of matter remains a challenge. Here, we develop a stochastic functional approach for interacting topological insulators including both charge and spin channels. We find that the Mott transition of the Kane-Mele-Hubbard model may be described by the variational principle with one equation. We present different views of this equation from the electron Green’s function, the free-energy and the Hellmann-Feynman theorem. The band gap remains finite at the transition and the Mott phase is characterized by antiferromagnetism in the x−y plane. The interacting topological phase is described through a \mathbbZ_2 number related to helical edge modes. Our results then show that improving stochastic approaches can give further insight on the understanding of interacting phases of matter.

2019

1. PhysRevB

   Topological proximity effects in a Haldane graphene bilayer system

   Cheng, Peng, Klein, Philipp W., Plekhanov, Kirill, Sengstock, Klaus, Aidelsburger, Monika, Weitenberg, Christof, and Le Hur, Karyn

   Physical Review B Aug 2019

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   We reveal a proximity effect between a topological band (Chern) insulator described by a Haldane model and spin-polarized Dirac particles of a graphene layer. Coupling weakly the two systems through a tunneling term in the bulk, the topological Chern insulator induces a gap and an opposite Chern number on the Dirac particles at half-filling resulting in a sign flip of the Berry curvature at one Dirac point. We study different aspects of the bulk-edge correspondence and present protocols to observe the evolution of the Berry curvature as well as two counter-propagating (protected) edge modes with different velocities. In the strong-coupling limit, the energy spectrum shows flat bands. Therefore we build a perturbation theory and address further the bulk-edge correspondence. We also show the occurrence of a topological insulating phase with Chern number one when only the lowest band is filled. We generalize the effect to Haldane bilayer systems with asymmetric Semenoff masses. We propose an alternative definition of the topological invariant on the Bloch sphere.

2018

1. PhysRevB

   Topological superconductivity in the Kondo-Kitaev model

   Choi, Wonjune, Klein, Philipp W., Rosch, Achim, and Kim, Yong Baek

   Physical Review B Oct 2018

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   We investigate possible topological superconductivity in the Kondo-Kitaev model on the honeycomb lattice, where the Kitaev spin liquid is coupled to conduction electrons via the Kondo coupling. We use the self-consistent Abrikosov-fermion mean-field theory to map out the phase diagram. Upon increasing the Kondo coupling, a first order transition occurs from the decoupled phase of spin liquid and conduction electrons to a ferromagnetic topological superconductor of Class D with a single chiral Majorana edge mode. This is followed by a second order transition into a paramagnetic topological superconductor of Class DIII with a single helical Majorana edge mode. These findings offer a novel route to topological superconductivity in the Kondo lattice system. We discuss the connection between topological nature of the Kitaev spin liquid and topological superconductors obtained in this model.