Low-energy electronic structure of ͑unbiased and undoped͒ bilayer graphene consists of two Fermi points with quadratic dispersions if trigonal warping is ignored. We show that short-range ͑or screened Coulomb͒ interactions are marginally relevant and use renormalization group to study their effects on low-energy properties of the system. We find that the two quadratic Fermi points spontaneously split into four Dirac points. This results in a nematic state that spontaneously breaks the sixfold lattice rotation symmetry ͑combined with layer permutation͒ down to a twofold one, with a finite transition temperature. Critical properties of the transition and effects of trigonal warping are also discussed. This Rapid Communication is motivated by the observation that in noninteracting systems with susceptibilities diverging as the temperature approaches zero, the inclusion of arbitrarily small interaction leads to a finite but also arbitrarily small transition temperature into an ordered state. The analytical method of choice in this case is the renormalization group ͑RG͒, which has the virtue of unbiased determination of the leading instability. 1 Here we apply the RG method to the bilayer graphene with A-B stacking. 2-5 While in general, the motion of the noninteracting electrons in such potential does not lead to diverging susceptibilities due to trigonal warping, 3,4 if only nearest-neighbor ͑nn͒ hopping is considered each set of four Dirac points merges into a single degenerate point with parabolic dispersion ͑see Fig. 1͒. As the nearest-neighbor hopping amplitudes are the largest, the latter is the natural starting point of theoretical analysis. 6,7 The finite density of states associated with the parabolic dispersion leads to screening that renders Coulomb interaction short ranged and to diverging susceptibilities in several channels. We find that the leading instability triggered by the run-away RG flow is in the nematic channel, which effectively makes hopping amplitudes stronger along preferred direction ͓see Eqs. ͑17͒ and ͑18͔͒, and leads to spontaneous splittings of the Fermi points and breaking of the lattice rotation symmetry. Among other effects, this should lead to anisotropic transport in sufficiently clean samples, as well as suppression of the low-energy density of state: an effect, in principle, observable in STM.We start with the tight-binding Hamiltonian for electrons hopping on the bilayer honeycomb lattice with Bernal stackingwhere, in the nn approximation, the ͑real͒ hopping amplitudes t connect the in-plane nn sites belonging to different sublattices and, for one of the sublattices, also the sites vertically above it with amplitude t Ќ . Since there are four sites in the unit cell, there are four bands whose dispersion for the above model comes from the solution of the eigenvalue problem,K 0 K t 2t 3t 0 t 2t 3t K K' a 1 t b 1 a 2 t t 0.95K 1.05K K 0.4 0.2 0 0.2 0.4 FIG. 1. ͑Color online͒ ͑Upper left inset͒ Honeycomb bilayer unit cell. Atoms in the lower layer ͑2͒ are marked as smaller ͑black͒ c...

