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Register a new userFlat-band solutions in $D$-dimensional decorated diamond and pyrochlore lattices: Reduction to molecular problem
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Flat-band models have been of particular interest from both fundamental aspects and realization in materials. Beyond the canonical examples such as Lieb lattices and line graphs, a variety of tight-binding models are found to possess flat bands. However, analytical treatment of dispersion relations is limited, especially when there are multiple flat bands with different energies. In this paper, we present how to determine flat-band energies and wave functions in tight-binding models on decorated diamond and pyrochlore lattices in generic dimensions $D geq 2$. For two and three dimensions, such lattice structures are relevant to various organic and inorganic materials, and thus our method will be useful to analyze the band structures of these materials.
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Electronic properties of kagome lattice have drawn great attention recently. In associate with flat-band induced by destructive interference and Dirac cone-type dispersion, abundant exotic phenomena have been theoretically discussed. The material realization of electronic kagome lattice is a crucial step towards comprehending kagome physics and achieving novel quantum phases. Here, combining angle-resolved photoemission spectroscopy, transport measurements and first-principle calculations, we expose a planar flat-band in paramagnetic YCr6Ge6 as a typical signature of electronic kagome lattice. We unearth that the planar flat-band arises from the dz2 electrons with intra-kagome-plane hopping forbidden by destructive interference. On the other hand, the destructive interference and flatness of the dx2-y2 and dxy bands are decomposed possibly due to additional in-plane hopping terms, but the Dirac cone-type dispersion is reserved near chemical potential. We explicitly unveil that orbital character plays an essential role to realize electronic kagome lattice in bulk materials with transition metal kagome layers. Paramagnetic YCr6Ge6 provides an opportunity to comprehend intrinsic properties of electronic kagome lattice as well as its interplays with spin orbit coupling and electronic correlation of Cr-3d electrons, and be free from complications induced by strong local moment of ions in kagome planes.
In flat bands, superconductivity can lead to surprising transport effects. The superfluid mobility, in the form of the superfluid weight $D_s$, does not draw from the curvature of the band but has a purely band-geometric origin. In a mean-field description, a non-zero Chern number or fragile topology sets a lower bound for $D_s$, which, via the Berezinskii-Kosterlitz-Thouless mechanism, might explain the relatively high superconducting transition temperature measured in magic-angle twisted bilayer graphene (MATBG). For fragile topology, relevant for the bilayer system, the fate of this bound for finite temperature and beyond the mean-field approximation remained, however, unclear. Here, we use numerically exact Monte Carlo simulations to study an attractive Hubbard model in flat bands with topological properties akin to those of MATBG. We find a superconducting phase transition with a critical temperature that scales linearly with the interaction strength. We then investigate the robustness of the superconducting state to the addition of trivial bands that may or may not trivialize the fragile topology. Our results substantiate the validity of the topological bound beyond the mean-field regime and further stress the importance of fragile topology for flat-band superconductivity.
Flat bands play an important role in diffraction-free photonics and attract fundamental interest in many-body physics. Here we report the engineering of flat-band localization of collective excited states of atoms in Creutz superradiance lattices with tunable synthetic gauge fields. Magnitudes and phases of the lattice hopping coefficients can be independently tuned to control the state components of the flat band and the Aharonov-Bohm phases. We can selectively excite the flat band and control the flat-band localization with the synthetic gauge field. Our study provides a room-temperature platform for flat bands of atoms and holds promising applications in exploring correlated topological materials.
We propose a hybrid quantum architecture for engineering a photonicMott insulator-superfluid phase transition in a two-dimensional (2D) square lattice of a superconducting transmission line resonator (TLR) coupled to a single nitrogen-vacancy (NV) center encircled by a persistent current qubit. The localization-delocalization transition results from the interplay between the on-site repulsion and the nonlocal tunneling. The phase boundary in the case of photon hopping with real-valued and complex-valued amplitudes can be obtained using the mean-field approach. Also, the quantum jump technique is employed to describe the phase diagram when the dissipative effects are considered. The unique feature of our architecture is the good tunability of effective on-site repulsion and photon-hopping rate, and the local statistical property of TLRs which can be analyzed readily using presentmicrowave techniques. Our work opens new perspectives in quantum simulation of condensed-matter and many-body physics using a hybrid spin circuit-QED system. The experimental challenges are realizable using currently available technologies.
We demonstrate that the concept of moire flat bands can be generalized to achieve electronic band engineering in all three spatial dimensions. For many two dimensional van der Waals materials, twisting two adjacent layers with respect to each other leads to flat electronic bands in the two corresponding spatial directions -- a notion sometimes referred to as twistronics as it enables a wealth of physical phenomena. Within this two dimensional plane, large moire patterns of nanometer size form. The basic concept we propose here is to stack multiple twisted layers on top of each other in a predefined pattern. If the pattern is chosen such that with respect to the stacking direction of layers, the large spatial moire features are spatially shifted from one twisted layer to the next, the system exhibits twist angle controlled flat bands in all of the three spatial directions. With this, our proposal extends the use of twistronic to three dimensions. We exemplify the general concept by considering graphitic systems, boron nitride and WSe$_2$ as candidate materials, but the approach is applicable to any two-dimensional van der Waals material. For hexagonal boron nitride we develope an ab initio fitted tight binding model that captures the corresponding three dimensional low-energy electronic structure. We outline that interesting three dimensional correlated phases of matter can be induced and controlled following this route, including quantum magnets and unconventional superconducting states.
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