Numerical tests of the large charge expansion

We perform Monte-Carlo measurements of two and three point functions of charged operators in the critical O(2) model in 3 dimensions. Our results are compatible with the predictions of the large charge superfluid effective field theory. To obtain reliable measurements for large values of the charge, we improved the Worm algorithm and devised a measurement scheme which mitigates the uncertainties due to lattice and finite size effects.Comment: 16 pages, 12 figures. v2: Improved finite size scaling. v3: Added comparison between Monte Carlo update

From Bloch Oscillations to a Steady-State Current in Strongly Biased Mesoscopic Devices

It has long been known that quantum particles in a periodic lattice exhibit an oscillatory motion that is solely driven by a constant and uniform force field. In a strongly biased mesoscopic device, this would appear as an ongoing time-dependent current oscillation (a Bloch oscillation) but, even when electrons can move coherently and without scattering, a steady-state regime of charge transport (a Landauer current) have been seen to quickly emerge. Here, we theoretically investigate the non-equilibrium current dynamics of a strongly biased two-terminal mesoscopic device, in order to show that such a system can exhibit Bloch oscillations as a transient regime that relaxes into a Landauer steady-state from charge being drained into the leads. Analytical results from the one-dimensional Wannier-Stark ladder problem are combined with numerical quantum time-evolution of a tight-binding toy model with finite leads to characterize the decay times of transient Bloch oscillations and establish the conditions under which they can occur.Comment: Preliminary Version (13 pages + 12 Figures). Comments and Suggestions are Welcome

Twisted bilayer graphene: low-energy physics, electronic and optical properties

Van der Waals (vdW) heterostructures ---formed by stacking or growing two-dimensional (2D) crystals on top of each other--- have emerged as a new promising route to tailor and engineer the properties of 2D materials. Twisted bilayer graphene (tBLG), a simple vdW structure where the interference between two misaligned graphene lattices leads to the formation of a moir\'e pattern, is a test bed to study the effects of the interaction and misalignment between layers, key players for determining the electronic properties of these stackings. In this chapter, we present in a pedagogical way the general theory used to describe lattice mismatched and misaligned vdW structures. We apply it to the study of tBLG in the limit of small rotations and see how the coupling between the two layers leads both to an angle dependent renormalization of graphene's Fermi velocity and appearance of low-energy van Hove singularities. The optical response of this system is then addressed by computing the optical conductivity and the dispersion relation of tBLG surface plasmon-polaritons

Anomalous Transport Signatures in Weyl Semimetals with Point Defects

We present the first theoretical study of transport properties of Weyl semimetals with point defects. Focusing on a class of time-reversal symmetric Weyl lattice models, we show that dilute lattice vacancies induce a finite density of quasi-localized states at and near the nodal energy, causing strong modifications to the low-energy spectrum. This generates novel transport effects, namely (i) an oscillatory behaviour of the dc-conductivity with the charge carrier density in the absence of magnetic fields, and (ii) a plateau-shaped dissipative optical response for photon frequencies below the inter-band threshold, $E_{F}\!\lesssim\!\hbar\omega\!\lesssim\!2E_{F}$.Our results provide a path to engineer unconventional quantum transport effects in Weyl semimetals by means of common point defects.Comment: 6 pages + 1 page of Supplementary Material; 4 + 2 Figures. Slight Changes Relative to V