Inte

rsub

band

Inte

rsub

band

Res

pons

e:R

espo

nse:

Line

shap

eLi

nesh

ape ,

Cou

lom

b R

enor

mal

izat

ion,

, C

oulo

mb

Ren

orm

aliz

atio

n,

and

and

Mic

roca

vity

Mic

roca

vity

Effe

cts

Effe

cts

F. T

. Vas

koF.

T. V

asko

Inst

. of S

emic

ondu

ctor

Phy

sics

In

st. o

f Sem

icon

duct

or P

hysi

cs

Kie

v,K

iev,

Ukr

aine

Ukr

aine

In c

olla

bora

tion

with

:A.

V. K

orov

inan

dO

.E. R

aich

ev(In

st. S

emic

ond.

Phy

s.,U

krai

ne)

A.H

erna

ndez

-Cab

rera

and

P. A

ceitu

no(U

niv.

La

Lagu

na, S

pain

)

Mot

ivat

ion:

Mid

-IR

–TH

z spe

ctra

l reg

ion

(sol

id st

ate

devi

ces f

or g

ener

atio

n,de

tect

ion,

and

mod

ulat

ion)

.Tw

o (m

ulti)

-leve

l phy

sics

(coh

eren

ce, e

.g. m

acro

-qbi

t for

med

~ 10

6el

ectr

ons)

.

•QW

: lev

els,

diso

rder

, e-e

inte

ract

ion,

sp

in-fl

ip, a

nd m

icro

cavi

ty•E

-E re

norm

aliz

atio

n: d

epol

ariz

atio

n an

d ex

chan

ge•

Line

shap

e: h

omog

eneo

us a

nd

•in

hom

ogen

eous

broa

deni

ng

•Spi

n-fli

p tr

ansi

tions

•Sh

ort-r

ange

scat

teri

ng: b

eyon

d th

eBo

rn

appr

oxim

atio

n•M

icro

cavi

tyef

fect

Dis

orde

rQ

W le

vels

IR P

umpin

g

E

dd

GaA

sor

InA

s

AlG

aAs

orIn

GaA

s

ε 1

δd

ε

d

ε 2

l c

δd

Inho

mog

eneo

usB

road

enin

g:

n+p2 /2

mD

ispe

rsio

n la

w:

δεn=

ε n(2

δd/d

)in

-pla

ne m

otio

n

EE-in

tera

ctio

nM

icro

cavi

tyef

fect

MQ

Ws

Met

als

ε 2

dM

QW

sε 1

Mom

entu

m tr

ansf

er:

( ∆q,

~d

-1)

ε 2D

iele

ctri

c w

aveg

uide

( ε1>

ε 2 )

Spin

spl

ittin

g

E

pσ=-1

σ=+1

Vs a

ppea

rs d

ue to

:Tr

ansv

erse

fiel

d H

eter

ojun

ctio

n po

tent

ial

Bul

k as

ymm

etry

Uns

cree

ned

inho

mog

enei

ties

Diff

eren

t ran

dom

pot

entia

ls +

the

sing

le P

oiss

on e

quat

ion

Non

-scr

eene

d po

tent

ial

Scre

ened

pot

enti

als:

Cur

rent

den

sity

:

Wig

nere

q. fo

r

pola

rizat

ion:

Ener

gy s

plitt

ing

Pertu

rbat

rion

Indu

ced

dens

ity

Excange

Basic Equations

The

2D-li

mit:

qd<<

1

a Bis

the

Borh

radi

us

Cou

lom

b m

atrix

elem

ent:

Kin.

eq.

for p

olar

izat

ion

(inte

gral

eqs

.):

The

loca

l app

roxi

mat

ion

(

, a

lgeb

r. eq

s.):

∞→

cl

,),

()

/2()

('

2'

∑=

px

px

ssss

fL

nδ

δ,)

,(

)/2(

)(

'2

'∑

=p

xp

vx

iss

ssf

Lδ

δTh

e hy

drod

ynam

ics

chai

n fo

r:

1-2

Tran

sitio

ns:

2112

nn

nδ

δδ

±=

±

The

rela

tive

abso

rptio

n:

The

lines

hape

trans

form

atio

n:

Lore

ntzi

an--

Gau

ssia

n

dd

s/

~21

δε

γ∝

JETP

93,1

270

(200

1)

Phys

.Rev

. B 6

6,12

5303

(200

2)

Spin

-flip

tran

sitio

ns

ξ ω

ε F

ωm

in

ε

ωm

ax

ωm

axω

ωm

inp Sing

le p

arti

cle

abso

rpti

on a

t T=

0

Ham

ilton

ian:

Pert

urba

tion

:

In-p

lane

cur

rent

den

sity

:

Line

ariz

ed k

inet

ic E

q.:

(inte

gral

equ

ntio

n)

Dis

trib

utio

n fu

ncti

on:

VQ

is th

e C

oulo

mb

mat

rix e

lem

ent

2D a

ppro

xim

atio

n:

2 x

2 m

atri

x eq

.:

)sin

,(cos

φφ

φ=

nMomentum relaxation rate

JETP

96,1

02 (2

003)

J. P

hys.

D 3

6,11

66(2

003)

Line

shap

e of

abs

orpt

ion

at T

=0,

InG

aAs

stru

ctur

e:

Leve

l spl

ittin

g

Ener

gy o

f tr

ansi

tions

The

rela

tive

abso

rptio

n:

Eff

ect o

f exc

hang

e:

“spr

ead”

of l

ine,

wea

k sh

ift

Intr

subb

and

Tran

siti

ons

in B

iase

d SL

Cur

rent

Intr

subb

and

tran

sitio

ns

In th

e B

orn

appr

oxim

atio

n

abso

rptio

n =0

Iden

tical

QW

s,Eq

uipo

pula

ted

leve

ls

?B

ut th

ere

is a

bsor

ptio

n/ga

in fo

r unb

iase

d SL

, w

ith cos

-dis

pers

ion

law

??

