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1.
Science ; 382(6676): 1260-1264, 2023 Dec 15.
Article En | MEDLINE | ID: mdl-38096376

Flying qubits encode quantum information in propagating modes instead of stationary discrete states. Although photonic flying qubits are available, the weak interaction between photons limits the efficiency of conditional quantum gates. Conversely, electronic flying qubits can use Coulomb interactions, but the weaker quantum coherence in conventional semiconductors has hindered their realization. In this work, we engineered on-demand injection of a single electronic flying qubit state and its manipulation over the Bloch sphere. The flying qubit is a Leviton propagating in quantum Hall edge channels of a high-mobility graphene monolayer. Although single-shot qubit readout and two-qubit operations are still needed for a viable manipulation of flying qubits, the coherent manipulation of an itinerant electronic state at the single-electron level presents a highly promising alternative to conventional qubits.

2.
Nat Commun ; 13(1): 5473, 2022 Sep 17.
Article En | MEDLINE | ID: mdl-36115841

Over the past 20 years, many efforts have been made to understand and control decoherence in 2D electron systems. In particular, several types of electronic interferometers have been considered in GaAs heterostructures, in order to protect the interfering electrons from decoherence. Nevertheless, it is now understood that several intrinsic decoherence sources fundamentally limit more advanced quantum manipulations. Here, we show that graphene offers a unique possibility to reach a regime where the decoherence is frozen and to study unexplored regimes of electron interferometry. We probe the decoherence of electron channels in a graphene quantum Hall PN junction, forming a Mach-Zehnder interferometer1,2, and unveil a scaling behavior of decay of the interference visibility with the temperature scaled by the interferometer length. It exhibits a remarkable crossover from an exponential decay at higher temperature to an algebraic decay at lower temperature where almost no decoherence occurs, a regime previously unobserved in GaAs interferometers.

3.
Phys Rev Lett ; 126(14): 146803, 2021 Apr 09.
Article En | MEDLINE | ID: mdl-33891444

Graphene is a very promising test bed for the field of electron quantum optics. However, a fully tunable and coherent electronic beam splitter is still missing. We report the demonstration of electronic beam splitters in graphene that couple quantum Hall edge channels having opposite valley polarizations. The electronic transmission of our beam splitters can be tuned from zero to near unity. By independently setting the beam splitters at the two corners of a graphene p-n junction to intermediate transmissions, we realize a fully tunable electronic Mach-Zehnder interferometer. This tunability allows us to unambiguously identify the quantum interferences due to the Mach-Zehnder interferometer, and to study their dependence with the beam-splitter transmission and the interferometer bias voltage. The comparison with conventional semiconductor interferometers points toward universal processes driving the quantum decoherence in those two different 2D systems, with graphene being much more robust to their effect.

4.
Phys Rev B ; 100(13)2019.
Article En | MEDLINE | ID: mdl-33644522

An inelastic neutron scattering study has been performed in an S = 3/2 bilayer honeycomb lattice compound Bi3Mn4O12(NO3) at ambient and high magnetic fields. Relatively broad and monotonically dispersive magnetic excitations were observed at ambient field, where no long-range magnetic order exists. In the magnetic-field-induced long-range ordered state at 10 T, the magnetic dispersions become slightly more intense, albeit still broad as in the disordered state, and two excitation gaps, probably originating from an easy-plane magnetic anisotropy and intrabilayer interactions, develop. Analyzing the magnetic dispersions using the linear spin-wave theory, we estimated the intraplane and intrabilayer magnetic interactions, which are almost consistent with those determined by ab initio density functional theory calculations [M. Alaei et al., Phys. Rev. B 96, 140404(R) (2017)], except the third and fourth neighbor intrabilayer interactions. Most importantly, as predicted by the theory, there is no significant frustration in the honeycomb plane but frustrating intrabilayer interactions probably give rise to the disordered ground state.

