Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid

The combination of Rashba spin-orbit coupling and potential disorder induces a random current operator for the edge states of a 2D topological insulator. We prove that charge transport through such an edge is ballistic at any temperature, with or without Luttinger liquid interactions. The solution exploits a mapping to a spin 1/2 in a time-dependent field that preserves the projection along one randomly undulating component (integrable dynamics). Our result is exact and rules out random Rashba backscattering as a source of temperature-dependent transport, absent integrability-breaking terms.Comment: 6+3 pages, 2+1 figure

Origin of π\pi-shifted three-dimensional charge density waves in kagome metal AV3_3Sb5_5

Understanding the nature of charge density wave (CDW) and superconductivity in kagome metal AV$_3$Sb$_5$ (A=Cs,Rb,K) is a recent subject of intensive study. Due to the presence of van Hove singularities, electron-electron interaction has been suggested to play an important role in the formation of such broken symmetry states. Recent experiments show that the CDW order is three-dimensional and it is staggered across different kagome layers. However, the experimental interpretation for the precise structure of CDW varies in terms of whether it is the star of David (SD), inverse star of David (ISD) or the alternation of the two among neighboring layers. In this work, we show that the origin of these distinct CDW orders can be understood in a unified picture by considering intra- and inter-layer electron-electron interactions as well as the coupling between electrons and lattice distortions. Utilizing an effective 9-band model with V $d$ orbitals and out-of-plane Sb $p$ orbitals, it is demonstrated that the repulsive electron-electron interaction favors charge bond order which induces either SD or ISD upon including lattice distortions. As the inter-layer interaction is introduced, $\pi$-shifted CDW develops with the staggered ordering along the $c$-axis. We also find that the phase with alternating SD and ISD can be stabilized as the ground state under strong inter-layer interaction

Massive Dirac fermions in moir\'e superlattices: a route towards topological flat minibands

We demonstrate a generic mechanism to realize topological flat minibands by confining massive Dirac fermions in a periodic moir\'e potential, which can be achieved in a heterobilayer of transition metal dichalcogenides. We show that the topological phase can be protected by the symmetry of moir\'e potential and survive to arbitrarily large Dirac band gap. We take the MoTe$_2$/WSe$_2$ heterobilayer as an example and find that the topological phase can be driven by a vertical electric field. By projecting the Coulomb interaction onto the topological fat minibands, we identify a correlated Chern insulator at half filling and a quantum valley-spin Hall insulator at full filling which explains the topological states observed in the MoTe$_2$/WSe$_2$ in experiment. Our work clarifies the importance of Dirac structure for the topological minibands and unveils a general strategy to design topological moir\'e materials.Comment: 13 pages, 12 figure

Superconductivity and bosonic fluid emerging from Moir\'e flat bands

Although evidence of inter-valley attraction-mediated by phonon or topological fluctuations is accumulating, the origin of superconductivity in the flat-band quantum moir\'e materials remains an open question. Here, instead of attempting to pinpoint the origin of the superconductivity, we aim at identifying universal properties of moir\'e flat bands that shall emerge in the presence of inter-valley attractions. We show that by matching the interaction strength of inter-valley attraction with intra-valley repulsion, the flat-band limit becomes exactly solvable. Away from the flat-band limit, the system can be simulated via quantum Monte Carlo (QMC) methods without sign problem for any fillings. Combining analytic solutions with large-scale numerical simulations, we show that upon increasing temperature, the superconducting phase melts into a bosonic fluid of Cooper pairs with large/diverging compressibility. In contrast to flat-band attractive Hubbard models, where similar effects arise only for on-site interactions, our study indicates this physics is a universal property of moir\'e flat bands, regardless of microscopic details such as the range of interactions and/or spin-oribt couplings. At higher temperature, the boson fluid phase gives its way to a pseudo gap phase, where some Cooper pairs are torn apart by thermal fluctuations, resulting in fermion density of states inside the gap. Unlike the superconducting transition temperature, which is very sensitive to doping and twisting angles, the gap and the temperature scale of the boson fluid phase and the pseudo gap phase are found to be nearly independent of doping level and/or flat-band bandwidth. The relevance of these phases with experimental discoveries in the flat band quantum moir\'e materials is discussed

Evolution from quantum anomalous Hall insulator to heavy-fermion semimetal in magic-angle twisted bilayer graphene

