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Register a new userTheoretical phase diagram of two-component composite fermions in double layer graphene
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Theory predicts that double layer systems realize two-component composite fermions, which are formed when electrons capture both intra- and inter-layer vortices, to produce a wide variety of new strongly correlated liquid and crystal states as a function of the layer separation. Recent experiments in double layer graphene have revealed a large number of layer-correlated fractional quantum Hall states in the lowest Landau level, many of which have not been studied quantitatively in previous theoretical works. We consider the competition between various liquid and crystal states at several of these filling factors (specifically, the states at total filling factors $ u=3/7$, $4/9$, $6/11$, $4/7$, $3/5$, $2/3$, and $4/5$) to determine the theoretical phase diagram as a function of the layer separation. We compare our results with experiments and identify various observed states. In particular, we show that at small layer separations the states at total fillings $ u=3/7$ and $ u=3/5$ are partially pseudospin polarized, where pseudospin refers to the layer index. For certain fractions, such as $ u=3/7$, interlayer correlations are predicted to survive to surprisingly large interlayer separations.
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Pairing interaction between fermionic particles leads to composite Bosons that condense at low temperature. Such condensate gives rise to long range order and phase coherence in superconductivity, superfluidity, and other exotic states of matter in the quantum limit. In graphene double-layers separated by an ultra-thin insulator, strong interlayer Coulomb interaction introduces electron-hole pairing across the two layers, resulting in a unique superfluid phase of interlayer excitons. In this work, we report a series of emergent fractional quantum Hall ground states in a graphene double-layer structure, which is compared to an expanded composite fermion model with two-component correlation. The ground state hierarchy from bulk conductance measurement and Hall resistance plateau from Coulomb drag measurement provide strong experimental evidence for a sequence of effective integer quantum Hall effect states for the novel two-component composite fermions (CFs), where CFs fill integer number of effective LLs (Lambda-level). Most remarkably, a sequence of incompressible states with interlayer correlation are observed at half-filled Lambda-levels, which represents a new type of order involving pairing states of CFs that is unique to graphene double-layer structure and beyond the conventional CF model.
The phase diagram of the simplest approximation to Double-Exchange systems, the bosonic Double-Exchange model with antiferromagnetic super-exchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions and Variational Mean-Field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segment like ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase-transition, only short-range ordering would be found in neutron-scattering. Researchers looking for a Quantum Critical Point in manganites should be wary of this possibility. Finite-Size Scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes.
We investigate a three component fermion mixture in the presence of weak attractive interactions. We use a combination of the equation of motion and the Gaussian variational mean-field approaches, which both allow for simultaneous superfluid and magnetic ordering in an unbiased way, and capture the interplay between the two order parameters. This interplay significantly modifies the phase diagram, especially the superfluid-normal phase boundaries. In the close vicinity of the critical temperature and for small chemical potential imbalances, strong particle-hole symmetry breaking leads to a phase diagram similar to the one predicted by Cherng et al. [Phys. Rev. Lett. 99, 130406 (2007)], however, the overall phase diagram is markedly different: new chemical potential-driven first and second order transitions and triple points emerge as well as more exotic second order multicritical points, and bicritical lines with O(2,2) symmetry. We identify the terms which are necessary to capture this complex phase diagram in a Ginzburg-Landau approach, and determine the corresponding coefficients.
In the recent advancement in Graphene heterostructures, it is possible to create a double layer tunnel decoupled Graphene system which has strong interlayer electronic interaction. In this work, we restrict the parameters in the Hamiltonian using simple symmetry arguments. We study the ground state of this system in the Hartree-Fock approximation at $ u_1= u_2=0$. In addition to the phases found in monolayer Graphene, we found the existence of layer correlated phase which breaks the layer $U(1)$ symmetry. At non-zero Zeeman coupling strength ($E_z$) this layer correlated state has a small magnetization, which vanishes as $E_z$ goes to zero. We discuss the bulk gapless modes using the Goldstone theorem. We also comment on the edge structure for the layer correlated phase.
Hall viscosity, also known as the Lorentz shear modulus, has been proposed as a topological property of a quantum Hall fluid. Using a recent formulation of the composite fermion theory on the torus, we evaluate the Hall viscosities for a large number of fractional quantum Hall states at filling factors of the form $ u=n/(2pnpm 1)$, where $n$ and $p$ are integers, from the explicit wave functions for these states. The calculated Hall viscosities $eta^A$ agree with the expression $eta^A=(hbar/4) {cal S}rho$, where $rho$ is the density and ${cal S}=2ppm n$ is the shift in the spherical geometry. We discuss the role of modular invariance of the wave functions, of the center-of-mass momentum, and also of the lowest-Landau-level projection. Finally, we show that the Hall viscosity for $ u={nover 2pn+1}$ may be derived analytically from the microscopic wave functions, provided that the overall normalization factor satisfies a certain behavior in the thermodynamic limit. This derivation should be applicable to a class of states in the parton construction, which are products of integer quantum Hall states with magnetic fields pointing in the same direction.
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