Pair Density Waves from Local Band Geometry.

A band-projection formalism is developed for calculating the superfluid weight in two-dimensional multiorbital superconductors with an orbital-dependent pairing. It is discovered that, in this case, the band geometric superfluid stiffness tensor can be locally nonpositive definite in some regions of the Brillouin zone. When these regions are large enough or include nodal singularities, the total superfluid weight becomes nonpositive definite due to pairing fluctuations, resulting in the transition of a BCS state to a pair density wave (PDW). This geometric BCS-PDW transition is studied in the context of two-orbital superconductors, and proof of the existence of a geometric BCS-PDW transition in a generic topological flat band is established.

Quantum parity Hall effect in Bernal-stacked trilayer graphene.

The quantum Hall effect has recently been generalized from transport of conserved charges to include transport of other approximately conserved-state variables, including spin and valley, via spin- or valley-polarized boundary states with different chiralities. Here, we report a class of quantum Hall effect in Bernal- or ABA-stacked trilayer graphene (TLG), the quantum parity Hall (QPH) effect, in which boundary channels are distinguished by even or odd parity under the system's mirror reflection symmetry. At the charge neutrality point, the longitudinal conductance [Formula: see text] is first quantized to [Formula: see text] at a small perpendicular magnetic field [Formula: see text], establishing the presence of four edge channels. As [Formula: see text] increases, [Formula: see text] first decreases to [Formula: see text], indicating spin-polarized counterpropagating edge states, and then, to approximately zero. These behaviors arise from level crossings between even- and odd-parity bulk Landau levels driven by exchange interactions with the underlying Fermi sea, which favor an ordinary insulator ground state in the strong [Formula: see text] limit and a spin-polarized state at intermediate fields. The transitions between spin-polarized and -unpolarized states can be tuned by varying Zeeman energy. Our findings demonstrate a topological phase that is protected by a gate-controllable symmetry and sensitive to Coulomb interactions.

Topological Braiding of Non-Abelian Midgap Defects in Classical Metamaterials.

Nontrivial braid-group representations appear as non-Abelian quantum statistics of emergent Majorana zero modes in one- and two-dimensional topological superconductors. Here, we generate such representations with topologically protected domain-wall modes in a classical analog of the Kitaev superconducting chain, with a particle-holelike symmetry and a Z_{2} topological invariant. The midgap modes are found to exhibit distinct fusion channels and rich non-Abelian braiding properties, which are investigated using a T-junction setup. We employ the adiabatic theorem to explicitly calculate the braiding matrices for one and two pairs of these midgap topological defects.

Substrate-Dependent Band Structures in Trilayer Graphene/h-BN Heterostructures.

The tight-binding model has been spectacularly successful in elucidating the electronic and optical properties of a vast number of materials. Within the tight-binding model, the hopping parameters that determine much of the band structure are often taken as constants. Here, using ABA-stacked trilayer graphene as the model system, we show that, contrary to conventional wisdom, the hopping parameters and therefore band structures are not constants, but are systematically variable depending on their relative alignment angle between h-BN. Moreover, the addition or removal of the h-BN substrate results in an inversion of the K and K^{'} valley in trilayer graphene's lowest Landau level. Our work illustrates the oft-ignored and rather surprising impact of the substrates on band structures of 2D materials.

Counterpropagating Fractional Hall States in Mirror-Symmetric Dirac Semimetals.

The Landau bands of mirror symmetric 2D Dirac semimetals (e.g., odd layers of ABA graphene) can be identified by their parity with respect to mirror symmetry. This symmetry facilitates a new class of counterpropagating Hall states. We predict the presence of a Laughlin-like correlated liquid state, at the charge neutrality point, with opposite but equal electron and hole filling factors |ν_{±}|=1/m (m odd). This state exhibits fractionally charged quasiparticle-hole pair excitations and counterpropagating edge states with opposite parity. Using a bosonized one-dimensional edge state theory, we show that the fractionally quantized two-terminal longitudinal conductance, σ_{xx}=2e^{2}/(mh), is robust to short-ranged intermode interactions.

Tunable Lifshitz Transitions and Multiband Transport in Tetralayer Graphene.

As the Fermi level and band structure of two-dimensional materials are readily tunable, they constitute an ideal platform for exploring the Lifshitz transition, a change in the topology of a material's Fermi surface. Using tetralayer graphene that host two intersecting massive Dirac bands, we demonstrate multiple Lifshitz transitions and multiband transport, which manifest as a nonmonotonic dependence of conductivity on the charge density n and out-of-plane electric field D, anomalous quantum Hall sequences and Landau level crossings that evolve with n, D, and B.

Natural Regulation of Energy Flow in a Green Quantum Photocell.

Manipulating the flow of energy in nanoscale and molecular photonic devices is of both fundamental interest and central importance for applications in light energy harvesting optoelectronics. Under erratic solar irradiance conditions, unregulated power fluctuations in a light-harvesting photocell lead to inefficient energy storage in conventional solar cells and potentially fatal oxidative damage in photosynthesis. Here, we compare the theoretical minimum energy fluctuations in nanoscale quantum heat engine photocells that incorporate one or two photon-absorbing channels and show that fluctuations are naturally suppressed in the two-channel photocell. This intrinsic suppression acts as a passive regulation mechanism that enables the efficient conversion of varying incident solar power into a steady output for absorption over a broad range of the solar spectrum on Earth. Remarkably, absorption in the green portion of the spectrum provides no inherent regulatory benefit, indicating that green light should be rejected in a photocell whose primary role is the regulation of energy flow.

