FSU Physics Department Pairing instability of composite fermions in double layer quantum Hall system Huan D. Tran Quantum Hall effect Composite fermion FQHE in double layer electron system Proposal work 4/30/2019 FSU Physics Department
FSU Physics Department Quantum Hall Effect 4/30/2019 FSU Physics Department
Quantum Hall Effect (cont.) Strong B Low T IQHE: n = 1, 2, … (‘80) FQHE: n =1/3, 2/5, … (‘82) (more than 50) 4/30/2019 FSU Physics Department
Quantum Hall Effect (cont.) Störmer, RMP 71, 875 (‘99) 4/30/2019 FSU Physics Department
Quantum Hall Effect (cont.) IQHE, physics of non-interacting electron system Quantized cyclotron orbits (Landau levels) n: number of filled Landau levels 4/30/2019 FSU Physics Department
Quantum Hall Effect (cont.) B1 B2 RH B n = 2 n: number of electrons per flux quantum 4/30/2019 FSU Physics Department
Quantum Hall Effect (cont.) Disorder localized & extended states Localized & extended states plateaus & steps Laughlin, PRB 23, 5632 (‘81) 4/30/2019 FSU Physics Department
Quantum Hall Effect (cont.) FQHE observed at non-integer filling Tsui et.al., PRL 48, 1559 (‘82) Non-interacting electrons No energy gap! Electron interaction must be considered 4/30/2019 FSU Physics Department
Quantum Hall Effect (cont.) Laughlin wavefunction, theory of filling factors 1/(2p+1) Laughlin, PRL 50, 1395 (‘83) The filling factors 1/3, 1/5, 1/7, … are explained Remaining filling factors 2/5, 3/7, 4/7, … need further treatment 4/30/2019 FSU Physics Department
FSU Physics Department Composite Fermions Jain, PRL 63, 199 (‘89) Y -Y Roughly speaking, each electron captures 2m flux quanta to become a composite fermion denoted by 2mCF More rigorously, a gauge transform is needed to form composite fermions from electrons 4/30/2019 FSU Physics Department
Composite Fermions (cont.) B B* n = 2/5 n* = 2 CFs see an effective (smaller) magnetic field FQHE of electrons IQHE of 2mCFs 4/30/2019 FSU Physics Department
Composite Fermions (cont.) FQHE of electrons IQHE of 2mCFs FQHE of electrons at n=p/(2mp±1) IQHE of 2mCFs at n*=p Jain’s series p/(2mp±1) (1/3, 2/5, 3/5, 3/7, …) 4/30/2019 FSU Physics Department
Composite Fermions (cont.) n = ½ state B* = 0 B Halperin, Lee, and Read, PRB 47, 7312 (‘93) CFs behave as though there is NO field at all No QHE at this filling factor Experiments: Fermi sea, SdH oscillation,… 4/30/2019 FSU Physics Department
Composite Fermions (cont.) n = ½ state B* = 0 dr1 B0 CFs see strongly fluctuating effective magnetic field “B” Gauge field: a “B” = × a 4/30/2019 FSU Physics Department
Double-Layer Electron System (DLES) Layer index is introduced as an additional degree of freedom Inter-layer correlation leads to new physics, i.e. new FQHE states… States of system depend critically on d and tunneling Layer spacing d and tunneling t12 (DSAS) are important parameters d t12 4/30/2019 FSU Physics Department
FSU Physics Department DLES (cont.) Double-layer electron system at ntot=1 B = (hc/e) n d Each layer now has n = ½ 4/30/2019 FSU Physics Department
FSU Physics Department DLES (cont.) Double-layer composite fermion metal at ntot=1 d B* = 0 RL QHE exists at this system 4/30/2019 FSU Physics Department
FSU Physics Department DLES (cont.) a(1) & a(2) a(+) & a(-) B* = 0 dr1 dr2 a(1) a(2) In-phase gauge-field fluctuations of DLCFM at ntot=1 4/30/2019 FSU Physics Department
FSU Physics Department DLES (cont.) B* = 0 dr1 dr2 Out-of-phase fluctuation, a new feature of DLES 4/30/2019 FSU Physics Department
FSU Physics Department DLES (cont.) BCS-like pairing of CFs B* = 0 dr1 dr2 4/30/2019 FSU Physics Department
FSU Physics Department DLES (cont.) Bonesteel et. al., PRL 77, 3009 (‘97) Murphy et.al., PRL 72, 728 (‘94) Keeping only a(-) at n = 1 No tunneling, large d, small q TC and D 1/d2 Paired QH state at zero tunneling! No QHE observed at n = 1, zero tunneling, d/l0 ≥ 2 4/30/2019 FSU Physics Department
FSU Physics Department My Project The formation of composite fermion pairing in DLES, stable or unstable? Consider the CF pairing state using the Eliashberg equations with as few approx. as possible. How does a(+) affect critical temperature TC and energy gap D of the pairing state? Coupling parameter l will be carried out with contributions from full spectrum of q. 4/30/2019 FSU Physics Department
FSU Physics Department My Project (cont.) Experimental regions 4/30/2019 FSU Physics Department
FSU Physics Department My Project (cont.) The presence of both a(+) and a(-) lead to composite pairing, which may result quantum Hall effect The pairing is suppressed very strongly (more than 3 orders) when the a(+) is taken. This may give an explanation for the absence of experimental observation 4/30/2019 FSU Physics Department
Thank you for your patience! 4/30/2019 FSU Physics Department