Introduction Hybridization of the ground states Hybridization with an excited state Summary Molecular states in a one–electron double quantum dot Andreas K. Hüttel LS Prof. J. P . Kotthaus, Center for NanoScience, and SFB 631 EP2DS-16, Albuquerque, New Mexico, USA July 14, 2005
Introduction Hybridization of the ground states Hybridization with an excited state Summary The material system – lateral quantum dots • GaAs/AlGaAs heterostructure F E -E 2DEG C • two-dimensional electron gas • SEM lithography 0 • split–gate technique AlGaAs GaAs AlGaAs:Si AlGaAs GaAs 10nm 10nm 60nm 20nm 20nm z 2DEG e − mean free path l ≃ 5 µ m, 2DES depth z ≃ 120 nm, Fermi wavelength λ F ≃ 60 nm, e − mobility µ ≃ 75 m2 e − sheet density n ≃ 1 . 8 · 10 15 1 m2 , Vs
Introduction Hybridization of the ground states Hybridization with an excited state Summary Deforming a single quantum dot gC gC gL gL QD gR gR D D QPC QPC gX gX S S • triangular gate geometry • U gC , U gX more negative (M. Ciorga et al. , PRB 61 , R16315) • U gL , U gR less negative • single quantum dot − → double well potential • N = 1 electrons
Introduction Hybridization of the ground states Hybridization with an excited state Summary Measured stability diagram Side gates used to tune potentials! U I DQD gR (V) -0.45 g C µ D g L g R µ L 1 µ R -0.5 0.1 QPC g X 0.01 µ S 0.001 (nA) U (V) -0.5 -0.4 gL � - �� 0 � >>0 � - � D � S � D � S � + � + cond-mat/0501012, to appear in PRB
Introduction Hybridization of the ground states Hybridization with an excited state Summary Measured stability diagram Side gates used to tune potentials! U U I DQD d I QPC gR gR 0/2 0/2 (V) (V) d U gL 0/1 0/1 -0.45 -0.45 1/1 1/1 g C µ D g L 0/0 0/0 g R µ L 1 0.1 µ R -0.5 1/0 -0.5 1/0 0 0.1 QPC 2/0 g X -0.1 0.01 -0.2 µ S 0.001 -0.3 (nA) (a.u.) U (V) U (V) -0.5 -0.4 -0.5 -0.4 gL gL � - �� 0 � >>0 � - � D � S � D � S � + � + cond-mat/0501012, to appear in PRB
Introduction Hybridization of the ground states Hybridization with an excited state Summary DQD: Finite U SD , weak tunnel coupling • Transport window m S µ S ≥ µ R ≥ µ L ≥ µ D m R m D • Triplepoints expand to triangles, size ↔ U SD m L • µ R � = µ L → relaxation required U gR 0/1 1/1 TP2 TP1 � 1/0 / N N � L R A.C. Johnson et al. , 0/0 cond-mat/0410679 U gL
Introduction Hybridization of the ground states Hybridization with an excited state Summary Finite U SD , strong tunnel coupling — current U (V) 10 gR ~e U SD 1 � - III � + � S 0.1 ~2t 0 0.01 � D -0.48 II 0.001 � L � R I I (nA) -0.49 U SD =�-0.75mV -0.42 -0.41 -0.4 U (V) -0.41 -0.4 U (V) gL gL curved lines ↔ molecular states ∆ = µ R − µ L q ∆ 2 + t 2 µ − − µ + = 2 0 2 cond-mat/0501012, to appear in PRB
Introduction Hybridization of the ground states Hybridization with an excited state Summary Finite U SD , strong tunnel coupling — current U (V) 10 gR ~e U SD 1 � - III � + � - � S 0.1 ~2t 0 � + 0.01 -0.48 II � D 0.001 I I (nA) -0.49 U SD =�-0.75mV -0.42 -0.41 -0.4 U (V) -0.41 -0.4 U (V) gL gL curved lines ↔ molecular states ∆ = µ R − µ L q ∆ 2 + t 2 µ − − µ + = 2 0 2 cond-mat/0501012, to appear in PRB
Introduction Hybridization of the ground states Hybridization with an excited state Summary Finite U SD , strong tunnel coupling — current U (V) 10 gR ~e U SD 1 � - III � + � S 0.1 ~2t 0 � - � + 0.01 -0.48 II � D 0.001 I I (nA) -0.49 U SD =�-0.75mV -0.42 -0.41 -0.4 U (V) -0.41 -0.4 U (V) gL gL curved lines ↔ molecular states ∆ = µ R − µ L q ∆ 2 + t 2 µ − − µ + = 2 0 2 cond-mat/0501012, to appear in PRB
Introduction Hybridization of the ground states Hybridization with an excited state Summary Finite U SD , strong tunnel coupling — current U (V) 10 gR ~e U SD 1 � - III � + � S 0.1 ~2t 0 0.01 � R -0.48 II � D � L 0.001 I I (nA) -0.49 U SD =�-0.75mV -0.42 -0.41 -0.4 U (V) -0.41 -0.4 U (V) gL gL curved lines ↔ molecular states ∆ = µ R − µ L q ∆ 2 + t 2 µ − − µ + = 2 0 2 cond-mat/0501012, to appear in PRB
Introduction Hybridization of the ground states Hybridization with an excited state Summary Finite U SD , strong tunnel coupling — current U (V) 10 gR ~e U SD 1 � - III � + � S 0.1 ~2t 0 0.01 -0.48 II � D 0.001 I I (nA) -0.49 U SD =�-0.75mV -0.42 -0.41 -0.4 U (V) -0.41 -0.4 U (V) gL gL curved lines ↔ molecular states ∆ = µ R − µ L q ∆ 2 + t 2 µ − − µ + = 2 0 2 cond-mat/0501012, to appear in PRB