Double layer quantum Hall systems have interesting properties associated with interlayer correlations. At ν = 1/m where m is an odd integer they exhibit spontaneous symmetry breaking equivalent to that of spin 1/2 easy-plane ferromagnets, with the layer degree of freedom playing the role of spin. We explore the rich variety of quantum and finite temperature phase transitions in these systems. In particular, we show that a magnetic field oriented parallel to the layers induces a highly collective commensurate-incommensurate phase transition in the magnetic order. 73.20.Dx, 64.60.Cn Recent technological progress has allowed production of double-layer quantum Hall systems of extremely high mobility. The separation d of the two 2D electron gases is so small (d ∼ 100Å) as to be comparable to the spacing between electrons in the same layer and quantum states with strong correlations between the layers have been observed experimentally and discussed theoretically [1][2][3]. Wen and Zee have pointed out that at Landau level filling factor ν = 1/m and in the absence of interlayer tunneling, this system exhibits a spontaneously broken U(1) gauge symmetry [4]. (m is an odd integer.) The corresponding Goldstone mode is a neutral density wave in which the densities in the two layers oscillate out of phase. A finite temperature Kosterlitz-Thouless (KT) phase transition is expected to be associated with this broken symmetry.In this paper we focus for convenience on the case ν = 1 and show that this system can be viewed as an easy-plane quantum itinerant ferromagnet. Following Ref.[5] (but with a rotated coordinate system) we will use an 'isospin' magnetic language in which isospin 'up' ('down') refers to an electron in the 'upper' ('lower') layer [6]. Using this language and building upon recent progress in understanding the case of single-layer systems at ν = 1 with real spin [7,8] we explore the consequences of the mixing of charge and isospin degrees of freedom and discuss the rich variety of phase transitions controlled by temperature, layer separation, tunneling between layers, layer charge imbalance and magnetic field tilt angles. In addition to the KT transition we find a 'commensurateincommensurate' phase transition as a function of B , the component of the magnetic field in the plane. Furthermore we demonstrate that the Meissner screening of the in-plane component of the magnetic field (B ) predicted by Ezawa and Iwazaki does not occur. A portion of this rich set of phenomena is captured in the schematic zerotemperature phase diagram illustrated in Fig. 1. The present paper will be devoted to explication of the physical picture underlying this phase diagram. Technical details of the microscopic calculations on which it is based will be presented elsewhere [9].It is helpful to begin by discussing the limit of zero temperature, zero tunneling amplitude between the layers and layer spacing d = 0. We work entirely in the lowest Landau level and take the unit of length to be l ≡ (hc/eB) 1/2 . Coulomb repulsion induces ...

Using an asymptotically exact real space renormalization procedure, we find that the Heisenberg antiferromagnetic spin-1 chain undergoes an impurity driven second order phase transition from the Haldane phase to the random singlet phase, as the bond distribution is broadened. In the Haldane phase and near the critical point, there is a Griffiths region in which the gap is filled and the susceptibility diverges in a non-universal manner. The correlation length critical exponent is ν ≈ 2.3.

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The COVID‐19 pathogen, SARS‐CoV‐2, requires its main protease (SC2MPro) to digest two of its translated long polypeptides to form a number of mature proteins that are essential for viral replication and pathogenesis. Inhibition of this vital proteolytic process is effective in preventing the virus from replicating in infected cells and therefore provides a potential COVID‐19 treatment option. Guided by previous medicinal chemistry studies about SARS‐CoV‐1 main protease (SC1MPro), we have designed and synthesized a series of SC2MPro inhibitors that contain β‐(S‐2‐oxopyrrolidin‐3‐yl)‐alaninal (Opal) for the formation of a reversible covalent bond with the SC2MPro active‐site cysteine C145. All inhibitors display high potency with Ki values at or below 100 nM. The most potent compound, MPI3, has as a Ki value of 8.3 nM. Crystallographic analyses of SC2MPro bound to seven inhibitors indicated both formation of a covalent bond with C145 and structural rearrangement from the apoenzyme to accommodate the inhibitors. Virus inhibition assays revealed that several inhibitors have high potency in inhibiting the SARS‐CoV‐2‐induced cytopathogenic effect in both Vero E6 and A549/ACE2 cells. Two inhibitors, MPI5 and MPI8, completely prevented the SARS‐CoV‐2‐induced cytopathogenic effect in Vero E6 cells at 2.5–5 μM and A549/ACE2 cells at 0.16–0.31 μM. Their virus inhibition potency is much higher than that of some existing molecules that are under preclinical and clinical investigations for the treatment of COVID‐19. Our study indicates that there is a large chemical space that needs to be explored for the development of SC2MPro inhibitors with ultra‐high antiviral potency.

