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

Abstract

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...

Photonic zero-energy modes in a metal-based Lieb lattice

“…0 and π. Different from previous line states found in the Lieb lattice under bearded truncations [30], here we observe this additional noncompact state in the photonic Lieb lattice under flat truncations, which is compatible with that in infinite systems. They all belong to the missing states that result from the singular touching at k y =π/a, and can supplement the flat band complete.…”

“…However, there are another noncompact modes existing due to the triply degeneracy of Lieb lattice, which not yet to be observed in photonic system. Moreover, the noncompact flat band modes for higher order states (such as the dipolar state) have not been explored, which may contain more interesting mechanism in higher orbital dynamics [15,30,31].…”

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

“…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.…”

Multi-orbital tight binding model for cavity-polariton lattices

“…Such confined modes have been realized by fully etching the semiconductor structure [21,22], by partial etching of the upper cavity mirror [23,24], by growth interruption and etching of the cavity spacer [25,26], and in half cavities closed by an external mirror [27][28][29]. By laterally coupling the photonic modes of the resonators, lattices of different geometries have been implemented, including one-dimensional regular [30][31][32], Stub [33], Su-Schrieffer-Heeger (SSH) lattices [5] and aperiodic lattices [34], and twodimensional honeycomb [4,10] and Lieb lattices [23,24], showing a wide variety of dispersions and topological features. One of the great assets of this system is the possibility of designing lattices with synthetic strain, which have been recently employed to engineer new types of Dirac cones [35] and are promising to engineer artificial gauge fields [36,37].…”