Kagome lattice from an exciton-polariton perspective

Gulevich, Dmitry R.; Yudin, Dmitry; Iorsh, I. V.; Shelykh, I. A.

doi:10.1103/physrevb.94.115437

Cited by 41 publications

(48 citation statements)

References 81 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is a variety of two-dimensional lattices that support flat energy bands [9][10][11], with the so-called Lieb lattice being on of the most straightforward examples [12]. Lieb lattices have been studied extensively in recent years and flatband states have been observed in photonic [13][14][15] as well as cold atom systems [16].…”

mentioning

confidence: 99%

Polariton condensation in S- and P-flatbands in a two-dimensional Lieb lattice

Klembt

Harder

Egorov

et al. 2017

Applied Physics Letters

View full text Add to dashboard Cite

We study the condensation of exciton-polaritons in a two-dimensional Lieb lattice of micropillars. We show selective polariton condensation into the flatbands formed by S and Px,y orbital modes of the micropillars under non-resonant laser excitation. The real space mode patterns of these condensates are accurately reproduced by the calculation of related Bloch modes of S-and Pflatbands. Our work emphasizes the potential of exciton-polariton lattices to emulate Hamiltonians of advanced potential landscapes. Furthermore, the obtained results provide a deeper inside into the physics of flatbands known mostly within the tight-binding limit.Dispersionless energy bands or flatbands (FBs) appear in a large variety of condensed matter systems and are linked to a wide range of topological many-body phenomena such as graphene edge modes [1], the fractional quantum Hall effect [2][3][4][5] and flat band ferromagnetism [6][7][8].There is a variety of two-dimensional lattices that support flat energy bands [9][10][11], with the so-called Lieb lattice being on of the most straightforward examples [12]. Lieb lattices have been studied extensively in recent years and flatband states have been observed in photonic [13][14][15] as well as cold atom systems [16]. Creating artificial lattices in order to emulate and simulate complex many-body systems with additional degrees of freedom has attracted considerable scientific interest [17][18][19]. Exciton-polariton gases in periodic lattice potential landscapes have emerged as a very promising solid state system to emulate many-body physics [20,21]. Polaritons are eigenstates resulting of strong coupling between a quantum well exciton and a photonic cavity mode. The excitonic fraction provides a strong nonlinearity while the photonic part results in a low effective mass, allowing the formation of driven-dissipative BoseEinstein condensation [22,23]. These so-called quantum fluids of light [24] can be placed in an artificial lattice potential landscape using a variety of well developed semiconductor etching techniques [9,25,26], thin metal films [27], surface acoustic waves [28], or optically imprinted lattices [29,30]. In this work we investigate the polariton photoluminescence (PL) emission in a two-dimensional Lieb lattice ( Fig. 1(a)). Due to destructive interference of next neighbor tunneling J, flatbands form. Fig. 1(b) shows a tightbinding calculation of the first Brillouin zone (BZ) band structure, with the flatband dispersion highlighted in red. High symmetry points of the BZ are found in the inset.The two-dimensional polaritonic Lieb lattice was fabricated using an electron beam lithography process * sebastian.klembt@physik.uni-wuerzburg.de and a consecutive reactive ion etching step on an AlAs λ/2-cavity with three stacks of four 13 nm wide GaAs quantum wells (QWs) placed in the antinode of the electric field, with a 32.5 (36) fold AlAs/Al 0.20 Ga 0.80 As top (bottom) distributed Bragg reflector (DBR) (Fig. 1(c,d)). The Rabi splitting of the sample is 9.5 meV. Only the top D...

show abstract

mentioning

confidence: 99%

Polariton condensation in S- and P-flatbands in a two-dimensional Lieb lattice

Klembt

Harder

Egorov

et al. 2017

Applied Physics Letters

View full text Add to dashboard Cite

show abstract

“…It is at the origin of a very large variety of spin-related effects, such as the optical spin Hall effect [44,45], half-integer topological defects [46,47], Berry phase for photons [48], and the generation of topologically protected spin currents in polaritonic molecules [49]. The combination of a TE-TM SOC and a Zeeman field in a honeycomb lattice has indeed been found to yield a QAH phase [29,[50][51][52][53][54][55], and the related model represents a generalization of the seminal Haldane-Raghu proposal [56] of photonic topological insulator, recovered for large TE-TM SOC.In this manuscript, we demonstrate the role played by the winding number of the SOC on the QAH phases. We establish the complete phase diagram for both the photonic and electronic graphene.…”

mentioning

confidence: 99%

Photonic versus electronic quantum anomalous Hall effect

Bleu¹,

Solnyshkov²,

Malpuech³

2017

Phys. Rev. B

View full text Add to dashboard Cite

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 ...

show abstract

“…Recently, microcavities have been actively investigated as quantum simulators of condensed matter systems. Polaritons have been proposed to simulate XY Hamiltonian [25], topological insulators [26,27], various types of lattices [28][29][30][31] among other interesting proposals [32] many of which were realized experimentally. In fact, the quasi one-dimensional zigzag chain considered here may be a more practical system to study the effects of interactions in presence of spin-orbit coupling as compared to the full two-dimensional systems mentioned above.…”

Section: Discussionmentioning

confidence: 99%

Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains

et al. 2019

View full text Add to dashboard Cite

We consider a system of generalized coupled Discrete Nonlinear Schrödinger (DNLS) equations, derived as a tight-binding model from the Gross-Pitaevskii-type equations describing a zigzag chain of weakly coupled condensates of exciton-polaritons with spin-orbit (TE-TM) coupling. We focus on the simplest case when the angles for the links in the zigzag chain are ±π/4 with respect to the chain axis, and the basis (Wannier) functions are cylindrically symmetric (zero orbital angular momenta). We analyze the properties of the fundamental nonlinear localized solutions, with particular interest in the discrete gap solitons appearing due to the simultaneous presence of spin-orbit coupling and zigzag geometry, opening a gap in the linear dispersion relation. In particular, their linear stability is analyzed. We also find that the linear dispersion relation becomes exactly flat at particular parameter values, and obtain corresponding compact solutions localized on two neighboring sites, with spin-up and spindown parts π/2 out of phase at each site. The continuation of these compact modes into exponentially decaying gap modes for generic parameter values is studied numerically, and regions of stability are found to exist in the lower or upper half of the gap, depending on the type of gap modes. , integrating over x and y, using the orthogonality of Wannier functions and neglecting all overlaps beyond nearest neighbors, we obtain from (4) a 1D lattice equation of the following form for the site amplitudes of the spin-up component:

show abstract

Kagome lattice from an exciton-polariton perspective

Cited by 41 publications

References 81 publications

Polariton condensation in S- and P-flatbands in a two-dimensional Lieb lattice

Polariton condensation in S- and P-flatbands in a two-dimensional Lieb lattice

Photonic versus electronic quantum anomalous Hall effect

Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains

Contact Info

Product

Resources

About