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70349635750
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note
-
We have fabricated tunnel junction consisting of SrTiO3-LaAlO3 -Au trilayers and measured the tunnel currents. To obtain significant tunnel currents, the LaAlO3 layer has to be at most 4 unit cells thick, i.e., 1.6 nm. The changes in the capacitance described in the paper are expected to occur also at larger thicknesses. Even for a 1.6 nm thick barrier, the effects of the tunnel currents on the energy of the capacitances are small.
-
-
-
-
19
-
-
70349634841
-
-
note
-
For clarity, we point out that the expression "external potential" used in characterizing Eext,i does not refer to the electrochemical voltage applied to the capacitor plates by an external voltage source. The electrochemical potential is the thermodynamic conjugate variable to the total charge Q and is derived from the total energy through V (Q) =dE (Q) /dQ, i.e., from the sum of all energy terms in Eq..
-
-
-
-
20
-
-
70349650723
-
-
note
-
We use the term "homogeneous electron system" in the following, standard sense: a homogeneous electron system is an electron system with a positive background charge density n=N/V that is uniformly spread through the volume V, where N is the number of electrons in the neutral system. The positive background is supposed to be inelastic. The charged capacitor carries the additional electronic charge ±Q on each of the plates.
-
-
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21
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70349646034
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-
note
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Δ/e, which directly identifies C [Eq.] as the capacitance. Alternatively, one may define C′ =Q (V) /V and derive the relations C′-1 = C-1 + (Δ/e) /Q and C′ =C [1- (Δ/e) /V] with C-1 from Eq..
-
-
-
-
23
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-
70349642030
-
-
note
-
s ≃40 all phases have approximately equal energies (Ref.).
-
-
-
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24
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70349640103
-
-
note
-
s =100±20 (Refs.).
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70349638969
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A multiband calculation also has to include modified exchange and correlation terms, an important subtlety that we do not address in this paper.
-
A multiband calculation also has to include modified exchange and correlation terms, an important subtlety that we do not address in this paper.
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0 =-0.2760;" following the possible misprint, the correlation energy would be negative.
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0 =-0.2760;" following the possible misprint, the correlation energy would be negative.
-
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-
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51
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70349651694
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-
r =1 it is senseless to discuss a transition to negative capacitance regime as d cannot be as small as a Bohr radius.
-
r =1 it is senseless to discuss a transition to negative capacitance regime as d cannot be as small as a Bohr radius.
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s at least in a qualitative way.
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70349633914
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As discussed in the introductory paragraphs of Sec., the ground state for a symmetric capacitor is characterized by a SILC in the absence of self-charging. However, the coherence may be lost, if the symmetry is broken, for example, by a finite bias or asymmetric configurations. Here, we consider the unpolarized homogeneous electron gas on a parallel-plate capacitor in the absence of SILC as a "model system" in the expectation that it shares some general features with capacitors comprising strongly correlated electron systems in the presence of a bias.
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