We investigate low-temperature magneto-transport in recently developed, high-quality multiterminal suspended bilayer graphene devices, enabling the independent measurement of the longitudinal and ...transverse resistance. We observe clear signatures of the fractional quantum Hall effect with different states that are either fully developed, and exhibit a clear plateau in the transverse resistance with a concomitant dip in longitudinal resistance or incipient, and exhibit only a longitudinal resistance minimum. All observed states scale as a function of filling factor ν, as expected. An unprecedented even-denominator fractional state is observed at ν = −1/2 on the hole side, exhibiting a clear plateau in R xy quantized at the expected value of 2h/e 2 with a precision of ∼0.5%. Many of our observations, together with a recent electronic compressibility measurement performed in graphene bilayers on hexagonal boron-nitride (hBN) substrates, are consistent with a recent theory that accounts for the effect of the degeneracy between the N = 0 and N = 1 Landau levels in the fractional quantum Hall effect and predicts the occurrence of a Moore-Read type ν = −1/2 state. Owing to the experimental flexibility of bilayer graphene, which has a gate-dependent band structure, can be easily accessed by scanning probes, and can be contacted with materials such as superconductors, our findings offer new possibilities to explore the microscopic nature of even-denominator fractional quantum Hall effect.
We consider a disordered Hubbard model and show that, at sufficiently weak disorder, a single spin-down mobile impurity can thermalize an extensive initially localized system of spin-up particles. ...Thermalization is enabled by resonant processes that involve correlated hops of the impurity and localized particles. This effect indicates that Anderson localized insulators behave as "supercooled" systems, with mobile impurities acting as ergodic seeds. We provide analytical estimates, supported by numerical exact diagonalization, showing how the critical disorder strength for such mechanism depends on the particle density of the localized system. In the U→∞ limit, doublons are stable excitations, and they can thermalize mesoscopic systems by a similar mechanism. The emergence of an additional conservation law leads to an eventual localization of doublons. Our predictions apply to fermionic and bosonic systems and are readily accessible in ongoing experiments simulating synthetic quantum lattices with tunable disorder.
Describing dynamics of quantum many-body systems is a formidable challenge due to rapid generation of quantum entanglement between remote degrees of freedom. A promising approach to tackle this ...challenge, which has been proposed recently, is to characterize the quantum dynamics of a many-body system and its properties as a bath via the Feynman-Vernon influence matrix (IM), which is an operator in the space of time trajectories of local degrees of freedom. Physical understanding of the general scaling of the IM's temporal entanglement and its relation to basic dynamical properties is highly incomplete to the present day. In this paper, we analytically compute the exact IM for a family of integrable Floquet models-the transverse-field kicked Ising chain-finding a Bardeen-Cooper-Schrieffer-like "wave function" on the Schwinger-Keldysh contour with algebraically decaying correlations. We demonstrate that the IM exhibits area-law temporal entanglement scaling for all parameter values. Furthermore, the entanglement pattern of the IM reveals the system's phase diagram, exhibiting jumps across transitions between distinct Floquet phases. Near criticality, a nontrivial scaling behavior of temporal entanglement is found. The area-law temporal entanglement allows us to efficiently describe the effects of sizable integrability-breaking perturbations for long evolution times by using matrix-product-state methods. This work shows that tensor-network methods are efficient in describing the effect of noninteracting baths on open quantum systems and provides an approach to studying quantum many-body systems with weakly broken integrability.
We investigate thermalization dynamics of a driven dipolar many-body quantum system through the stability of discrete time crystalline order. Using periodic driving of electronic spin impurities in ...diamond, we realize different types of interactions between spins and demonstrate experimentally that the interplay of disorder, driving, and interactions leads to several qualitatively distinct regimes of thermalization. For short driving periods, the observed dynamics are well described by an effective Hamiltonian which sensitively depends on interaction details. For long driving periods, the system becomes susceptible to energy exchange with the driving field and eventually enters a universal thermalizing regime, where the dynamics can be described by interaction-induced dephasing of individual spins. Our analysis reveals important differences between thermalization of long-range Ising and other dipolar spin models.