5.
Transplant Proc ; 50(8): 2526-2530, 2018 Oct.
Article En | MEDLINE | ID: mdl-30316391

INTRODUCTION: Lymphatic leakage after kidney transplantation is a relatively frequent complication but sometimes resistant to treatment, and there is no fixed treatment algorithm. The effectiveness of therapeutic lymphangiography for postoperative lymphatic or chyle leakage has been reported, but few reports are available regarding patients who have undergone kidney transplantation. In this study, we report our experience with lymphangiography as a therapeutic tool for lymphatic leakage after kidney transplantation. PATIENTS AND METHODS: Intranodal lymphangiography for lymphatic leakage was performed in 4 patients (3 male, 1 female; age range, 38 to 70 years old) after living kidney transplantation at the Osaka City University Hospital in Japan. The amount of drainage before lymphangiography was 169 to 361 mL/day. The procedure for intranodal lymphangiography was as follows: the inguinal lymph node was punctured under ultrasound guidance, and the tip of the needle was instilled at the junction between the cortex and the hilum, after which Lipiodol was slowly and manually injected. RESULTS: Lymphangiography was technically successful in 3 out of the 4 patients. In all successful cases, the amount of drainage decreased and leakage finally stopped without additional therapy such as sclerotherapy or fenestration. In 2 cases, we were able to directly detect the leakage site using lymphangiography. The time between lymphangiography and leakage resolution ranged from 8 to 13 days. There were neither complications of lymphangiography nor recurrence of lymphatic leakage in the successful cases. CONCLUSIONS: Intranodal lymphangiography may be not only a diagnostic tool but also an effective, minimally-invasive, and safe method for treatment of lymphatic leakage resistant to drainage after kidney transplantation.


Kidney Transplantation/adverse effects , Lymphography/methods , Postoperative Complications/diagnostic imaging , Adult , Aged , Female , Humans , Japan , Lymph Nodes/diagnostic imaging , Lymphatic Vessels/diagnostic imaging , Male , Middle Aged
6.
Sci Rep ; 6: 38393, 2016 12 06.
Article En | MEDLINE | ID: mdl-27922114

We have observed the well-kown quantum Hall effect (QHE) in epitaxial graphene grown on silicon carbide (SiC) by using, for the first time, only commercial NdFeB permanent magnets at low temperature. The relatively large and homogeneous magnetic field generated by the magnets, together with the high quality of the epitaxial graphene films, enables the formation of well-developed quantum Hall states at Landau level filling factors v = ±2, commonly observed with superconducting electro-magnets. Furthermore, the chirality of the QHE edge channels can be changed by a top gate. These results demonstrate that basic QHE physics are experimentally accessible in graphene for a fraction of the price of conventional setups using superconducting magnets, which greatly increases the potential of the QHE in graphene for research and applications.

7.
Transplant Proc ; 48(3): 775-80, 2016 Apr.
Article En | MEDLINE | ID: mdl-27234734

INTRODUCTION: This study describes our clinical experience of late conversion from antimetabolites with standard exposure calcineurin inhibitors (CNIs) to everolimus with CNI minimization in stable kidney transplant recipients with good graft function. PATIENTS AND METHODS: A 1-year retrospective pilot study of 26 kidney recipients converted from antimetabolites with standard exposure CNIs to everolimus with CNI minimization was performed. The recipients enrolled in this study had normal or slightly impaired renal function defined as a serum creatinine value <2.0 mg/dL, and normal or slightly increased albuminuria defined as a urinary albumin excretion rate <100 mg/g creatinine. RESULTS: The median time from transplant to conversion was 39.5 months posttransplant (range, 3-275). Treatment with everolimus was stopped owing to adverse events in 11 patients (42.3%). In the analysis of the patients in whom everolimus was maintained, the mean estimated glomerular filtration rate (eGFR) significantly increased from 50.7 ± 11.9 mL/min/1.73 m(2) at baseline to 53.6 ± 13.9 mL/min/1.73 m(2) at 1 year after conversion. In the patients in whom everolimus was stopped during the observation period, there was no difference in eGFR between baseline and 1 year after conversion. CONCLUSIONS: This study demonstrated that, among the patients converted to everolimus at a late stage, there was no deterioration in renal function whether everolimus was maintained or stopped within 1 year after conversion.


Calcineurin Inhibitors/therapeutic use , Everolimus/therapeutic use , Immunosuppressive Agents/therapeutic use , Kidney Transplantation , Transplant Recipients , Adult , Aged , Drug Substitution , Female , Glomerular Filtration Rate , Humans , Male , Middle Aged , Pilot Projects , Retrospective Studies , Young Adult
8.
Nat Commun ; 6: 8068, 2015 Sep 04.
Article En | MEDLINE | ID: mdl-26337067

Graphene offers a unique system to investigate transport of Dirac Fermions at p-n junctions. In a magnetic field, combination of quantum Hall physics and the characteristic transport across p-n junctions leads to a fractionally quantized conductance associated with the mixing of electron-like and hole-like modes and their subsequent partitioning. The mixing and partitioning suggest that a p-n junction could be used as an electronic beam splitter. Here we report the shot noise study of the mode-mixing process and demonstrate the crucial role of the p-n junction length. For short p-n junctions, the amplitude of the noise is consistent with an electronic beam-splitter behaviour, whereas, for longer p-n junctions, it is reduced by the energy relaxation. Remarkably, the relaxation length is much larger than typical size of mesoscopic devices, encouraging using graphene for electron quantum optics and quantum information processing.

9.
Transplant Proc ; 46(2): 532-6, 2014.
Article En | MEDLINE | ID: mdl-24656005

INTRODUCTION: The adverse effects of tacrolimus are known to play major roles in new-onset diabetes after transplantation. The purpose of this study was to investigate the effects of conversion from a twice-daily tacrolimus (Tac-BID) to a once-daily tacrolimus (Tac-OD) on glucose metabolism in stable kidney transplant recipients. PATIENTS AND METHODS: Twenty-six patients were converted from Tac-BID to Tac-OD on a 1:1 mg basis and examined for its effects on glucose metabolism. Unless rejection or tacrolimus toxicity was suspected, we did not perform dose adjustments of Tac-OD or reconversion to Tac-BID until 4 weeks after conversion. Subsequent dose adjustments were allowed to maintain tacrolimus target trough concentration within the. Changes in clinical parameters were compared between baseline and 24 weeks after conversion. RESULTS: Conversion from Tac-BID to Tac-OD on a 1:1 mg basis resulted in a significant decrease in tacrolimus trough level at 4 weeks after conversion. Because dose adjustments were performed, the trough level did not differ significantly between baseline and 24 weeks after conversion. At 4 and 24 weeks after conversion, the homeostasis model assessment of pancreas ß-cell function (HOMA-ß) increased significantly. CONCLUSIONS: Although there was no change in tacrolimus trough level between baseline and 24 weeks after transplantation, HOMA-ß at 24 weeks after conversion was significantly higher than that at baseline. These results indicated that conversion from Tac-BID to Tac-OD may improve pancreas ß-cell function in kidney transplant recipients.


Glucose/metabolism , Immunosuppressive Agents/administration & dosage , Kidney Transplantation , Tacrolimus/administration & dosage , Adult , Female , Humans , Male , Middle Aged , Prospective Studies
10.
Nat Nanotechnol ; 9(3): 177-81, 2014 Mar.
Article En | MEDLINE | ID: mdl-24509659

The model of interacting fermion systems in one dimension known as a Tomonaga-Luttinger liquid (TLL) provides a simple and exactly solvable theoretical framework that predicts various intriguing physical properties. Evidence of a TLL has been observed as power-law behaviour in electronic transport on various types of one-dimensional conductor. However, these measurements, which rely on d.c. transport involving electron tunneling processes, cannot identify the long-awaited hallmark of charge fractionalization, in which an injection of elementary charge e from a non-interacting lead is divided into the non-trivial effective charge e* and the remainder, e-e* (refs 6, 7, 8). Here, we report time-resolved transport measurements on an artificial TLL composed of coupled integer quantum Hall edge channels, in which we successfully identify single charge fractionalization processes. A wave packet of charge q incident from a non-interacting region breaks up into several fractionalized charge wave packets at the edges of the artificial TLL, from which transport eigenmodes can be evaluated directly. These results are informative for elucidating the nature of TLLs and low-energy excitations in the edge channels.

11.
Phys Rev Lett ; 113(26): 266601, 2014 Dec 31.
Article En | MEDLINE | ID: mdl-25615366

We investigate resonant edge magnetoplasmons (EMPs) and their decay in graphene by high-frequency electronic measurements. From EMP resonances in disk shaped graphene, we show that the dispersion relation of EMPs is nonlinear due to interactions, giving rise to the intrinsic decay of EMP wave packets. We also identify extrinsic dissipation mechanisms due to interaction with localized states in bulk graphene from the decay time of EMP wave packets. We indicate that, owing to the linear band structure and the sharp edge potential, EMP dissipation in graphene can be lower than that in GaAs systems.

