Abstract: The zeroth Landau level of graphene under a magnetic field is a particularly interesting strongly interacting flat band because interelectron interactions are predicted to induce a rich variety of broken-symmetry states with distinct topological and lattice-scale orders. Evidence for these states stems mostly from indirect transport experiments that suggest that broken-symmetry states are tunable by boosting the Zeeman energy or by dielectric screening of the Coulomb interaction. In this talk, I will describe three distinct broken-symmetry phases in graphene that we imaged using scanning tunneling spectroscopy. We explored the phase diagram by tuning the screening of the Coulomb interaction by a low- or high-dielectric-constant environment, and with a magnetic field. In the unscreened case, we find a Kekulé bond order. Under dielectric screening, a sublattice-unpolarized ground state emerges at low magnetic fields, and transits to a charge-density-wave order with partial sublattice polarization at higher magnetic fields. The Kekulé and charge-density-wave orders furthermore coexist with additional, secondary lattice-scale orders that enrich the phase diagram beyond current theory predictions.
Abstract: I will discuss the role of geometrically frustrated interactions on electronic transport in two different settings. In the first part, I will discuss the transport properties of a solvable lattice model of electrons in the strongly coupled limit, where geometric frustration leads to a new regime of unconventional transport accompanied by T-linear resistivity and "bad" metallicity. Next, I will describe the problem of a weakly interacting electronic fluid scattering off the paramagnetic fluctuations of a frustrated spin model at high temperatures. Remarkably, this problem does not behave as the standard high-temperature limit of the superficially similar problem of electrons scattering off phonons.
Abstract: Predicting the fate of an interacting system in the limit where the electronic bandwidth is quenched is often highly non-trivial. The complex interplay between interactions and quantum fluctuations driven by the band geometry can drive a competition between various ground states, such as charge density wave order and superconductivity. In this work, we study an electronic model of topologically-trivial flat bands with a continuously tunable Fubini-Study metric in the presence of on-site attraction and nearest-neighbor repulsion, using numerically exact quantum Monte Carlo simulations. By varying the electron filling and the spatial extent of the localized flat-band Wannier wavefunctions, we obtain a number of intertwined orders. These include a phase with coexisting charge density wave order and superconductivity, i.e., a supersolid. In spite of the non-perturbative nature of the problem, we identify an analytically tractable limit associated with a "small" spatial extent of the Wannier functions, and derive a low-energy effective Hamiltonian that can well describe our numerical results.
Abstract: Electrical resistance is usually associated with lattice imperfections. However, even a perfect ballistic crystal free of defects or faults shows finite resistance, determined by the number of channels available for conduction. This resistance usually appears at the contacts and is known as Quantum resistance. Recent works have shown that electrons can behave as viscous fluid, raising the fundamental question- what is the ultimate conductance limit of strongly interacting hydrodynamic electrons? Here, using a single electron transistor as an ultra-sensitive electrostatic detector, we image the potential of flowing electrons in high mobility graphene Corbino disk. Our measurements at low temperature in the ballistic regime show that the Quantum resistance is no longer confined to the contact but is distributed throughout the device's bulk, emanating from the gradient in the number of conduction modes and revealing its phase space origin. At elevated temperatures, in the hydrodynamic regime, we show complete elimination of the Quantum resistance from the bulk of the device. Our work shows that the constraints of ballistic electrons can be lifted by viscous electronic fluid, with significant impact for future science and technology.
Abstract: I will discuss thermal diffusion, quantum many body chaos (scrambling) and their relation, in a toy model of strongly coupled anharmonic quantum solids, motivated by recent experiments of Planckian thermal diffusion in a host of complex insulating compounds.
Abstract: We propose a device in which a sheet of graphene is coupled to a Weyl semimetal, allowing for the physical access to the study of tunneling from two-dimensional to three dimensional massless Dirac fermions. Due to the reconstructed band structure, we find that this device acts as a robust valley filter for electrons in the graphene sheet. We show that, by appropriate alignment, the Weyl semimetal draws away current in one of the two graphene valleys while allowing current in the other to pass unimpeded. In contrast to other proposed valley filters, the mechanism of our proposed device occurs in the bulk of the graphene sheet, obviating the need for carefully shaped edges or dimensions.
