Chiral Bogoliubov excitations in nonlinear bosonic systems

We derive the diagram of the topological phases accessible within a generic Hamiltonian describing quantum anomalous Hall effect for photons and electrons in honeycomb lattices in presence of a Zeeman field and Spin-Orbit Coupling (SOC). The two cases differ crucially by the winding number of their SOC, which is 1 for the Rashba SOC of electrons, and 2 for the photon SOC induced by the energy splitting between the TE and TM modes. As a consequence, the two models exhibit opposite Chern numbers ±2 at low field. Moreover, the photonic system shows a topological transition absent in the electronic case. If the photonic states are mixed with excitonic resonances to form interacting exciton-polaritons, the effective Zeeman field can be induced and controlled by a circularly polarized pump. This new feature allows an all-optical control of the topological phase transitions. PACS numbers:The discovery of the quantum Hall effect [1] and its explanation in terms of topology [2,3] have refreshed the interest to the band theory in condensed matter physics leading to the definition of a new class of insulators [4,5]. They include quantum anomalous Hall (QAH) phase [6] with broken time reversal (TR) symmetry [7][8][9] (also called Chern or Z insulators) and Quantum Spin Hall (QSH or Z 2 ) Topological Insulators with conserved TR symmetry [10][11][12]. The QSH effect was initially predicted to occur in honeycomb lattices because of the intrinsic Spin-Orbit Coupling (SOC) of the atoms forming the lattice, whereas the extrinsic Rashba SOC is detrimental for QSH [11]. On the other hand, the classical anomalous Hall effect is now known to arise from a combination of extrinsic Rashba SOC and of an effective Zeeman field [13]. In a 2D lattice with Dirac cones it leads to the formation of a QAH phase, for which the intrinsic SOC is detrimental [14][15][16]. In the large Rashba SOC limit, this description was found to converge towards an extended Haldane model [14]. Another field, which has considerably grown these last years, is the emulation of such topological insulators with different types of particles, such as fermions (either charged, as electrons in nanocrystals [17,18], or neutral, such as fermionic atoms in optical lattices [19,20]) and bosons (atoms, photons, or mixed light-matter quasiparticles) [21][22][23][24][25][26][27][28][29]. The main advantage of artificial analogs is the possibility to tune the parameters [30], to obtain inaccessible regimes, and to measure quantities out of reach in the original systems. These analogs also call for their own applications, beyond those of the originals. Photonic systems have indeed allowed the first demonstration the QAHE [31,32], later implemented in electronic [33] and atomic systems [34]. They have allowed the realization of topological bands with high Chern numbers (C n ) [35], making possible to work with superpositions of chiral edge states. From an applied point of view, they open the way to non-reciprocal photonic transport, highly desirable to implement logical photonic ...

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confidence: 79%

Photonic versus electronic quantum anomalous Hall effect

Bleu¹,

Solnyshkov²,

Malpuech³

2017

“…[1][2][3][4][5][6][7][8][9][11][12][13]20 On the one hand, these bosonic systems often break conservation of the quasi-particle number even at the level of respective quadratic Hamiltonian. 8,9,[11][12][13][14][15][16]19,[21][22][23][24][25][26][27] Thereby, one naturally wonders if the quasi-particle flow along the topological edge modes is still robust against such particle-number-nonconserving perturbations or not. In other words, one may raise a question whether two quantum Hall regimes with different Chern integers are topologically distinguishable even in the absence of the U(1) symmetry associated with the quasi-particle number conservation.…”

