Minimal models for topological Weyl semimetals

Topological Weyl semimetals (TWS) can be classified as type-I TWS, in which the density of states vanishes at the Weyl nodes, and type-II TWS where an electron and a hole pocket meet with finite density of states at the nodal energy. The dispersions of type-II Weyl nodes are tilted and break Lorentz invariance, allowing for physical properties distinct from those in a type-I TWS. We present minimal lattice models for both time-reversal-breaking and inversion-breaking type-II Weyl semimetals, and investigate their bulk properties and topological surface states. These lattice models capture the extended Fermi pockets and the connectivities of Fermi arcs. In addition to the Fermi arcs, which are topologically protected, we identify surface "track states" that arise out of the topological Fermi arc states at the transition from type-I to type-II with multiple Weyl nodes, and persist in the type-II TWS.Comment: 13 pages, 9 figure

Scaling and data collapse from local moments in frustrated disordered quantum spin systems

Recently measurements on various spin-1/2 quantum magnets such as H$_3$LiIr$_2$O$_6$, LiZn$_2$Mo$_3$O$_8$, ZnCu$_3$(OH)$_6$Cl$_2$ and 1T-TaS$_2$ -- all described by magnetic frustration and quenched disorder but with no other common relation -- nevertheless showed apparently universal scaling features at low temperature. In particular the heat capacity C[H,T] in temperature T and magnetic field H exhibits T/H data collapse reminiscent of scaling near a critical point. Here we propose a theory for this scaling collapse based on an emergent random-singlet regime extended to include spin-orbit coupling and antisymmetric Dzyaloshinskii-Moriya (DM) interactions. We derive the scaling $C[H,T]/T \sim H^{-\gamma} F_q[T/H]$ with $F_q[x] = x^{q}$ at small $x$, with $q \in$ (0,1,2) an integer exponent whose value depends on spatial symmetries. The agreement with experiments indicates that a fraction of spins form random valence bonds and that these are surrounded by a quantum paramagnetic phase. We also discuss distinct scaling for magnetization with a $q$-dependent subdominant term enforced by Maxwell's relations.Comment: v2. Expanded argument in Appendix 2 and revised for clarity. v3. Fixed typo in Fig 3 caption. Main text 4 pages 4 figures, Appendix 6 pages 1 figur

High-temperature magnetic anomaly in the Kitaev hyperhoneycomb compound β-Li2IrO3

We report the existence of a high-temperature magnetic anomaly in the three-dimensional Kitaev candidate material, β-Li2IrO3. Signatures of the anomaly appear in magnetization, heat capacity, and muon spin relaxation measurements. The onset coincides with a reordering of the principal axes of magnetization, which is thought to be connected to the onset of Kitaev-like correlations in the system. The anomaly also shows magnetic hysteresis with a spatially anisotropic magnitude that follows the spin-anisotropic exchange anisotropy of the underlying Kitaev Hamiltonian. We discuss possible scenarios for a bulk and impurity origin

Featureless and non-fractionalized Mott insulators on the honeycomb lattice at 1/2 site filling

Within the Landau paradigm, phases of matter are distinguished by spontaneous symmetry breaking. Implicit here is the assumption that a completely symmetric state exists: a paramagnet. At zero temperature such quantum featureless insulators may be forbidden, triggering either conventional order or topological order with fractionalized excitations. Such is the case for interacting particles when the particle number per unit cell, f, is not an integer. But, can lattice symmetries forbid featureless insulators even at integer f? An especially relevant case is the honeycomb (graphene) lattice --- where free spinless fermions at f=1 (the two sites per unit cell mean f=1 is half filling per site) are always metallic. Here we present wave functions for bosons, and a related spin-singlet wave function for spinful electrons, on the f=1 honeycomb, and demonstrate via quantum to classical mappings that they do form featureless Mott insulators. The construction generalizes to symmorphic lattices at integer f in any dimension. Our results explicitly demonstrate that in this case, despite the absence of a non-interacting insulator at the same filling, lack of order at zero temperature does not imply fractionalization.Comment: v2: major revision including new result on SU(2) spinful electron state and additional author. v3: PNAS published version. 7 pages, 5 figures; appendix 5 pages, 3 figure

Quark Masses: An Environmental Impact Statement

We investigate worlds that lie on a slice through the parameter space of the Standard Model over which quark masses vary. We allow as many as three quarks to participate in nuclei, while fixing the mass of the electron and the average mass of the lightest baryon flavor multiplet. We classify as "congenial" worlds that satisfy the environmental constraint that the quark masses allow for stable nuclei with charges one, six, and eight, making organic chemistry possible. Whether a congenial world actually produces observers depends on a multitude of historical contingencies, beginning with primordial nucleosynthesis, which we do not explore. Such constraints may be independently superimposed on our results. Environmental constraints such as the ones we study may be combined with information about the a priori distribution of quark masses over the landscape of possible universes to determine whether the measured values of the quark masses are determined environmentally, but our analysis is independent of such an anthropic approach. We estimate baryon masses as functions of quark masses and nuclear masses as functions of baryon masses. We check for the stability of nuclei against fission, strong particle emission, and weak nucleon emission. For two light quarks with charges 2/3 and -1/3, we find a band of congeniality roughly 29 MeV wide in their mass difference. We also find another, less robust region of congeniality with one light, charge -1/3 quark, and two heavier, approximately degenerate charge -1/3 and 2/3 quarks. No other assignment of light quark charges yields congenial worlds with two baryons participating in nuclei. We identify and discuss the region in quark-mass space where nuclei would be made from three or more baryon species.Comment: 40 pages, 16 figures (in color), 4 tables. See paper for a more detailed abstract. v4: Cleaning up minor typo

Disorder-controlled relaxation in a 3D Hubbard model quantum simulator

Understanding the collective behavior of strongly correlated electrons in materials remains a central problem in many-particle quantum physics. A minimal description of these systems is provided by the disordered Fermi-Hubbard model (DFHM), which incorporates the interplay of motion in a disordered lattice with local inter-particle interactions. Despite its minimal elements, many dynamical properties of the DFHM are not well understood, owing to the complexity of systems combining out-of-equilibrium behavior, interactions, and disorder in higher spatial dimensions. Here, we study the relaxation dynamics of doubly occupied lattice sites in the three-dimensional (3D) DFHM using interaction-quench measurements on a quantum simulator composed of fermionic atoms confined in an optical lattice. In addition to observing the widely studied effect of disorder inhibiting relaxation, we find that the cooperation between strong interactions and disorder also leads to the emergence of a dynamical regime characterized by \textit{disorder-enhanced} relaxation. To support these results, we develop an approximate numerical method and a phenomenological model that each capture the essential physics of the decay dynamics. Our results provide a theoretical framework for a previously inaccessible regime of the DFHM and demonstrate the ability of quantum simulators to enable understanding of complex many-body systems through minimal models