We study the effects of random bonds on spin chains that have an excitation gap in the absence of randomness. The dimerized spin-1/2 chain is our principal example. Using an asymptotically exact real space decimation renormalization group procedure, we find that dimerization is a relevant perturbation at the random singlet fixed point. For weak dimerization, the dimerized chain is in a Griffiths phase with short range spin-spin correlations and a divergent susceptibility. The string topological order, however, is not destroyed by bond randomness and dimerization is stabilized by the confinement of topological defects. We conjecture that random integer spin chains in the Haldane phase exhibit similar thermodynamic and topological properties.Comment: RevTex3.0, 12 pages, no figur

We report on numerical studies of two-dimensional electron systems in the presence of a perpendicular magnetic field, with a high Landau level (index N $ 2) half filled by electrons. Strong and sharp peaks are found in the wave-vector dependence of both the static density susceptibility and the equal-time density-density correlation function, in finite-size systems with up to twelve electrons. Qualitatively different from the partially filled lowest (N 0) Landau level, these results are suggestive of a tendency toward charge-density-wave ordering in these systems. The ordering wave vector is found to decrease with increasing N. PACS numbers: 73.20.Dx, 73.40.Kp, 73.50.Jt Two-dimensional (2D) electron gas systems subject to a perpendicular magnetic field display remarkable phenomena, reflecting the importance of electronic correlations. The most important among them is the fractional quantum Hall effect (FQHE), which was found in the strong field limit, where the electrons are confined to the lowest (N 0) or the second (N 1) Landau levels. The physics of FQHE is reasonably well understood [1]: the kinetic energy of the electrons is quenched by the strong perpendicular magnetic field and the Coulomb interaction dominates the physics of the partially filled Landau level; at certain Landau level filling factors (n, defined to be the ratio of the number of electrons to the number of Landau orbitals in each Landau level) the electrons condense into a highly correlated, incompressible quantum fluid, giving rise to quantized Hall resistivity (r xy ) and thermally activated longitudinal resistivity (r xx ).Experimentally, the FQHE has never been found at filling factors n . 4, when the partially filled Landau level has Landau level index N $ 2 (taking into account the two spin species of the electrons). Nevertheless, recent experiments [2,3] on high quality samples have revealed remarkable transport anomalies for n . 4, especially when n is near a half integer, which means the partially filled Landau level is nearly half filled. Such anomalies include a strong anisotropy and nonlinearity in r xx . They reflect intriguing correlation physics at work in these systems that is qualitatively different from the FQHE and yet to be completely understood.It was argued [4], before the discovery of the FQHE, that the ground state of a 2D electron gas in a strong magnetic field may possess charge density wave (CDW) order. Recent Hartree-Fock (HF) calculations [5-7] find that single-Slater determinant states with CDW order have energies lower than the Laughlin-type liquid states for N $ 2. The CDW state with 1D stripe order, or stripe phase [5][6][7], which is predicted to be stable near half filling for the partially filled Landau level, can in principle give rise to transport anisotropy as the orientation of the stripe picks out a special direction in space. Questions remain, however, with regard to the stability of the HF states against quantum fluctuations as well as disorder, especially when N is not too large.In this paper we ...

Topological Dirac semimetal is a newly discovered class of materials which has attracted intense attentions. This material can be viewed as a three-dimensional (3D) analog of graphene and has linear energy dispersion in bulk, leading to a range of exotic transport properties. Here we report direct quantum transport evidence of the 3D Dirac semimetal phase of layered material ZrTe 5 by angular dependent magnetoresistance measurements under high magnetic fields up to 31 T. We observed very clear negative longitudinal magnetoresistance induced by chiral anomaly under the condition of the magnetic field aligned only along the current direction. Pronounced Shubnikov-de Hass (SdH) quantum oscillations in both longitudinal magnetoresistance and transverse Hall resistance were observed, revealing anisotropic light cyclotron masses and high mobility of the system. In particular, a nontrivial π-Berry phase in the SdH oscillations gives clear evidence for 3D Dirac semimetal phase. Furthermore, we observed clear Landau level splitting under high magnetic field, suggesting possible splitting of the Dirac point into Weyl points due to broken time reversal symmetry. Our results indicate that ZrTe 5 is an ideal platform to study 3D massless Dirac and Weyl fermions in a layered compound.