mentioning

confidence: 99%

Integer quantum magnon Hall plateau-plateau transition in a spin-ice model

Ohtsuki

Shindou

2016

Low-energy magnon bands in a two-dimensional spin ice model become integer quantum magnon Hall bands under an out-of-plane field. By calculating the localization length and the two-terminal conductance of magnon transport, we show that the magnon bands with disorders undergo a quantum phase transition from an integer quantum magnon Hall regime to a conventional magnon localized regime. Finite size scaling analysis as well as a critical conductance distribution shows that the quantum critical point belongs to the same universality class as that in the quantum Hall transition. We characterize thermal magnon Hall conductivity in disordered quantum magnon Hall system in terms of robust chiral edge magnon transport. PACS numbers:Bosonic analogue of integer quantum Hall states have been proposed in a number of quasi-particle boson systems with broken time-reversal symmetry such as photon, 1-6 phonon, 7 exciton, 8 exciton-polariton, 9 triplon, 10 magnon 11-19 and surface magnon-polariton. 20 Typically, their quasi-particle excitations have extended bulk bands with topological integers and topological edge modes whose chiral dispersions cross band gaps among these bulk bands. Due to its chiral (unidirectional) nature, a quasi-particle boson flow along the edge mode is believed to be robust against generic elastic backward scatters, fostering a rich prospect of their future applications. [1][2][3][4][5][6][7][8][9][11][12][13]20 On the one hand, these bosonic systems often break conservation of the quasi-particle number even at the level of respective quadratic Hamiltonian. 8,9,[11][12][13][14][15][16]19,[21][22][23][24][25][26][27] Thereby, one naturally wonders if the quasi-particle flow along the topological edge modes is still robust against such particle-number-nonconserving perturbations or not. In other words, one may raise a question whether two quantum Hall regimes with different Chern integers are topologically distinguishable even in the absence of the U(1) symmetry associated with the quasi-particle number conservation.In this rapid communication, we study effects of generic disorder potentials in a simplest spin model in a quantum magnon Hall regime. Our numerical results and the following argument clarify that, even without the explicit U(1) symmetry at the Hamiltonian level, the topological magnon edge mode provides a robust quantized magnon conductance and therefore quantum magnon Hall regimes with different topological integers are always distinguished by a quantum critical point with delocalized bulk magnon band. Thermal conductance distributions calculated at the critical point clearly shows that the quantum critical point belongs to the same universality class as the two-dimensional integer quantum Hall plateau-plateau transition. Based on these knowledge, we give a generic expression for the thermal Hall conductivity in disordered integer quantum bosonic Hall systems from edge transport picture.We study spin excitations in a square-lattice spin ice model 28-31 under out-of-plane Zeeman field H Z ;

“…Note that in order for the scheme to work the photonic and excitonic periodic potentials should be commensurate. It might be possible to circumvent the corresponding finetuning by internally creating a periodic exciton potential from exciton-exciton interactions [23]. We imagine creating an exciton background by driving a mode of the photonic crystal (e.g., q = 0) at energies far away from the photonic Dirac point.…”

Section: Discussionmentioning

confidence: 99%

“…Concepts that were recently developed to avoid this difficulty include the use of (quasi-) time-periodic systems [10,11] or suitably coupled optical cavities or resonators [12][13][14][15][16][17][18]. Another promising direction is hybrid systems where photons interact with mechanical [19] or excitonic [20][21][22][23][24] degrees of freedom. In particular, it is possible to break time-reversal symmetry by coupling photons to Zeeman-split excitons [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Topological polaritons from photonic Dirac cones coupled to excitons in a magnetic field

Karzig

2016

Self Cite

We introduce an alternative scheme for creating topological polaritons (topolaritons) by exploiting the presence of photonic Dirac cones in photonic crystals with triangular lattice symmetry. As recently proposed, topolariton states can emerge from a coupling between photons and excitons combined with a periodic exciton potential and a magnetic field to open up a topological gap. We show that in photonic crystals the opening of the gap can be substantially simplified close to photonic Dirac points. Coupling to Zeeman-split excitons breaks time reversal symmetry and allows to gap out the Dirac cones in a nontrival way, leading to a topological gap similar to the strength of the periodic exciton potential. Compared to the original topolariton proposal [T. Karzig et al., Phys. Rev. X 5, 031001 (2015)], this scheme significantly increases the size of the topological gap over a wide range of parameters. Moreover, the gap opening mechanism highlights an interesting connection between topolaritons and the scheme of [F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008)] to create topological photons in magneto-optically active materials.