The influence of particle size and shape effects on average and punctual surface-enhanced Raman scattering (SERS) enhancement factors (EFs) is investigated using exact T-matrix electrodynamic calculations of silver and gold spheroids over a large parameter space. This study extends the conventional treatment of these effects within the frameworks of the electrostatics approximation, its generalizations, or Mie theory for spheres. It confirms the qualitative features of these approaches, but provides in addition quantitative predictions of SERS EFs in the case of large non-spherical particles, where the lightning-rod effect (shape effect) and radiation damping (size effect) operate simultaneously. Finally, the localization effect at large SERS EF (hot-spots) is shown to be dictated only by shape, not size, in the case of metallic spheroids at the dipolar localized surface plasmon resonance.

We study the universal critical properties of the QED3-Gross-Neveu-Yukawa model with N flavors of four-component Dirac fermions coupled to a real scalar order parameter at four-loop order in the ǫ expansion below four dimensions. For N = 1, the model is conjectured to be infrared dual to the SU (2)-symmetric noncompact CP 1 model, which describes the deconfined quantum critical point of the Néel-valence-bond-solid transition of spin-1/2 quantum antiferromagnets on the two-dimensional square lattice. For N = 2, the model describes a quantum phase transition between an algebraic spin liquid and a chiral spin liquid in the spin-1/2 kagomé antiferromagnet. For general N we determine the order parameter anomalous dimension, the correlation length exponent, the stability critical exponent, as well as the scaling dimensions of SU (N ) singlet and adjoint fermion mass bilinears at the critical point. We use Padé approximants to obtain estimates of critical properties in 2+1 dimensions.

The critical properties of the QED3 Gross-Neveu-Yukawa (GNY) model in 2+1 dimensions with N flavors of two-component Dirac fermions are computed to first order in the 1/N expansion. For the specific case of N = 2, the critical point is conjectured to be dual to the Néel-to-valence-bond-solid (VBS) deconfined critical point of quantum antiferromagnets on the square lattice. It is found that Aslamazov-Larkin diagrams, missed by previous -and 1/N -expansion studies with four-component fermions, give important contributions to the scaling dimensions of various operators. With the inclusion of these diagrams, the resummed scaling dimensions of the adjoint fermion bilinear and scalar field at the QED3 GNY critical point are in reasonable agreement with numerical studies of the Néel-to-VBS transition, in support of the duality conjecture. arXiv:1812.02720v2 [cond-mat.str-el]

The algebraic spin liquid is a long-sought-after phase of matter characterized by the absence of quasiparticle excitations, a low-energy description in terms of emergent Dirac fermions and gauge fields interacting according to (2+1)D quantum electrodynamics (QED3), and power-law correlations with universal exponents. The prototypical algebraic spin liquid is the Affleck-Marston π-flux phase, originally proposed as a possible ground state of the spin-1/2 Heisenberg model on the 2D square lattice. While the latter model is now known to order antiferromagnetically at zero temperature, recent sign-problem-free quantum Monte Carlo simulations of spin-1/2 fermions coupled to a compact U (1) gauge field on the square lattice have shown that quantum fluctuations can destroy Néel order and drive a direct quantum phase transition to the π-flux phase. We show this transition is in the universality class of the chiral Heisenberg QED3-Gross-Neveu-Yukawa model with a single SU (2) doublet of four-component Dirac fermions (i.e., N f = 1), pointing out important differences with the corresponding putative transition on the kagomé lattice. Using an expansion below four spacetime dimensions to four-loop order, and a large-N f expansion up to second order, we show the transition is continuous and compute various thermodynamic and susceptibility critical exponents at this transition, setting the stage for future numerical determinations of these quantities. As a byproduct of our analysis, we also obtain charge-density-wave and valence-bond-solid susceptibility exponents at the semimetal-antiferromagnetic insulator transition in graphene. arXiv:1905.03719v1 [cond-mat.str-el]

In this paper we follow the analysis and protocols of recent experiments, combined with simple theory, to arrive at a physical understanding of quasi-condensation in two dimensional Fermi gases. We find that quasi-condensation mirrors Berezinskiȋ-Kosterlitz-Thouless behavior in many ways, including the emergence of a strong zero momentum peak in the pair momentum distribution. Importantly, the disappearance of this quasi-condensate occurs at a reasonably well defined crossover temperature. The resulting phase diagram, pair momentum distribution, and algebraic power law decay are compatible with recent experiments throughout the continuum from BEC to BCS.Understanding two dimensional (2D) fermionic superfluidity has a long history relating to the Mermin- Thus recent reports [9, 10] of a form of pair condensation in 2D fermionic gases are particularly exciting. These follow earlier work addressing the ground state [11] and the higher temperature regime, away from condensation [12]. These experiments [9,10] show that strong normal state pairing is an essential component of 2D Fermi superfluids, even in the BCS regime. In fact, much of the theory invoked to explain these experiments was based upon true Bose systems. A characteristic feature of 2D superfluidity at finite T is the presence of narrow peaks in the momentum distribution of the pairs, without macroscopic occupation of the zero momentum state. Throughout the paper this will be our definition of "quasi-condensation." This quasi-condensation in momentum space is associated with algebraic decay of coherence in real space. Importantly, the BKT-related transition temperature is manifested as a sudden change in slope of a normalized peak momentum distribution for pairs.In this paper we present a theory of a 2D Fermi gas near quantum degeneracy and show how it reproduces rather well the results of these recent experiments [9,10] through an analysis of the phase diagram, the pair momentum distribution and algebraic power laws. Given the ground breaking nature of the experiments, it is important to have an accompanying theoretical study which follows exactly the same protocols without any adjustments or phenomenology. Our approach is to be distinguished from other studies of 2D Fermi gases [4,[13][14][15][16][17][18][19][20][21][22][23]. In particular, those addressing BKT physics [4,[13][14][15][16]20], use existing formulae [24,25] and determine the unknown parameters to obtain T BKT c . By contrast here we reverse the procedure and follow experimental protocols to thereby provide a new formula, involving composite bosons, for the transition temperature associated with quasi-condensation. In the homogeneous case, this is analytically tractable and presented as Eq. (6) below.Importantly, there is a rather abrupt crossover out of a quasi-condensed phase at a fairly well defined temperature T qc . In the BEC regime this matches earlier theoretical estimates of the BKT transition temperature which are based on different theoretical formalisms [4,[13][14][15][16]. We ...