[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Annual review of condensed matter physics

We show that the pseudorelativistic physics of graphene near the Fermi level can be extended to three dimensional (3D) materials. Unlike in phase transitions from inversion symmetric topological to normal insulators, we show that particular space groups also allow 3D Dirac points as symmetry protected degeneracies. We provide criteria necessary to identify these groups and, as an example, present ab initio calculations of β-cristobalite BiO(2) which exhibits three Dirac points at the Fermi level. We find that β-cristobalite BiO(2) is metastable, so it can be physically realized as a 3D analog to graphene.

Dirac Semimetal in Three Dimensions

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

We present the critical theory of a number of zero-temperature phase transitions of quantum antiferromagnets and interacting boson systems in two dimensions. The most important example is the transition of the $S=1∕2$ square lattice antiferromagnet between the N\'eel state (which breaks spin rotation invariance) and the paramagnetic valence bond solid (which preserves spin rotation invariance but breaks lattice symmetries). We show that these two states are separated by a second-order quantum phase transition. This conflicts with Landau-Ginzburg-Wilson theory, which predicts that such states with distinct broken symmetries are generically separated either by a first-order transition, or by a phase with co-existing orders. The critical theory of the second-order transition is not expressed in terms of the order parameters characterizing either state, but involves fractionalized degrees of freedom and an emergent, topological, global conservation law. A closely related theory describes the superfluid-insulator transition of bosons at half filling on a square lattice, in which the insulator has a bond density wave order. Similar considerations are shown to apply to transitions of antiferromagnets between the valence bond solid and the ${Z}_{2}$ spin liquid: the critical theory has deconfined excitations interacting with an emergent $\mathrm{U}(1)$ gauge force. We comment on the broader implications of our results for the study of quantum criticality in correlated electron systems.

Quantum criticality: beyond the Landau-Ginzburg-Wilson paradigm

Twisted bilayer graphene displays insulating and superconducting phases caused by flattening of its energy band. In the superconducting dome near hole half-filling, the threefold lattice rotation symmetry is broken, and the superconductor is also a nematic. The authors argue that superconductivity can be properly described by a patch model near twelve Van Hove points and show that there is nearly equal attractive interaction in two different superconducting channels. They go on to explicitly demonstrate that when both orders develop, the superconducting state is also a nematic.

Nematic superconductivity in twisted bilayer graphene

We study the quantum many-body instabilities of interacting electrons with $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetry in spin and orbital degrees of freedom on the triangular lattice near van-Hove filling. Our work is motivated by effective models for the flat bands in hexagonal moir\'e heterostructures like twisted bilayer boron nitride and trilayer graphene-boron nitride systems. We consider an extended Hubbard model including onsite Hubbard and Hund's couplings, as well as nearest-neighbor exchange interactions, and analyze the different ordering tendencies with the help of an unbiased functional renormalization group approach. We find three classes of instabilities controlled by the filling and bare interactions. For a nested Fermi surface at van-Hove filling, Hund-like couplings induce a weak instability towards spin or orbital density wave phases. An SU(4) exchange interaction moves the system towards a Chern insulator, which is robust with respect to perturbations from Hund-like interactions or deviations from perfect nesting. Further, in an extended range of fillings and interactions, we find topological $d\ifmmode\pm\else\textpm\fi{}id$ and (spin-singlet)-(orbital-singlet) $f$-wave superconductivity.

Competing phases of interacting electrons on triangular lattices in moiré heterostructures

Thermal phase transitions are successfully described by fluctuations of an appropriate order parameter, which further allows classification of the transition into first or second order However, some quantum analogs of thermal phase transitions defy this description and identifying the mechanisms behind these unconventional processes will fundamentally improve our understanding of matter Here, the authors provide a thorough study of such a transition, which has been experimentally accessed in graphene: the emergence of a Kekul\'e valence bond solid Additional gapless quantum fluctuations of Dirac electrons change the nature of this transition from first to second order Using a nonperturbative functional renormalization group approach, the authors advance the state-of-the-art estimates for the corresponding critical exponents and predict measurable corrections to scaling

Fluctuation-induced continuous transition and quantum criticality in Dirac semimetals

Van Hove points are special points in the energy dispersion, where the density of states exhibits analytic singularities When a Van Hove point is close to the Fermi level, tendencies towards density wave orders, Pomeranchuk orders, and superconductivity can all be enhanced, often in more than one channel, leading to a competition between different orders and unconventional ground states Here we consider the effects from higher-order Van Hove points, around which the dispersion is flatter than near a conventional Van Hove point, and the density of states has a power-law divergence We argue that such points are present in intercalated graphene and other materials We use an effective low-energy model for electrons near higher-order Van Hove points and analyze the competition between different ordering tendencies using an unbiased renormalization-group approach For purely repulsive interactions, we find that two key competitors are ferromagnetism and chiral superconductivity For a small attractive interaction, we find an unconventional spin Pomeranchuk order, in wich the spin oder parameter winds around the Fermi surface The supermetal state, predicted for a single higher-order Van Hove point, is an unstable fixed point in our case

Competing orders at higher-order Van Hove points

We analyze density wave and Pomeranchuk orders in twisted bilayer graphene. This complements our earlier analysis of the pairing instabilities. We assume that near half filling of either conduction or valence band, the Fermi level is close to Van Hove points, where the density of states diverges, and study potential instabilities in the particle-hole channel within a patch model with two valley degrees of freedom. The hexagonal symmetry of twisted bilayer graphene allows for either six or twelve Van Hove points. We consider both cases and find the same two leading candidates for particle-hole order. One is an SU(2)-breaking spin state with ferromagnetism within a valley. A subleading intervalley hopping induces antiferromagnetism between the valleys. The same state has also been obtained in strong-coupling approaches, indicating that this order is robust. The other is a mixed state with ${120}^{\ensuremath{\circ}}$ complex spin order and orthogonal complex charge order. In addition, we find a weaker but still attractive interaction in nematic channels, and discuss the type of a nematic order.

Laura Classen

Papers

Nematic superconductivity in twisted bilayer graphene

Competing phases of interacting electrons on triangular lattices in moiré heterostructures

Fluctuation-induced continuous transition and quantum criticality in Dirac semimetals

Competing orders at higher-order Van Hove points

Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene