Evidence of Soft-Mode Quantum Phase Transitions in Electron Double Layers

Pellegrini, Vittorio; Pinczuk, A.; Dennis, B. S.; Plaut, A. S.; Pfeiffer, L. N.; West, K. W.

doi:10.1126/science.281.5378.799

Cited by 87 publications

(82 citation statements)

References 17 publications

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“…The phase transition occurs seemingly between the ν = 1 + 1 compound state and the ν = 2 "coherent state". Phase transitions have also been observed at ν = 2 in optical experiments by Pellegrini et al: first they used samples with different densities [8]; second they tilted samples in the magnetic field [9]. In each of them, they have found two distinctive phases with respect to spin-excitation modes.…”

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confidence: 68%

Interlayer coherence inν=1andν=2bilayer quantum Hall states

et al. 1999

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We have measured the Hall-plateau width and the activation energy of the bilayer quantum Hall (BLQH) states at the Landau-level filling factor ν = 1 and 2 by tilting the sample and simultaneously changing the electron density in each quantum well. The phase transition between the commensurate and incommensurate states are confirmed at ν = 1 and discovered at ν = 2. In particular, three different ν = 2 BLQH states are identified; the compound state, the coherent commensurate state, and the coherent incommensurate state.A spontaneous development of interlayer quantum coherence [1,2] is one of the most interesting phenomena in bilayer quantum Hall (BLQH) systems. One can experimentally prove the existence of such an interlayer quantum coherence by manipulating the macroscopic quantum conjugate observables; the phase difference and the interlayer electron number difference. The interlayer phase difference, if exists, can be controlled by applying a parallel magnetic field between the two layers, which can be achieved by tilting the bilayer system in a magnetic field. Murphy et al. [3] have found an activation-energy anomaly together with a phase transition in the ν = 1 BLQH state by increasing the parallel magnetic field. It was suggested to be a signal of the interlayer quantum coherence [4,5]. The interlayer number difference can also be controlled experimentally by applying gate bias voltages to the two layers. When the interlayer coherence exists, the BLQH state persists even if the electron density is arbitrarily unbalanced between two quantum wells. Sawada et al. [6] have found precisely this behavior in certain BLQH states; furthermore they have found that the activation energy increases as the density difference becomes larger. This behavior is presumably due to a capasitive charging energy stored in Skyrmions excited across the two layers in the coherent state [7]. These two experiments [3,6] indicate strongly the spontaneous development of the interlayer coherence in the ν = 1 BLQH state.An intriguing problem is whether an interlayer coherence develops also in the ν = 2 BLQH systems. Sawada et al. have found [6] a phase transition at ν = 2 by changing the electron density continuously. The phase transition occurs seemingly between the ν = 1 + 1 compound state and the ν = 2 "coherent state". Phase transitions have also been observed at ν = 2 in optical experiments by Pellegrini et al.: first they used samples with different densities [8]; second they tilted samples in the magnetic field [9]. In each of them, they have found two distinctive phases with respect to spin-excitation modes. They have concluded a phase transition between spin polarized and unpolarized states at ν = 2. It is important to relate the phase transitions found in the magnetotransport [6] and optical [8,9] experiments, if any.In this paper, we report the results of experiments on the ν = 1 and 2 BLQH states, where we have measured the Hall-plateau width and the activation energy by changing the density in each quantum well and simultaneo...

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confidence: 68%

Interlayer coherence inν=1andν=2bilayer quantum Hall states

et al. 1999

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“…Finally, we mention recent light scattering experiments [4] on double layer quantum Hall systems which have explored both sides of a magnetic ordering transition. Simulations at n = 3, but in the presence of a magnetic field can lead to specific predictions for this system.…”

Section: Implications For Experimentsmentioning

confidence: 99%

“…The n = 3 case also describes the quantum Hall experiments of Ref. [4], where φ α now measures the difference in the magnetization of the two layers.…”

Section: Introductionmentioning

confidence: 99%

“…Recent light scattering experiments [4] have probed the fluctuation of the magnetic order parameter in the vicinity of the quantum transitions between the states. (iii ) Microwave measurements [5] of the magnetic penetration depth of high temperature superconductors with a number of different T c 's show that the superfluid stiffness satisfies the scaling relation…”

Section: Introductionmentioning

confidence: 99%

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Universal relaxational dynamics near two-dimensional quantum critical points

Sachdev¹

1999

Phys. Rev. B

104

152

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We describe the nonzero temperature (T ), low frequency (ω) dynamics of the order parameter near quantum critical points in two spatial dimensions (d), with a special focus on the regimehω ≪ k B T . For the case of a 'relativistic', O(n)-symmetric, bosonic quantum field theory we show that, for small ǫ = 3 − d, the dynamics is described by an effective classical model of waves with a quartic interaction. We provide analytical and numerical analyses of the classical wave model directly in d = 2. We describe the crossover from the finite frequency, "amplitude fluctuation", gapped quasiparticle mode in the quantum paramagnet (or Mott insulator), to the zero frequency "phase" (n ≥ 2) or "domain wall" (n = 1) relaxation mode near the ordered state. For static properties, we show how a surprising, duality-like transformation allows an exact treatment of the strong-coupling limit for all n. For n = 2, we compute the universal T dependence of the superfluid density below the Kosterlitz-Thouless temperature, and discuss implications for the high temperature superconductors. For n = 3, our computations of the dynamic structure factor relate to neutron scattering experiments on La 1.85 Sr 0.15 CuO 4 , and to light scattering experiments on double layer quantum Hall systems. We expect that closely related effective classical wave models will apply also to other quantum critical points in d = 2. Although computations in appendices do rely upon technical results on the ǫ-expansion of quantum critical points obtained in earlier papers, the physical discussion in the body of the paper is self-contained, and can be read without consulting these earlier works.

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“…Comparable ground state competition has also been studied in double quantum wells in GaAs 2-dimensional electron systems (2DESs) 26 . Quantum phase transitions, in particular from canted antiferromagnetic to ferromagnetic ordering, can occur in those systems as an in-plane magnetic field is applied (Zeeman energy is increased) 27,28 .…”

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Evidence for a spin phase transition at charge neutrality in bilayer graphene

et al. 2013

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The most celebrated property of the quantum spin Hall effect is the presence of spin-polarized counter-propagating edge states 1-3 . This novel edge state configuration has also been predicted to occur in graphene when spin-split electron-and hole-like Landau levels are forced to cross at the edge of the sample 4-7 . In particular, a quantum spin Hall analogue has been predicted at ν = 0 in bilayer graphene if the ground state is a spin ferromagnet 8,9 . Previous studies have demonstrated that the bilayer ν = 0 state is an insulator in a perpendicular magnetic field [10][11][12][13][14][15][16] , though the exact nature of this state has not been identified. Here we present measurements of the ν = 0 state in a dual-gated bilayer graphene device in tilted magnetic field. The application of an in-plane magnetic field and perpendicular electric field allows us to map out a full phase diagram of the ν = 0 state as a function of experimentally tunable parameters. At large in-plane magnetic field we observe a quantum phase transition to a metallic state with conductance of order 4e 2 /h, consistent with predictions for the ferromagnet.Under a strong perpendicular magnetic field, bilayer graphene (BLG) develops a ν = 0 quantum Hall (QH) state at the charge neutrality point (CNP) which displays anomalous insulating behavior [10][11][12][13][14][15][16] . Transport studies in a dual-gated geometry 12-14 indicate that this gapped state results from an interaction-driven spontaneous symmetry breaking in the valley-spin space 17 . However, the exact order of the resulting ground state remains controversial. In high-mobility suspended BLG devices, a broken symmetry state at charge neutrality has also been observed at zero magnetic field whose nature has been under intense theoretical 9,18-22 and experimental 12,[14][15][16]23 investigation. Some experiments indicate there may be a connection between these two insulating states 14,16 .The ν = 0 state in BLG occurs at half filling of the lowest Landau level. Although the BLG zero-energy Landau level has an additional orbital degeneracy stemming from two accidentally degenerate magnetic oscillator wavefunctions 24 , minimization of exchange energy favors singlet pairs in the orbital space at all even filling factors 25 . This leaves an approximate SU(4) spin and pseudospin symmetry for the remaining ordering of the ground state. Comparable ground state competition has also been studied in double quantum wells in GaAs 2-dimensional electron systems (2DESs) 26 . Quantum phase transitions, in particular from canted antiferromagnetic to ferromagnetic ordering, can occur in those systems as an in-plane magnetic field is applied (Zeeman energy is increased) 27,28 .Our experiment is carried out in BLG samples with top and bottom gates in which thin single crystal hBN serves as a high quality dielectric on both sides (Fig. 1 bottom inset). By controlling top gate voltage (V T G ) and bottom gate voltage (V BG ) we can adjust carrier density n and perpendicular electric displacement fi...

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Evidence of Soft-Mode Quantum Phase Transitions in Electron Double Layers

Cited by 87 publications

References 17 publications

Interlayer coherence inν=1andν=2bilayer quantum Hall states

Interlayer coherence inν=1andν=2bilayer quantum Hall states

Universal relaxational dynamics near two-dimensional quantum critical points

Evidence for a spin phase transition at charge neutrality in bilayer graphene

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