12.
Transplant Proc ; 45(4): 1535-9, 2013 May.
Article En | MEDLINE | ID: mdl-23726614

BACKGROUND: Although new-onset diabetes after transplantation has been demonstrated to have a significant negative impact on allograft and patient survival, the role of glucose intolerance (impaired fasting glucose [IFG] and/or impaired glucose tolerance [IGT], as asymptomatic hyperglycemia and borderline diabetes, has not been identified in renal transplant recipients. METHODS: We enrolled 32 renal transplant recipients (at least 1 year after transplantation) without prior evidence of diabetes at our institution in this study. Transplant recipients were divided into 2 groups (normal glucose tolerance group and glucose intolerance group) according to the results of their oral glucose tolerance test with 75 g of glucose. Glucose intolerance included IFG, IGT, and IFG/IGT. Normal glucose tolerance was detected in 19 patients, and glucose intolerance in 13: had 6 IGT, 2 IFG, and 5 IGT/IFG. Bilateral brachial-ankle pulse-wave velocity (baPWV) and intimal-media thickness (IMT) measured as markers of atherosclerosis were compared between the 2 groups. Insulin resistance was estimated with the homeostasis model assessment of insulin resistance (HOMA-R), and pancreatic ß-cell function evaluated by the homeostasis model assessment of ß-cell function and insulinogenic index. RESULTS: The patients in the glucose intolerance group showed significantly greater baPWV and IMT than those in the normal glucose tolerance group. HOMA-R in the glucose intolerance patients was significantly higher than in the normal glucose tolerance patients. Linear regression analysis showed the increased IMT in the renal transplant recipients to be significantly correlated with HOMA-R. CONCLUSIONS: Renal transplant recipients with glucose intolerance had increased IMT and baPWV, suggesting that glucose intolerance in renal transplant recipients may induce atherosclerosis and that the rise in insulin resistance may contribute to the increased IMT in renal transplant recipients.


Carotid Arteries/pathology , Glucose Tolerance Test , Kidney Transplantation , Pulse Wave Analysis , Tunica Intima/pathology , Aged , Female , Humans , Islets of Langerhans/physiopathology , Male , Middle Aged
13.
Transplant Proc ; 45(4): 1540-3, 2013 May.
Article En | MEDLINE | ID: mdl-23726615

BACKGROUND: Several reports have suggested an association between hepatitis C virus (HCV) infection and new-onset diabetes after transplantation (NODAT). NODAT is a common complication after renal transplantation, and it has been associated with increased long-term morbidity and mortality. HCV-positive recipients may have abnormal glucose metabolism, even though NODAT has never been previously diagnosed. The aim of this study was to analyze the pathogenic factors responsible for glucose metabolism in a series of HCV-positive renal transplant recipients. METHODS: The study population comprised 16 renal transplant patients who received their grafts from deceased or living donors with anti-HCV antibodies. HCV-negative transplant recipients were individually matched with these HCV-positive recipients by year of transplantation, sex, age, serum creatinine levels, and type of calcineurin inhibitors. None of the patients had been diagnosed with diabetes. Insulin secretion and insulin resistance were determined by a 75-g oral glucose tolerance test (OGTT) and compared between the 2 groups. Categories of glucose tolerance were defined according to World Health Organization criteria. RESULTS: Glucose intolerance (impaired fasting glucose, impaired glucose tolerance, diabetes mellitus) as assessed by OGTT was detected in 7 of the HCV-positive recipients (43.8%) and 3 of the HCV-negative recipients. The homeostasis model assessment of insulin resistance was greater in the HCV-positive recipients than in the HCV-negative recipients. The homeostasis model assessment of ß-cell function was higher in the HCV-positive recipients than in the HCV-negative recipients. CONCLUSIONS: The frequency of glucose intolerance tended to be higher in HCV-positive recipients. Furthermore, insulin resistance was greater and insulin secretion higher in HCV-positive recipients, which indicated that the increase in insulin secretion compensated for insulin resistance observed in these patients. However, HCV-positive renal transplant recipients may ultimately develop NODAT as this compensation diminishes with time.