The ground states of twisted bilayer graphene (TBG) at chiral and flat-band limit with integer fillings are known from exact solutions, while their dynamical and thermodynamical properties are revealed by unbiased quantum Monte Carlo (QMC) simulations. However, to elucidate experimental observations of correlated metallic, insulating and superconducting states and their transitions, investigations on realistic, or non-chiral cases are vital. Here we employ momentum-space QMC method to investigate the evolution of correlated states in magic-angle TBG away from chiral limit at charge neutrality with polarized spin/valley, which approximates to an experimental case with filling factor $\nu=-3$. We find that the ground state evolves from quatum anomalous Hall insulator into an intriguing correlated semi-metallic state as AA hopping strength reaches experimental values. Such a state resembles the recently proposed heavy-fermion representations with localized electrons residing at AA stacking regions and delocalized electrons itinerating via AB/BA stacking regions. The spectral signatures of the localized and itinerant electrons in the heavy-fermion semimetal phase are revealed, with the connection to experimental results being discussed.Comment: 6 pages, 4 figures with supplementary material (6 pages, 11 figures

Igg, Igm and Iga Antibodies against the Novel Polyprotein in Active Tuberculosis

Background The present study was aimed to evaluate whether IgG, IgM and IgA antibodies levels detected against a novel Mycobacterium tuberculosis polyprotein 38 F-64 F (with 38 F being the abbreviation for 38kD-ESAT6-CFP10 and 64 F for Mtb8.4-MPT64-TB16.3-Mtb8) are suitable for diagnosing active tuberculosis, and for monitoring the efficacy of chemotherapy on TB patients. Methods In this study, a total of 371 active TB patients without treatment were selected and categorized into S+/C+ group (n = 143), S-/C+ group (n = 106) or S-/C- group (n = 122). A series of serum samples were collected from 82 active TB patients who had undergone anti-TB chemotherapy for 0–6 months at one month interval. Humoral responses (IgG, IgM and IgA) were determined for the novel Mycobacterium tuberculosis polyprotein using indirect ELISA methods in all of serum samples. Results For S+/C+, S-/C+ and S-/C- active tuberculosis patients before anti-TB chemotherapy, the sensitivities of tests based on IgG were 65.7%, 46.2% and 52.5% respectively; the sensitivities based on IgM were 21.7%, 24.5% and 18.9%; and the sensitivities based on IgA were 25.2%, 17.9% and 23.8%. By combination of three isotypes, for all active tuberculosis patients, the test sensitivity increased to 70.4% with the specificity being 91.5%. After anti-TB chemotherapy, there were no significant differences between groups with different courses of anti-TB chemotherapy. Conclusions The novel Mycobacterium tuberculosis polyprotein 38 F-64 F represents potential antigen suitable for measuring IgG, IgM and IgA antibodies. However, the serodiagnostic test based on the 38 F-64 F polyprotein appears unsuitable for monitoring the efficacy of chemotherapy

Topology and Symmetry in Weakly and Strongly Correlated Electronic Systems

This thesis studies topological phases in various electronic crystalline systems with a focus on the interplay between symmetry and topology, including the non-interacting topological insulators, higher-order topological insulators, topological semimetals as well as the strongly correlated systems with intrinsic topological order. First, we show that when the symmetry of the system is low, the symmetry representation of energy bands may not be sufficient to determine the topological index, but the symmetry can still be utilized to define a gauge-invariant quantity, which provides a gauge-independent way to compute the $Z_2$ topological index of topological insulators. Second, we proposed a generalization of the famous Fu-Kane-Mele Pfaffian formula from $Z_2$ topological insulators to higher-order topological insulators, which allows many important conclusions that have been well known for $Z_2$ topological insulators to be generalized to higher-order topological insulators. This generalization is made possible via a linear superposition of symmetry operator. Third, we proposed a diagnosis scheme for topological nodal lines with nontrivial monopole charge based on point group representations. This method predicts novel cage-like nodal structures around high-symmetry lines in the Brillouin zone beyond previous diagnosis schemes which require high-symmetry lines to be gapped. Lastly, we studied strongly correlated topological phases in twisted Moire systems and proposed to realize fractional Chern insulators in twisted bilayer transition metal dichalcogenides.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/170015/1/heqiuli_1.pd