Tunable Symmetries of Integer and Fractional Quantum Hall Phases in Heterostructures with Multiple Dirac Bands.

The copresence of multiple Dirac bands in few-layer graphene leads to a rich phase diagram in the quantum Hall regime. Using transport measurements, we map the phase diagram of BN-encapsulated ABA-stacked trilayer graphene as a function charge density n, magnetic field B, and interlayer displacement field D, and observe transitions among states with different spin, valley, orbital, and parity polarizations. Such a rich pattern arises from crossings between Landau levels from different subbands, which reflect the evolving symmetries that are tunable in situ. At D=0, we observe fractional quantum Hall (FQH) states at filling factors 2/3 and -11/3. Unlike those in bilayer graphene, these FQH states are destabilized by a small interlayer potential that hybridizes the different Dirac bands.

Proximity-induced ferromagnetism in graphene revealed by the anomalous Hall effect.

We demonstrate the anomalous Hall effect (AHE) in single-layer graphene exchange coupled to an atomically flat yttrium iron garnet (YIG) ferromagnetic thin film. The anomalous Hall conductance has magnitude of ∼0.09(2e(2)/h) at low temperatures and is measurable up to ∼300 K. Our observations indicate not only proximity-induced ferromagnetism in graphene/YIG with a large exchange interaction, but also enhanced spin-orbit coupling that is believed to be inherently weak in ideal graphene. The proximity-induced ferromagnetic order in graphene can lead to novel transport phenomena such as the quantized AHE which are potentially useful for spintronics.

Superconducting states in pseudo-Landau-levels of strained graphene.

We describe the formation of superconducting states in graphene in the presence of pseudo-Landau-levels induced by strain, when time reversal symmetry is preserved. We show that superconductivity in strained graphene is quantum critical when the pseudo-Landau-levels are completely filled, whereas at partial fillings superconductivity survives at weak coupling. In the weak coupling limit, the critical temperature scales linearly with the coupling strength and shows a sequence of quantum critical points as a function of the filling factor that can be accessed experimentally. We argue that superconductivity can be induced by electron-phonon coupling and that the transition temperature can be controlled with the amount of strain and with the filling fraction of the Landau levels.

Quantum Hall to charge-density-wave phase transitions in ABC-trilayer graphene.

ABC-stacked trilayer graphene's chiral band structure results in three (n=0, 1, 2) Landau level orbitals with zero kinetic energy. This unique feature has important consequences on the interaction-driven states of the 12-fold degenerate (including spin and valley) N=0 Landau level. In particular, at many filling factors ν(T) = ±5, ±4, ±2, ±1 a quantum phase transition from a quantum Hall liquid state to a triangular charge-density wave occurs as a function of the single particle-induced Landau level orbital splitting Δ(LL). Experimental signatures of this phase transition are also discussed.

Quantum Hall effects in graphene-based two-dimensional electron systems.

In this article we review the quantum Hall physics of graphene-based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed respectively as J D 1 and 2 chiral two-dimensional electron gases (C2DEGs), and why this property frames their quantum Hall physics. The current status of experimental and theoretical work on the role of electron-electron interactions is reviewed at length with an emphasis on unresolved issues in the field, including the role of disorder in current experiments. Special attention is given to the interesting low magnetic field limit, and to the relationship between quantum Hall effects and the spontaneous anomalous Hall effects that might occur in bilayer graphene systems in the absence of a magnetic field.

Fractionalization via Z(2) gauge fields at a cold-atom quantum Hall transition.

We study a single species of fermionic atoms in an "effective" magnetic field at total filling factor ν(f)=1, interacting through a p-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a ν(f)=1 fermionic integer quantum Hall state to ν(b)=1/4 bosonic fractional quantum Hall state as a function of detuning. The transition is in the (2+1)D Ising universality class. We formulate a dual theory in terms of quasiparticles interacting with a Z(2) gauge field and show that charge fractionalization follows from this topological quantum phase transition. Experimental consequences and possible tests of our theoretical predictions are discussed.

Anomalous exciton condensation in graphene bilayers.

In ordinary semiconductor bilayers, exciton condensates appear at total Landau-level filling factor nu{T}=1. We predict that similar states will occur in Bernal stacked graphene bilayers at many nonzero integer filling factors. For nu{T}=-3, 1 we find that the superfluid density of the exciton condensate vanishes and that a finite-temperature fluctuation-induced first order isotropic-smectic phase transition occurs when the layer densities are not balanced. These anomalous properties of bilayer graphene exciton condensates are due to the degeneracy of Landau levels with n=0 and n=1 orbital character.

Intra-Landau-level cyclotron resonance in bilayer graphene.

Interaction driven integer quantum-Hall effects are anticipated in graphene bilayers because of the near degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate k3/2 dispersion. We speculate on the possibility of unusual localization physics associated with these modes.

Chirality and correlations in graphene.

Graphene is described at low energy by a massless Dirac equation whose eigenstates have definite chirality. We show that the tendency of Coulomb interactions in lightly doped graphene to favor states with larger net chirality leads to suppressed spin and charge susceptibilities. Our conclusions are based on an evaluation of graphene's exchange and random-phase-approximation correlation energies. The suppression is a consequence of the quasiparticle chirality switch which enhances quasiparticle velocities near the Dirac point.