We have developed a device fabrication process to pattern graphene into nanostructures of arbitrary shape and control their electronic properties using local electrostatic gates. Electronic transport ...measurements have been used to characterize locally gated bipolar graphene p-n-p junctions. We observe a series of fractional quantum Hall conductance plateaus at high magnetic fields as the local charge density is varied in the p and n regions. These fractional plateaus, originating from chiral edge states equilibration at the p-n interfaces, exhibit sensitivity to interedge backscattering which is found to be strong for some of the plateaus and much weaker for other plateaus. We use this effect to explore the role of backscattering and estimate disorder strength in our graphene devices.
Previous studies reveal a crucial effect of symmetries on the properties of a single particle moving in a disorder potential. More recently, a phenomenon of many-body localization (MBL) has been ...attracting much theoretical and experimental interest. MBL systems are characterized by the emergence of quasilocal integrals of motion and by the area-law entanglement entropy scaling of its eigenstates. In this paper, we investigate the effect of a non-AbelianSU(2)symmetry on the dynamical properties of a disordered Heisenberg chain. WhileSU(2)symmetry is inconsistent with conventional MBL, a new nonergodic regime is possible. In this regime, the eigenstates exhibit faster than area-law, but still strongly subthermal, scaling of the entanglement entropy. Using extensive exact diagonalization simulations, we establish that this nonergodic regime is indeed realized in the strongly disordered Heisenberg chains. We use the real-space renormalization group (RSRG) to construct approximate excited eigenstates by tree tensor networks and demonstrate the accuracy of this procedure for systems of sizes up toL=26. As the effective disorder strength is decreased, a crossover to the thermalizing phase occurs. To establish the ultimate fate of the nonergodic regime in the thermodynamic limit, we develop a novel approach for describing many-body processes that are usually neglected by the RSRG. This approach is capable of describing systems of sizeL≈2000. We characterize the resonances that arise due to such processes, finding that they involve an ever-growing number of spins as the system size is increased. Crucially, the probability of finding resonances grows with the system’s size. Even at strong disorder, we can identify a large length scale beyond which resonances proliferate. Presumably, this proliferation would eventually drive the system to a thermalizing phase. However, the extremely long thermalization timescales indicate that a broad nonergodic regime will be observable experimentally. Our study demonstrates that, similar to the case of single-particle localization, symmetries control dynamical properties of disordered, many-body systems. The approach introduced here provides a versatile tool for describing a broad range of disordered many-body systems, well beyond sizes accessible in previous studies.
Symmetry-breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of ...the lattice, opening a band gap at the charge neutrality point. In a quantizing magnetic field, electron interactions can cause spontaneous symmetry-breaking within the spin and valley degrees of freedom, resulting in quantum Hall effect (QHE) states with complex order. Here, we report fractional QHE states in BLG that show phase transitions that can be tuned by a transverse electric field. This result provides a model platform with which to study the role of symmetry-breaking in emergent states with topological order.
We present a theory of electron-mediated interaction between adatoms in graphene. In the case of resonant scattering, relevant for hydrogenated graphene, a long-range 1/r interaction is found. This ...interaction can be viewed as a fermionic analog of the Casimir interaction, in which massless fermions play the role of photons. The interaction is an attraction or a repulsion depending on whether the adatoms reside on the same sublattice or on different sublattices, with attraction dominating for adatoms randomly distributed over both sublattices. The attractive nature of these forces creates an instability under which adatoms tend to aggregate.
Graphene and its multilayers have attracted considerable interest because their fourfold spin and valley degeneracy enables a rich variety of broken-symmetry states arising from electron-electron ...interactions, and raises the prospect of controlled phase transitions among them. Here we report local electronic compressibility measurements of ultraclean suspended graphene that reveal a multitude of fractional quantum Hall states surrounding filling factors ν=-1/2 and -1/4. Several of these states exhibit phase transitions that indicate abrupt changes in the underlying order, and we observe many additional oscillations in compressibility as ν approaches -1/2, suggesting further changes in spin and/or valley polarization. We use a simple model based on crossing Landau levels of composite fermions with different internal degrees of freedom to explain many qualitative features of the experimental data. Our results add to the diverse array of many-body states observed in graphene and demonstrate substantial control over their order parameters.
PDF
