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Register a new userEmergence and stability of spin-valley entangled quantum liquids in moire heterostructures
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Twisting moire heterostructures to the flatband regime allows for the formation of strongly correlated quantum states, since the dramatic reduction of the bandwidth can cause the residual electronic interactions to set the principal energy scale. An effective description for such correlated moire heterostructures, derived in the strong-coupling limit at integer filling, generically leads to spin-valley Heisenberg models. Here we explore the emergence and stability of spin liquid behavior in an SU(2)$^{mathrm{spin}}otimes$SU(2)$^{mathrm{valley}}$ Heisenberg model upon inclusion of Hunds-induced and longer-ranged exchange couplings, employing a pseudofermion functional renormalization group approach. We consider two lattice geometries, triangular and honeycomb (relevant to different moire heterostructures), and find, for both cases, an extended parameter regime surrounding the SU(4) symmetric point where no long-range order occurs, indicating a stable realm of quantum spin liquid behavior. For large Hunds coupling, we identify the adjacent magnetic orders, with both antiferromagnetic and ferromagnetic ground states emerging in the separate spin and valley degrees of freedom. For both lattice geometries the inclusion of longer-ranged exchange couplings is found to have both stabilizing and destabilizing effects on the spin liquid regime depending on the sign of the additional couplings.
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We consider fractional quantum Hall states in systems where two flat Chern number $C=pm 1$ bands are labeled by an approximately conserved valley index and interchanged by time reversal symmetry. At filling factor $ u=1$ this setting admits an unusual hierarchy of correlated phases of excitons, neutral particle-hole pair excitations of a fully valley-polarized `orbital ferromagnet parent state where all electrons occupy a single valley. Excitons experience an effective magnetic field due to the Chern numbers of the underlying bands. This obstructs their condensation in favor of a variety of crystalline orders and gapped and gapless liquid states. All these have the same quantized charge Hall response and are electrically incompressible, but differ in their edge structure, orbital magnetization, and hence valley and thermal responses. We explore the relevance of this scenario for Moire heterostructures of bilayer graphene on a hexagonal boron nitride substrate.
Quantum spin liquids provide paradigmatic examples of highly entangled quantum states of matter. Frustration is the key mechanism to favor spin liquids over more conventional magnetically ordered states. Here we propose to engineer frustration by exploiting the coupling of quantum magnets to the quantized light of an optical cavity. The interplay between the quantum fluctuations of the electro-magnetic field and the strongly correlated electrons results in a tunable long-range interaction between localized spins. This cavity-induced frustration robustly stabilizes spin liquid states, which occupy an extensive region in the phase diagram spanned by the range and strength of the tailored interaction. Remarkably, this occurs even in originally unfrustrated systems, as we showcase for the Heisenberg model on the square lattice.
Recent experiments have observed correlated insulating and possible superconducting phases in twisted homobilayer transition metal dichalcogenides (TMDs). Besides the spin-valley locked moire bands due to the intrinsic Ising spin-orbit coupling, homobilayer moire TMDs also possess either logarithmic or power-law divergent Van Hove singularities (VHS) near the Fermi surface, controllable by an external displacement field. The former and the latter are dubbed conventional and higher-order VHS, respectively. Here, we perform a perturbative renormalization group (RG) analysis to unbiasedly study the dominant instabilities in homobilayer TMDs for both the conventional and higher-order VHS cases. We find that the spin-valley locking largely alters the RG flows and leads to instabilities unexpected in the corresponding extensively-studied graphene-based moire systems, such as spin- and valley-polarized ferromagnetism and topological superconductivity with mixed parity. In particular, for the case with two higher-order VHS, we find a spin-valley-locking-driven metallic state with no symmetry breaking in the TMDs despite the diverging bare susceptibility. Our results show how the spin-valley locking significantly affects the RG analysis and demonstrate that moire TMDs are suitable platforms to realize various interaction-induced spin-valley locked phases, highlighting physics fundamentally different from the well-studied graphene-based moire systems.
We introduce and study a minimum two-orbital Hubbard model on a triangular lattice, which captures the key features of both the trilayer ABC-stacked graphene-boron nitride heterostructure and twisted transition metal dichalcogenides in a broad parameter range. Our model comprises first- and second-nearest neighbor hoppings with valley-contrasting flux that accounts for trigonal warping in the band structure. For the strong-coupling regime with one electron per site, we derive a spin-orbital exchange Hamiltonian and find the semiclassical ground state to be a spin-valley density wave. We show that a relatively small second-neighbor exchange interaction is sufficient to stabilize the ordered state against quantum fluctuations. Effects of spin- and valley Zeeman fields as well as thermal fluctuations are also examined.
Magnonic excitations in the two-dimensional (2D) van der Waals (vdW) ferromagnet CrI3 are studied. We find that bulk magnons exhibit a non-trivial topological band structure without the need for Dzyaloshinskii-Moriya (DM) interaction. This is shown in vdW heterostructures, consisting of single-layer CrI3 on top of different 2D materials as MoTe2, HfS2 and WSe2. We find numerically that the proposed substrates modify substantially the out-of-plane magnetic anisotropy on each sublattice of the CrI3 subsystem. The induced staggered anisotropy, combined with a proper band inversion, leads to the opening of a topological gap of the magnon spectrum. Since the gap is opened non-symmetrically at the K+ and K- points of the Brillouin zone, an imbalance in the magnon population between these two valleys can be created under a driving force. This phenomenon is in close analogy to the so-called valley Hall effect (VHE), and thus termed as magnon valley Hall effect (MVHE). In linear response to a temperature gradient we quantify this effect by the evaluation of the temperature-dependence of the magnon thermal Hall effect. These findings open a different avenue by adding the valley degrees of freedom besides the spin, in the study of magnons.
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