Abs

orpt

ion

Stim

ulat

ed

emis

sion

Spec

tral

func

tions

Ain

, Af

Dis

trib

utio

n fu

nctio

ns

f in, f

f

Bey

ond

the

Bor

n ap

prox

imat

ion:

α ∆ε∝

Ain

xA

f x∆f

αG

ain

∆ε

Abs

orpt

ion

Hig

h-fr

eque

ncy

curr

ent

& C

ompl

ex c

ondu

ctiv

ity

An

exac

t spe

ctra

l den

sity

func

tion:

Pert

urba

tion:

Line

ariz

ed K

inet

ic E

q.:

Abs

orpt

ion:

α ω∝

Reσ ω,

Results:

Phys

.Rev

. B 6

9,20

5309

(200

4)

The

aver

aged

spe

ctra

l de

nsity

func

tion:

Ave

ragi

ng o

ver r

ando

m

pote

ntia

ls in

r-th

QW

s:

Exci

toni

cm

icro

cavi

ty (a)S

chem

atic

s of

ban

d di

agra

m o

f stru

ctur

e an

d fie

ld d

istri

butio

n; (b

)Sch

emat

ics

of

stru

ctur

e; (c

)A c

oupl

ed o

scilla

tors

; (d)

Ener

gy o

f pe

aks

as a

func

tion

of d

etun

ing

betw

een

exci

tons

and

cavi

tyH

ayge

ns, 1

665

Mid

-IR

mic

roca

vity

(in

ters

ubba

ndpo

lari

ton)

Ref

lect

ance

of t

he s

ampl

e as

obt

aine

d at

diff

eren

t in

cide

nce

angl

es. I

n th

e in

set:

a co

mpa

rison

be

twee

n th

e ex

perim

enta

l and

cal

cula

ted

spec

trum

at

the

reso

nanc

e an

gle

of 6

0.05

°.

?

(a)T

rans

mitt

ance

of a

3.9

µm

thic

k la

yer o

f AlA

s em

bedd

ed in

GaA

sat

an

angl

e of

inci

denc

e of

60°

; th

e ar

row

indi

cate

s th

e en

ergy

of t

he c

hose

n in

ters

ubba

ndtra

nsiti

on (1

43 m

eV).

(b)S

chem

atic

vie

w o

f the

pris

m-s

hape

d m

icro

-re

sona

to;;

thic

knes

s va

lues

are

giv

en in

nm

. (D

. Din

i, et

al.

Phys

. Rev

. Let

t. 90

, 116

401,

200

3) .

Res

pons

e (L

oren

tzos

cilla

tors

):

?? V

irtua

l tra

nsiti

ons

to a

noth

er le

vels

??

to c

ontin

uum

??

cont

inuu

m

Ref

lect

ance

of t

he m

icro

cavi

tysa

mpl

e fo

r diff

eren

t ang

les

of in

cide

nce

in T

M

pola

rizat

ion.

das

hed

lines

are

just

a g

uide

to th

e ey

e. In

the

left

inse

t: th

e ex

p.

poin

ts c

orre

spon

ding

to th

e en

ergy

pos

ition

of t

he d

ips

are

repo

rted

and

the

solid

line

s ar

e fit

ted

with

a s

tand

ard

dipo

le o

scilla

tor d

ispe

rsio

n. T

he ri

ght i

nset

: a

spec

trum

reco

rded

und

er T

E po

lariz

atio

n.

12ε i

ε i

Kub

o fo

rmul

a +

sing

le p

artic

le a

ppro

xim

atio

n:f-m

ass

fule

(

,

)co

nst

=∆

→0

ωε0

=∆

∞→

ωε

nm nm

nm

Con

clus

ions

:C

oncl

usio

ns:

I. U

nscr

eene

d in

hom

ogen

eiti

esin

mul

ti-l

evel

sys

tem

due

to

the

si

ngle

Poi

sson

equ

atio

n.

II. E

E-re

norm

aliz

atio

n: d

epol

ariz

atio

n (s

elf-

cons

iste

nt f

ield

) +

non-

loca

l exc

hang

e

III.

Int

erpl

ay b

etw

een

EE-r

enor

mal

izat

ion

and

inho

mog

eneo

us

br

oade

ning

(fo

r no

n-lo

cal

resp

onse

)

IV. E

xcha

nge

effe

ct o

n sp

in-f

lip t

rans

itio

ns

V. G

ain

wit

hout

glo

bal i

nver

sion

in a

bia

sed

SL

VI.

Mic

roca

vity

pola

rito

nsp

litti

ng o

f in

ters

ubba

ndtr

ansi

tion

s

Q.:

Is

inte

rsub

band

exci

ton

poss

ible

?

Dou

blin

g of

inte

rsub

band

abs

orpt

ion

due

to n

on-lo

cal e

xcan

geD

QW

s

Abs

orpt

ion:

ω

BSL

DQ

Ws:

Phys

. Rev

. B 6

0,77

76 (1

999)

BSL

:Ph

ys. R

ev. B

66,

0753

06 (2

002)

New

inte

rsub

band

ex

cita

tion

(??)

Intr

eban

dex

cito

n

ε F

Inte

rsu

bban

dex

cito

n??