Introduction Hybridization of the ground states Hybridization with an excited state Summary Finite U SD , strong tunnel coupling — current U (V) 10 gR ~e U SD 1 � - III � + � S 0.1 ~2t 0 0.01 -0.48 II � D 0.001 I Coulomb�blockade N =1 I (nA) -0.49 U SD =�-0.75mV -0.42 -0.41 -0.4 U (V) -0.41 -0.4 U (V) gL gL curved lines ↔ molecular states ∆ = µ R − µ L q ∆ 2 + t 2 µ − − µ + = 2 0 2 cond-mat/0501012, to appear in PRB
Introduction Hybridization of the ground states Hybridization with an excited state Summary Finite U SD , strong tunnel coupling — conductance U (V) 1 gR ~e U SD � - 0.1 III � + � S ~2t 0 0.01 -0.48 II � D 0.001 I Coulomb�blockade N =1 2 G (e�/h) -0.49 U SD =�-0.75mV -0.42 -0.41 -0.4 U (V) -0.41 -0.4 U (V) gL gL curved lines ↔ molecular states ∆ = µ R − µ L q ∆ 2 + t 2 µ − − µ + = 2 0 2 cond-mat/0501012, to appear in PRB
Introduction Hybridization of the ground states Hybridization with an excited state Summary Tuning the tunnel coupling 10 charging�energy E 2 tunnel�splitting�2 t 0 model�curve Energy�(meV) 1 0.1 U gC =�-1.47�V B =�0�T 0.01 -1.4 -1.5 -1.6 0 1 2 U gC (V) B (T) U gC shifts the dots apart, B ⊥ compresses the dot states model ↔ WKB approximation cond-mat/0501012, to appear in PRB
Introduction Hybridization of the ground states Hybridization with an excited state Summary Effect of B ⊥ on the level structure B =1.4T B =1T B =0.5T -0.48 U (V) -0.41 -0.4 U (V) gR gL 0.1 -0.49 0.01 -0.41 -0.4 U (V) gL G�(e²/h) 0.001 -0.42 -0.41 -0.41 -0.4 U (V) -0.4 U (V) gL • overall G decreases, tunnel coupling at ∆ = 0 decreases • tip of triangle splits, additional line ↔ excited state
Introduction Hybridization of the ground states Hybridization with an excited state Summary Finite U SD , B ⊥ = 1 . 4 T: second level anticrossing 0.01 � - G ~ � � + � S -0.48 (e²/h) III 0.001 � � D I* U (V) � L � R gR I II B � = 1.4T U SD = -0.75mV -0.49 -0.41 -0.4 U (V) -0.41 -0.4 U (V) gL gL • ground state – ground state coupling very small 2 t 0 ≃ 0 . 06 meV • finite asymmetry ∆ − → excited state of left dot couples to ground state of right dot 2 t ∗ 0 ≃ 0 . 2 meV cond-mat/0507101
Introduction Hybridization of the ground states Hybridization with an excited state Summary Finite U SD , B ⊥ = 1 . 4 T: second level anticrossing 0.01 G ~ � � + � S -0.48 (e²/h) III � R 0.001 � � D I* U (V) � L gR I II B � = 1.4T U SD = -0.75mV -0.49 -0.41 -0.4 U (V) -0.41 -0.4 U (V) gL gL • ground state – ground state coupling very small 2 t 0 ≃ 0 . 06 meV • finite asymmetry ∆ − → excited state of left dot couples to ground state of right dot 2 t ∗ 0 ≃ 0 . 2 meV cond-mat/0507101
Introduction Hybridization of the ground states Hybridization with an excited state Summary Finite U SD , B ⊥ = 1 . 4 T: second level anticrossing 0.01 G ~ � � + � S -0.48 (e²/h) III � R 0.001 � D I* � L U (V) gR I II B � = 1.4T U SD = -0.75mV -0.49 -0.41 -0.4 U (V) -0.41 -0.4 U (V) gL gL • ground state – ground state coupling very small 2 t 0 ≃ 0 . 06 meV • finite asymmetry ∆ − → excited state of left dot couples to ground state of right dot 2 t ∗ 0 ≃ 0 . 2 meV cond-mat/0507101
Introduction Hybridization of the ground states Hybridization with an excited state Summary Finite U SD , B ⊥ = 1 . 4 T: second level anticrossing 0.01 G ~ � � S -0.48 (e²/h) � + III � R 0.001 � D I* U (V) � L gR I II B � = 1.4T U SD = -0.75mV -0.49 -0.41 -0.4 U (V) -0.41 -0.4 U (V) gL gL • ground state – ground state coupling very small 2 t 0 ≃ 0 . 06 meV • finite asymmetry ∆ − → excited state of left dot couples to ground state of right dot 2 t ∗ 0 ≃ 0 . 2 meV cond-mat/0507101
Introduction Hybridization of the ground states Hybridization with an excited state Summary Finite U SD , B ⊥ = 1 . 4 T: second level anticrossing 0.01 G ~ � � S -0.48 (e²/h) � + III � R 0.001 � D I* U (V) � L gR I II B � = 1.4T U SD = -0.75mV -0.49 -0.41 -0.4 U (V) -0.41 -0.4 U (V) gL gL • ground state – ground state coupling very small 2 t 0 ≃ 0 . 06 meV • finite asymmetry ∆ − → excited state of left dot couples to ground state of right dot 2 t ∗ 0 ≃ 0 . 2 meV cond-mat/0507101
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