Realization of Hofstadter's butterfly and a one-way edge mode in a polaritonic system

Abstract

We present a scheme to generate an artificial gauge field for the system of neutral bosons, represented by polaritons in micropillars arranged into a square lattice. The splitting between the two polarizations of the micropillars breaks the time-reversal symmetry (TRS) and results in the effective phase dependent hopping between cavities. This can allow for engineering a non-zero flux on the plaquette, corresponding to an artificial magnetic field. Changing the phase, we observe a characteristic Hofstadter's butterfly pattern and the appearance of chiral edge states for a finite size structure. For long-lived polaritons, we show that the propagation of wave packets at the edge is robust against disorder. Moreover, given the inherent driven-dissipative nature of polariton lattices, we find that the system can exhibit topological lasing, recently discovered for active ring cavity arrays. The results point to a static way to realize artificial magnetic field in neutral spinful systems, avoiding the periodic modulation of the parameters or strong spin-orbit interaction. Ultimately, the described system can allow for high-power topological single mode lasing which is robust to imperfections.

Structure of surface electronic states in strained mercury telluride

“…It follows from figures 2(b) and (c) that the DKh branch merges into the continuum of bulk conduction band in the case of tensile strain (see figure 2(b)) and the continuum of bulk valence band in the case of compressive strain (see figure 2(c)) at a some critical electron wave vector. The value of the critical wave vector, k s =k 0 , is defined by equations (16)- (18), where the energy of the surface electron states, ε, is equal to the energy of one of the two bulk electron branches, It should be noted that the spectrum of the DKh surface states in strained materials of HgTe-class crucially depends on the Luttinger parameters. To demonstrate this, we plotted the dispersion of the DKh surface states in figure 3 for the HgTe band parameter m 9.0 2 2 0  g = but for different Luttinger parameters γ 1 .…”

“…Solving equations (16)-(18) together with equation(20), one can find that k g 0 e µ | |. Thus, the increase of the strain-induced gap ε g shifts the existence domain of the DKh surface states to the region of large electron wave vectors, k s .…”

Nonreciprocal Transport of Exciton Polaritons in a Non-Hermitian Chain

“…Significant motivation has been drawn from topological photonics, where chiral edge states have been suggested for directionally dependent connections [17,18]. Theoretically, robust polaritonic edge states can be achieved in many ways: by lifting the spin degeneracy and using spin-orbit coupling [19][20][21][22][23][24][25][26]; by realizing Hofstadter's butterfly [27]; by using nonlinear interactions [28,29]; by using staggered honeycomb lattices [30]; or by Floquet engineering [31]. The scheme in Refs.…”

Optically induced topological spin-valley Hall effect for exciton polaritons

“…[23]. Several other theoretical proposals for realizing topological polaritons followed related to the same scheme [45][46][47][48][49][50][51][52][53][54], by using the polarization splitting inside the elliptical micropil-lars [55], by using vortices in staggered honeycomb lattices [56], and by Floquet engineering [57]. Apart from the linear effects, the nonlinearity of polaritons alone can induce topological phases, such as the appearance of the Haldane model [58,59] and antichiral edge states [60].…”