Hepatitis C/surgery , Insulin Resistance , Insulin/metabolism , Kidney Transplantation , Adult , Female , Glucose Tolerance Test , Humans , Insulin Secretion , Islets of Langerhans/physiopathology , Male
14.
Nat Commun ; 4: 1363, 2013.
Article En | MEDLINE | ID: mdl-23322051

Plasmons, which are collective charge oscillations, could provide a means of confining electromagnetic field to nanoscale structures. Recently, plasmonics using graphene have attracted interest, particularly because of the tunable plasmon dispersion, which will be useful for tunable frequency in cavity applications. However, the carrier density dependence of the dispersion is weak (proportional to n(1/4)) and it is difficult to tune the frequency over orders of magnitude. Here, by exploiting electronic excitation and detection, we carry out time-resolved measurements of a charge pulse travelling in a plasmon mode in graphene corresponding to the gigahertz range. We demonstrate that the plasmon velocity can be changed over two orders of magnitude by applying a magnetic field B and by screening the plasmon electric field with a gate metal; at high B, edge magnetoplasmons, which are plasmons localized at the sample edge, are formed and their velocity depends on B, n and the gate screening effect.

15.
Transplant Proc ; 44(1): 128-33, 2012 Jan.
Article En | MEDLINE | ID: mdl-22310596

BACKGROUND: The adverse effects of tacrolimus are known to play major roles in posttransplantation diabetes mellitus (PTDM). In the present study, we investigated the effects of conversion from a twice-daily (Tac BID) to a once-daily prolonged release of tacrolimus formulation (Tac OD) on glucose metabolism in stable kidney transplant recipients. PATIENTS AND METHODS: In this prospective study, 26 patients converted from Tac BID to the same milligram-milligram daily dose of Tac OD were examined for the effects on renal function, drug trough levels, and glucose metabolism over a 4-week period. RESULTS: Conversion from Tac BID to Tac OD on a 1:1 mg basis resulted in a significant decrease in tacrolimus trough levels, but no significant changes in renal function. At 4 weeks after conversion, a homeostasis model assessment of ß-cell function, and hemoglobin A1c (HbA1c) decreased significantly. CONCLUSIONS: This study demonstrated a significant reduction in tacrolimus trough levels after switching from Tac BID to Tac OD, which increased insulin secretion and decreased HbA1c, suggesting that it may decrease the frequency of PTDM among stable renal transplant recipients.


Blood Glucose/drug effects , Diabetes Mellitus/prevention & control , Immunosuppressive Agents/administration & dosage , Insulin-Secreting Cells/drug effects , Kidney Transplantation , Tacrolimus/administration & dosage , Adult , Biomarkers/blood , Blood Glucose/metabolism , Creatinine/blood , Delayed-Action Preparations , Diabetes Mellitus/blood , Diabetes Mellitus/etiology , Drug Administration Schedule , Drug Monitoring , Female , Glomerular Filtration Rate/drug effects , Glycated Hemoglobin/metabolism , Graft Rejection/immunology , Graft Rejection/prevention & control , Graft Survival/drug effects , Humans , Immunosuppressive Agents/adverse effects , Immunosuppressive Agents/pharmacokinetics , Insulin/blood , Insulin-Secreting Cells/metabolism , Japan , Kidney Transplantation/adverse effects , Kidney Transplantation/immunology , Male , Middle Aged , Prospective Studies , Tacrolimus/adverse effects , Tacrolimus/pharmacokinetics , Treatment Outcome
16.
Transplant Proc ; 44(1): 204-9, 2012 Jan.
Article En | MEDLINE | ID: mdl-22310615

INTRODUCTION: Due to the severe shortage of deceased donors in Japan, ABO-incompatible living donor kidney transplantation has been performed since the late 1980s. Excellent long-term outcomes have been achieved; the rates of graft survival among these patients are currently similar to those of recipients of ABO-compatible grafts. Our single-center experience describing the immunosuppressive protocols, complications, and grafts survivals is documented in this study. PATIENTS AND METHODS: Among 123 patients with end-stage renal disease who underwent living donor kidney transplantation between January 1999 and December 2010, 25 cases were ABO-incompatible grafts. All of these patients were followed until August 2011. Analyzing these patients, we focused on their immunosuppressive protocols, complications, and graft survivals. RESULTS: Patient and graft survival rates were 100%. One patient experienced antibody-mediated rejection and an intractable acute cellular rejection episode, 1 patient an antibody-mediated rejection, and 6 patients had acute cellular rejection episodes. However, there were no severe complications. CONCLUSION: Although ABO-incompatible kidney transplantation is a high-risk procedure, a short-term graft survival rate of 100% may be expected due to recent significant improvements in desensitization and recipient management.


