Doron L. Bergman

Flat bands and wigner crystallization in the honeycomb optical lattice

We study the ground states of cold atoms in the tight-binding bands built from p orbitals on a two dimensional honeycomb optical lattice. The band structure includes two completely flat bands. Exact many-body ground states with on-site repulsion can be found at low particle densities, for both fermions and bosons. We find crystalline order at n=1/6 with a sqrt[3] x sqrt[3] structure breaking a number of discrete lattice symmetries. In fermionic systems, if the repulsion is strong enough, we find the bonding strength becomes dimerized at n=1/2. Experimental signatures of crystalline order can be detected through the noise correlations in time of flight experiments.

Order-by-disorder and spiral spin-liquid in frustrated diamond-lattice antiferromagnets

Frustration refers to competition between different interactions that cannot be simultaneously satisfied—a familiar feature in many magnetic solids. Strong frustration leads to highly degenerate ground states and a large suppression of ordering by fluctuations. Key challenges in frustrated magnetism include the characterization of the fluctuating spin-liquid regime and determination of the mechanism of eventual order at lower temperature. Here, we study a model of a diamond-lattice antiferromagnet appropriate for numerous spinel materials. With sufficiently strong frustration, a massive ground-state degeneracy develops amongst spirals whose propagation wavevectors reside on a continuous two-dimensional ‘spiral surface’ in momentum space. We argue that an important ordering mechanism is entropic splitting of the degenerate ground states, an elusive phenomenon called ‘order by disorder’. A broad spiral spin-liquid regime emerges at higher temperatures, where the underlying spiral surface can be directly revealed through spin correlations. We discuss the agreement between these predictions and the well-characterized spinel MnSc2S4.

Topological Floquet Spectrum in Three Dimensions via a Two-Photon Resonance

Three dimensional (3D) topological insulators display an array of unique properties such as single Dirac-cone surface states and a strong magnetoelectric effect. Here we show how a 3D topological spectrum can be induced in a trivial insulator by a periodic drive and, in particular, using electromagnetic radiation. In contrast to the two-dimensional analog, we show that a two-photon resonance is required to transform an initially unremarkable band structure into a topological Floquet spectrum. We provide an intuitive, geometrical picture, alongside a numerical solution of a driven lattice model featuring a single surface Dirac mode. Also, we show that the polarization and frequency of the driving electromagnetic field control the details of the surface modes and particularly the Dirac mass. Specific experimental realizations of the 3D Floquet topological insulator are proposed.

Theory of dissipationless Nernst effects.

We develop a theory of transverse thermoelectric (Peltier) conductivity alpha(xy), in a strong magnetic field--this particular conductivity is often the most important contribution to the Nernst thermopower. We demonstrate that alpha(xy) of a free electron gas can be expressed purely and exactly as the entropy per carrier irrespective of temperature (which agrees with the seminal Hall bar result of Girvin and Jonson). In two dimensions we prove the universality of this result in the presence of disorder which allows explicit demonstration of a number of features of interest to experiments on graphene and other two-dimensional materials. We also exploit this relationship in the low-field regime and analyze the rich singularity structure in alpha(xy)(B,T) in three dimensions; we discuss its possible experimental implications.

Semiclassical dynamics and long-time asymptotics of the central-spin problem in a quantum dot

The spin of an electron trapped in a quantum dot is a promising candidate implementation of a qubit for quantum information processing. We study the central-spin problem of the effect of the hyperfine interaction between such an electron and a large number of nuclear moments. Using a spin coherent path integral, we show that in this limit the electron spin evolution is well described by classical dynamics of both the nuclear and electron spins. We then introduce approximate yet systematic methods to analyze aspects of the classical dynamics, and discuss the importance of the exact integrability of the central-spin Hamiltonian. This is compared with numerical simulation. Finally, we obtain the asymptotic long-time decay of the electron spin polarization. We show that this is insensitive to integrability, and determined instead by the transfer of angular momentum to very weakly coupled spins far from the center of the quantum dot. The specific form of the decay is shown to depend sensitively on the form of the electronic wave function.

Quantum effects in a half-polarized pyrochlore antiferromagnet.

We study quantum effects in a spin-3/2 antiferromagnet on the pyrochlore lattice in an external magnetic field, focusing on the vicinity of a plateau in the magnetization at half the saturation value, observed in CdCr2O4 and HgCr2O4. Our theory, based on quantum fluctuations, predicts the existence of a symmetry-broken state on the plateau, even with only nearest-neighbor microscopic exchange. This symmetry-broken state consists of a particular arrangement of spins polarized parallel and antiparallel to the field in a 3:1 ratio on each tetrahedron. It quadruples the lattice unit cell, and reduces the space group from Fd3m to P4(3)32. We also predict that for fields just above the plateau, the low-temperature phase has transverse spin order, describable as a Bose-Einstein condensate of magnons. Other comparisons to and suggestions for experiments are discussed.

Impurity effects in highly frustrated diamond-lattice antiferromagnets

We consider the effects of local impurities in highly frustrated diamond-lattice antiferromagnets, which exhibit large but nonextensive ground-state degeneracies. Such models are appropriate to many A-site magnetic spinels. We argue very generally that sufficiently dilute impurities induce an ordered magnetic ground state and provide a mechanism of degeneracy breaking. The states that are selected can be determined by a “swiss cheese model” analysis, which we demonstrate numerically for a particular impurity model in this case. Moreover, we present criteria for estimating the stability of the resulting ordered phase to a competing frozen (spin glass) one. The results may explain the contrasting finding of frozen and ordered ground states in CoAl_2O_4 and MnSc_2S_4, respectively.

Bulk metals with helical surface states

In the flurry of experiments looking for topological insulator materials, it has been recently discovered that some bulk metals very close to topological insulator electronic states support the same topological surface states that are the defining characteristic of the topological insulator. First observed in spin-polarized angle resolved photoemission spectroscopy (ARPES) in Sb [D. Hsieh et al., Science 323, 919 (2009)], the helical surface states in the metallic systems appear to be robust to at least mild disorder. We present here a theoretical investigation of the nature of these “helical metals”—bulk metals with helical surface states. We explore how the surface and bulk states can mix, in both clean and disordered systems. Using the Fano model, we discover that in a clean system, the helical surface states are not simply absorbed by hybridization with a nontopological parasitic metallic band. Instead, they are pushed away from overlapping in momentum and energy with the bulk states, leaving behind a finite-lifetime surface resonance in the bulk energy band. Furthermore, the hybridization may lead in some cases to multiplied surface-state bands, in all cases retaining the helical characteristic. Weak disorder leads to very similar effects—surface states are pushed away from the energy bandwidth of the bulk, leaving behind a finite-lifetime surface resonance in place of the original surface states.

Degenerate perturbation theory of quantum fluctuations in a pyrochlore antiferromagnet

We study the effect of quantum fluctuations on the half-polarized magnetization plateau of a pyrochlore antiferromagnet. We argue that an expansion around the easy axis limit is appropriate for discussing the ground state selection amongst the classically degenerate manifold of collinear states with a 3:1 ratio of spins parallel/anti-parallel to the magnetization axis. A general approach to the necessary degenerate perturbation theory is presented, and an effective quantum dimer model within this degenerate manifold is derived for arbitrary spin

The Origin of T_c Enhancement in Heterostructure Cuprate Superconductors

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