Localization of Dirac Fermions in Finite-Temperature Gauge Theory

It is by now well established that Dirac fermions coupled to non-Abelian gauge theories can undergo an Anderson-type localization transition. This transition affects eigenmodes in the lowest part of the Dirac spectrum, the ones most relevant to the low-energy physics of these models. Here we review several aspects of this phenomenon, mostly using the tools of lattice gauge theory. In particular, we discuss how the transition is related to the finite-temperature transitions leading to the deconfinement of fermions, as well as to the restoration of chiral symmetry that is spontaneously broken at low temperature. Other topics we touch upon are the universality of the transition, and its connection to topological excitations (instantons) of the gauge field and the associated fermionic zero modes. While the main focus is on Quantum Chromodynamics, we also discuss how the localization transition appears in other related models with different fermionic contents (including the quenched approximation), gauge groups, and in different space-time dimensions. Finally, we offer some speculations about the physical relevance of the localization transition in these models.

Crystalline symmetry-protected non-trivial topology in prototype compound BaAl4

The BaAl4 prototype crystal structure is the most populous of all structure types, and is the building block for a diverse set of sub-structures including the famous ThCr2Si2 family that hosts high-temperature superconductivity and numerous magnetic and strongly correlated electron systems. The MA4 family of materials (M = Sr, Ba, Eu; A = Al, Ga, In) themselves present an intriguing set of ground states including charge and spin orders, but have largely been considered as uninteresting metals. We predict the exemplary compound BaAl4 to harbor a three-dimensional Dirac spectrum with non-trivial topology and possible nodal lines crossing the Brillouin zone, wherein one pair of semi-Dirac points with linear dispersion along the kz direction and quadratic dispersion along the kx/ky direction resides on the rotational axis with C4v point group symmetry. An extremely large, unsaturating positive magnetoresistance in BaAl4 despite an uncompensated band structure is revealed, and quantum oscillations and angle-resolved photoemission spectroscopy measurements confirm the predicted multiband semimetal structure with pockets of Dirac holes and a Van Hove singularity (VHS) remarkably consistent with the theoretical prediction. We thus present BaAl4 as a topological semimetal, casting its prototype status into a role as a building block for a vast array of topological materials.

Effect of Rashba Impurities on Surface State of a Topological Kondo Insulator

In this communication, we report surface state, with Rashba impurities, of a generic topological Kondo insulator (TKI) system by performing a mean-field theoretic (MFT) calculation within the framework of slave-boson protocol. The surface metallicity together with bulk insulation is found to require very strong f-electron localization. The possibility of intra-band as well as inter-band unconventional plasmons exists for the surface state spectrum. The paramountcy of the bulk metallicity, and, in the presence of the Rashba impurities, the TKI surface comprising of ‘helical liquids’ are the important outcomes of the present communication. The access to the gapless Dirac spectrum leads to spin-plasmons with the usual wave vector dependence q1/2. The Rashba coupling does not impair the Kondo screening and does not affect the quantum critical point (QCP) for the bulk.

The Dirac Spectrum and the BEC-BCS Crossover in QCD at Nonzero Isospin Asymmetry

For large isospin asymmetries, perturbation theory predicts the quantum chromodynamic (QCD) ground state to be a superfluid phase of u and d ¯ Cooper pairs. This phase, which is denoted as the Bardeen-Cooper-Schrieffer (BCS) phase, is expected to be smoothly connected to the standard phase with Bose-Einstein condensation (BEC) of charged pions at μ I ≥ m π / 2 by an analytic crossover. A first hint for the existence of the BCS phase, which is likely characterised by the presence of both deconfinement and charged pion condensation, comes from the lattice observation that the deconfinement crossover smoothly penetrates into the BEC phase. To further scrutinize the existence of the BCS phase, in this article we investigate the complex spectrum of the massive Dirac operator in 2+1-flavor QCD at nonzero temperature and isospin chemical potential. The spectral density near the origin is related to the BCS gap via a generalization of the Banks-Casher relation to the case of complex Dirac eigenvalues (derived for the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential).

Chiral condensate and Dirac spectrum of one-and two-flavor QCD at nonzero θ-angle

In previous work we showed that the chiral condensate of one-flavor QCD exhibits a Silver Blaze phenomenon when the quark mass crosses m = 0: the chiral condensate remains constant while the quark mass crosses the spectrum of the Dirac operator, which is dense on the imaginary axis. This behavior can be explained in terms of exponentially large cancellations between contributions from the zero modes and from the nonzero modes when the quark mass is negative. In these proceedings we show that a similar Silver Blaze phenomenon takes places for QCD with one flavor and arbitrary θ- angle, and for QCD with two flavors with different quark masses m1 and m2. In the latter case the chiral condensate remains constant when m1 crosses zero at fixed m2 > 0 until the Dashen point m1 = –m2 is reached, where the chiral condensate has a discontinuity. In terms of contributions from the Dirac spectrum the shift of the discontinuity from m1 = 0 to m1 = -m2 also arises from exponentially large cancellations between the zero and nonzero modes when m1m2 < 0. All calculations are performed in the microscopic or ε-domain of QCD. Results for arbitrary θ-angle are discussed as well.