ABO Blood-Group System/immunology , Blood Group Incompatibility/immunology , Histocompatibility , Kidney Failure, Chronic/surgery , Kidney Transplantation/immunology , Adult , Cytomegalovirus Infections/drug therapy , Cytomegalovirus Infections/virology , Desensitization, Immunologic/methods , Female , Graft Rejection/immunology , Graft Rejection/prevention & control , Graft Survival , Humans , Immunosuppressive Agents/therapeutic use , Japan , Kidney Transplantation/adverse effects , Male , Middle Aged , Time Factors , Treatment Outcome
17.
Science ; 335(6070): 828-31, 2012 Feb 17.
Article En | MEDLINE | ID: mdl-22282477

The fractional quantum Hall (FQH) effect at filling factor ν = 5/2 has recently come under close scrutiny, as its ground state may possess quasi-particle excitations obeying nonabelian statistics, a property sought for topologically protected quantum operations. However, its microscopic origin remains unknown, and candidate model wave functions include those with undesirable abelian statistics. We report direct measurements of the electron spin polarization of the ν = 5/2 FQH state using resistively detected nuclear magnetic resonance. We find the system to be fully polarized, which unambiguously rules out the most likely abelian contender and lends strong support for the ν = 5/2 state being nonabelian. Our measurements reveal an intrinsically different nature of interaction in the first excited Landau level underlying the physics at ν = 5/2.

18.
Acta Crystallogr B ; 66(Pt 6): 594-602, 2010 Dec.
Article En | MEDLINE | ID: mdl-21099022

Single-crystal, synchrotron powder X-ray diffraction and neutron powder diffraction studies of the novel pyrochlore-type compound with the structural formula K(0.88)(OH)(0.54)H(1.66)(H(2)O)(1.04)Nb(2)O(6) suggests that the water molecules are located in 32e sites, and the hydroxide ions and potassium ions are located in 16d sites with a significant amount of 'free' protons in 96g sites. The total weight loss at temperatures up to 773 K is only about 8%, suggesting the oxygen escape from 48f sites can be excluded and 'free' protons must be preserved in the structure. The bulk conductivity in ambient air reaches 10(-2) S cm(-1) at 623 K. Owing to the extended stability range and resistance to water solubility, the compound can be considered as a candidate for intermediate temperature solid-oxide fuel-cell applications.

19.
Phys Rev Lett ; 105(12): 126802, 2010 Sep 17.
Article En | MEDLINE | ID: mdl-20867665

Spin relaxation of two-dimensional electrons in a GaAs/AlGaAs quantum well was studied by time-resolved Kerr rotation measurements using a two-color pump and probe technique. In quantum Hall ferromagnets, the spin-wave relaxation is strongly influenced by the photogenerated Skyrmion and anti-Skyrmion pairs. By tuning the pump and probe lights to the lowest optical transition, an intrinsic filling factor dependence of spin relaxation is obtained without photogeneration of Skyrmions. The relaxation time of the spin wave presents a sharp peak at odd filling factors, accompanied by dips on both sides of it. The peculiar filling factor dependence of the spin-wave relaxation around quantum Hall ferromagnets can be explained by the interaction between the spin wave and Skyrmion. Observation of a similar feature around ν=1, 3, and 5 may suggest the existence of Skyrmions around higher odd filling factors.

20.
Phys Rev Lett ; 104(5): 056802, 2010 Feb 05.
Article En | MEDLINE | ID: mdl-20366783

We investigate the quasiparticle excitation of the bilayer quantum Hall (QH) system at a total filling factor nu{T}=1 in the limit of negligible interlayer tunneling under a tilted magnetic field. We show that the intrinsic quasiparticle excitation is of purely pseudospin origin and solely governed by the inter- and intralayer electron interactions. A model based on exciton formation successfully explains the quantitative behavior of the quasiparticle excitation gap, demonstrating the existence of a link between the excitonic QH state and the composite fermion liquid. Our results provide a new insight into the nature of the phase transition between the two states.

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