Abstract: Though magnetic fields typically suppress superconductivity, it is known theoretically that re-entrant superconductivity is possible at much larger fields when pairing occurs predominantly within Landau levels. This regime may be more experimentally accessible in materials with large unit cells, e.g. moire systems, that exhibit the Hofstadter butterfly spectrum at lower fields. In our recent work (Phys. Rev. B 104, 184501), we investigated the nature of the superconducting state in such Hofstadter bands, taking advantage of the magnetic translation group (MTG) symmetries for rational values p/q of the flux per unit lattice in units of the flux quantum. Because the MTG contains a subset of the U(1) symmetry broken by the paired state, we show that some MTG symmetry must be broken by the paired state, resulting in degenerate ground states. Moreover, the superconducting gap functions realize novel irreducible representations (irreps) of the MTG distinct from the well-known single-particle irreps. The new irreps differ qualitatively for even and odd q, giving rise to different Z_2q or Z_q symmetric ground state respectively, affecting their topological properties including chiral Majorana zero modes and Bogoliubov Fermi surfaces.
Abstract: The true ground state of ν = 0 (charge neutrality) monolayer graphene quantum Hall has long been debated. Famously the symmetry of the monolayer graphene at ν = 0 (charge neutrality) was analyzed by J. Alicea and P. A. Fisher in 2006 (PRB 74, 075422), and canted anti-ferromagnet (CAF) was predicted by I. F. Herbut in 2007 (PRB 75, 165411). However, the complete picture of the Hamiltonian was missing until the seminal paper by M. Kharitonov in 2012 (PRB 85, 155439) which predicts a phase transition from a vanilla insulator (CAF) to a topological insulator Ferromagnetic phase (F) as one changes the Zeeman energy keeping the cyclotron energy fixed. This was later confirmed in the experiment by A. F. Young et. al. in 2014 (Nature 505, 528). Motivated by recent experiments (L. He et. al. PRB 100, 085437, Ali Yazdani et. al. Science abm3770, B. Sacepe arXiv:2110.02811) we revisit this phase diagram. We show that, generically, in the regime of interest there is a region of coexistence between magnetic and bond orders in the phase diagram. We demonstrate this result both in continuum and lattice models and argue that the coexistence phase naturally provides an explanation for unreconciled experimental observations on the quantum Hall effect in graphene.
Abstract: Topology is an emerging topic that has drawn attention of researchers with background in physics, mathematics and computer science. Our curiosity lies in meron, a unique type of topological defect that shows great promise for applications in electron spin-based electronics. The known meron particles have a magnetic origin, but can related particles be generated by electromagnetic fields? I will briefly share the journey that has led us to obtain a lattice (which resembles the delicious waffle shown in the picture!) of merons, by capturing information from light on the nanometer (10-9 m) and femtosecond (10-15 s) time scales.
Abstract: The Ising chain in a transverse field is a paradigmatic model for a host of physical phenomena, including spontaneous symmetry breaking, quantum criticality and duality. Although the quasi-one-dimensional ferromagnet CoNb2O6 has been regarded as the Ising chain’s best material realization, it exhibits substantial deviations from ideality. By combining terahertz spectroscopy and calculations, we show that CoNb2O6 is in fact described by a different model with bond-dependent interactions, which we call the ‘twisted Kitaev chain’, as these interactions are similar to those of the honeycomb Kitaev spin liquid. The ferromagnetic ground state of CoNb2O6 arises from the compromise between two axes. Owing to this frustration, even at zero field domain walls have quantum motion, which is described by the celebrated Su-Schriefer-Heeger model of polyacetylene and shows rich behaviour as a function of field. Nevertheless, close to the critical field, this model enters a universal regime in the Ising universality class. We observe that the excitation gap in the ferromagnet closes at a rate twice that of the paramagnet. This universal ratio originates in the Kramers–Wannier duality between domain walls and spin flips, and in the topological conservation of domain wall parity.
Ref: Morris, C.M., Desai, N., Viirok, J. et al. Duality and domain wall dynamics in a twisted Kitaev chain. Nat. Phys. 17, 832–836 (2021).