Edge States and Broken Symmetry Phases of Laterally Confined 3^3He Films

Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D) $^3$He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum, $L_z = (N/2) \hbar$, for $N/2$ Cooper pairs. The power law suppression of the angular momentum, $L_z(T) \simeq (N/2)\,\hbar\,[1 - \frac{2}{3}(\pi T/\Delta)^2 ]$ for $0 \le T \ll T_c$, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing surfaces on the edge currents, ground-state angular momentum and ground-state order parameter. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry at $D_{c2} \approx 16 \xi_0$. The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement length $D\rightarrow D_{c_2}$. The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and orignates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral "polar phase" at $D_{c1} \approx 9\xi_0$, in which a single p-wave orbital state of Cooper pairs is aligned along the channel.Comment: 16 pages, 16 figure

Exotic disordered phases in the quantum J1−J2J_1-J_2 model on the honeycomb lattice

We study the ground-state phase diagram of the frustrated quantum $J_1-J_2$ Heisenberg antiferromagnet on the honeycomb lattice using a mean field approach in terms of the Schwinger boson representation of the spin operators. We present results for the ground-state energy, local magnetization, energy gap and spin-spin correlations. The system shows magnetic long range order for $0\leq J_{2}/J_{1}\lesssim 0.2075$ (N\'eel) and $0.398\lesssim J_{2}/J_{1}\leq 0.5$ (spiral). In the intermediate region, we find two magnetically disordered phases: a gapped spin liquid phase which shows short-range N\'eel correlations $(0.2075 \lesssim J_{2}/J_{1} \lesssim 0.3732)$, and a lattice nematic phase $(0.3732 \lesssim J_{2}/J_{1}\lesssim 0.398)$, which is magnetically disordered but breaks lattice rotational symmetry. The errors in the values of the phase boundaries which are implicit in the number of significant figures quoted, correspond purely to the error in the extrapolation of our finite-size results to the thermodynamic limit.Comment: 11 pages, 9 figures, to appear in Phys. Rev.

Quantum phases in the frustrated Heisenberg model on the bilayer honeycomb lattice

We use a combination of analytical and numerical techniques to study the phase diagram of the frustrated Heisenberg model on the bilayer honeycomb lattice. Using the Schwinger boson description of the spin operators followed by a mean field decoupling, the magnetic phase diagram is studied as a function of the frustration coupling $J_{2}$ and the interlayer coupling $J_{\bot}$. The presence of both magnetically ordered and disordered phases is investigated by means of the evaluation of ground-state energy, spin gap, local magnetization and spin-spin correlations. We observe a phase with a spin gap and short range N\'eel correlations that survives for non-zero next-nearest-neighbor interaction and interlayer coupling. Furthermore, we detect signatures of a reentrant behavior in the melting of N\'eel phase and symmetry restoring when the system undergoes a transition from an on-layer nematic valence bond crystal phase to an interlayer valence bond crystal phase. We complement our work with exact diagonalization on small clusters and dimer-series expansion calculations, together with a linear spin wave approach to study the phase diagram as a function of the spin $S$, the frustration and the interlayer couplings.Comment: 10 pages, 9 figure