Ballistic transportBallistic transport under Quantum Hall effect under Quantum Hall effect

conditionsconditions

S.Nazin, V.Shikin, ISSP S.Nazin, V.Shikin, ISSP RAS RAS

OutlineOutline

1. 1. 1-D ballistic conductance definition1-D ballistic conductance definition 2.2. Hall-effect, Quantum Hall-effect (QHE) Hall-effect, Quantum Hall-effect (QHE)

definitionsdefinitions 3. Edge (ballistic) scenario for QHE 3. Edge (ballistic) scenario for QHE

realization (Halperin, 1982; Buttiker, 1986)realization (Halperin, 1982; Buttiker, 1986) 4. Technical service for Halperin-Buttiker 4. Technical service for Halperin-Buttiker

scenario .scenario . 5. Resume.5. Resume.

1-D channel ballistic coductance.1-D channel ballistic coductance.

kF

F

kF-

E

Narrow 1-D channel definitionNarrow 1-D channel definition

Conductance G(V)Conductance G(V)

2D Hall-bar setup2D Hall-bar setup

Shub-de-Haas oscillationsShub-de-Haas oscillations and the Hall resistance and the Hall resistance for 1-D ballistic channelfor 1-D ballistic channel. .

Conventional skipping states in magnetic fieldConventional skipping states in magnetic field

DataData:: Phys.Rev B 38 , 3625 Phys.Rev B 38 , 3625

B.I.Shklovskii et al., Phys. Rev. B46 (1992) p.4026

1-D channel electrostatics1-D channel electrostatics

The corresponding density profile n(x) and The corresponding density profile n(x) and the $x_l$ - point positions definitionthe $x_l$ - point positions definition

H=1.02………………….H=1.05H=1.02………………….H=1.05

Resume:Resume:

1. 1. Self consistent description of 1-D Self consistent description of 1-D channel ballistic conductance under channel ballistic conductance under QHE conditions is presented .QHE conditions is presented .

2. Benefice to B.Shklovski idea2. Benefice to B.Shklovski idea2. In general the activity around MES 2. In general the activity around MES

(magnetic edge states) is not so (magnetic edge states) is not so routine.routine.

External potentialExternal potential, , the profile n(x) of electron the profile n(x) of electron densitydensity, , position of static skin-position of static skin- layer and its relative layer and its relative

scalescale

QHE without edge statesQHE without edge states

H =0.6H =0.6

Saddle point influenceSaddle point influence