你 的鉛筆
會 超導嗎？
林秀豪
清華大學物理系
大綱
• 什麼是凝態物理？
• 你了解自己的鉛筆嗎？
• 你了解電子的自旋嗎？
• 你了解奈米傳輸嗎？
• 結語
什麼是 凝態物理？
arly seen on both experimental and
oretical curves. For the regions with only
From Wikipedia I
while the Hall coefficient reverses its sig
reflecting the fact that RH is proportional
Condensed matter physics is the field of physics that deals
with the macroscopic physical properties of matter. In particular,
it is concerned with the "condensed" phases that appear
whenever the number of constituents in a system is extremely
large and the interactions between the constituents are strong.
The most familiar examples of condensed phases are solids and
liquids, which arise from the bonding and electromagnetic force
between atoms. More exotic condensed phases include the
superfluid and the Bose-Einstein condensate found in certain
atomic systems at very low temperatures, the superconducting
phase exhibited by conduction electrons in certain materials,
and the ferromagnetic and antiferromagnetic phases of spins on
atomic lattices.
4
arly seen on both experimental and
oretical curves. For the regions with only
From Wikipedia II
while the Hall coefficient reverses its sig
reflecting the fact that RH is proportional
Condensed matter physics is by far the largest field of
contemporary physics.A lot of progress has also been made in
theoretical condensed matter physics. By one estimate, one
third of all American physicists identify themselves as
condensed matter physicists.
Historically, condensed matter physics grew out of solid-state
physics, which is now considered one of its main subfields. The
term "condensed matter physics" was apparently coined by
Philip Anderson when he renamed his research group previously "solid-state theory" - in 1967. In 1978, the Division of
Solid State Physics at the American Physical Society was
renamed as the Division of Condensed Matter Physics.
Condensed matter physics has a large overlap with chemistry,
materials science, nanotechnology and engineering.
5
arly seen on both experimental and
oretical curves. For the regions with only
From Wikipedia III
while the Hall coefficient reverses its sig
reflecting the fact that RH is proportional t
One of the reasons for calling the field "condensed matter
physics" is that many of the concepts and techniques developed
for studying solids actually apply to fluid systems. For instance,
the conduction electrons in an electrical conductor form a type of
quantum fluid with essentially the same properties as fluids
made up of atoms. In fact, the phenomenon of superconductivity,
in which the electrons condense into a new fluid phase in which
they can flow without dissipation, is very closely analogous to
the superfluid phase found in helium 3 at low temperatures.
6
Many Means Beauty?
格物致知？
化約主義的科學家？
數大便是美？
7
Why Many?
8
What is Temperature?
請問，一顆在磁場中繞圈圈的電子，
它的溫度是多少呢？
9
Temperature
因為無知，所以才有溫度的概念。
溫度是能量不
守恆的產物
10
Some Quantum Flavor
• 量子物理讓我們對
一顆粒子也可以很
無知。
• 所以，數不必大，
也可以很美。
• 因為無知，所以處
處驚奇。
11
Quantum Interferences
量子分身術
12
你了解 自己的鉛筆嗎？
Why pencil can write?
為什麼我們可以用
鉛筆寫字呢？
又為什麼可以用橡
皮擦來擦掉呢？
14
Shinny Graphite?
黑金黑金的…
為什麼呢？早點
想到可能可以拿
Nobel Prize 喔！
15
Cheap Nanotechnology
我黏，我撕，我黏
我做實驗！
16
r graphene), to
, and to study
Despite being
emain of high
nic transport is
distances. No
ss is known to
ontinuous under
LG, we demonct transistor in
annel can be
n and hole gases
.
e prepared by
ated peeling) of
ented pyrolytic
h was found to
d us to prepare
e. Thicker films
6m across and
Figure 1 shows
ilms, including
also (15)^. To
erties, we prorminal Hall bar
an oxidized Si
ge Vg could be
more than 60
e focus on the
thinnest (FLG)
st one, two, or
l FLG devices
ical electronic
2D semimetal,
e complex (2D
transforms the shallow-overlap semimetal
into either completely electron or completely
hole conductor through a mixed state where
both electrons and holes are present (Fig. 2).
The three regions of electric field doping are
clearly seen on both experimental and
theoretical curves. For the regions with only
way, as 1/ne. The resistivity also follows the
standard dependence Dj1 0 G 0 ne6 (where
6 is carrier mobility). In the mixed state, G
changes little with Vg, indicating the substitution of one type of carrier with another,
while the Hall coefficient reverses its sign,
reflecting the fact that RH is proportional to
Not-so-cheap Part...
Fig. 1. Graphene films. (A) Photograph (in normal white light) of a relatively large multilayer
graphene flake with thickness È3 nm on top of an oxidized Si wafer. (B) Atomic force microscope
(AFM) image of 2 6m by 2 6m area of this flake near its edge. Colors: dark brown, SiO2 surface;
orange, 3 nm height above the SiO2 surface. (C) AFM image of single-layer graphene. Colors: dark
brown, SiO2 surface; brown-red (central area), 0.8 nm height; yellow-brown (bottom left), 1.2 nm;
orange (top left), 2.5 nm. Notice the folded part of the film near the bottom, which exhibits a
differential height of È0.4 nm. For details of AFM imaging of single-layer graphene, see (15). (D)
Scanning electron microscope image of one of our experimental devices prepared from FLG. (E)
Schematic view of the device in (D).
這就不太便宜了…
17
Relativity in Pencil Flakes?
在鉛筆屑堆，找到相對論。
18
Birth of Carbon Era?
19
Magnetic Carbon Foam
20
-6
Magnetic Moment m (10 emu)
4
3
(a)
%6
猜猜看…
t
1
%6
0
0:5
0:5
t
s
哪個是打爛前？
哪個是打爛後？
-1
-2
-3
-5
0
5
Magnetic Field (kOe)
10
(b)
Esquinazi
et al., PRL 91, 227101 (2003)
-6
ent ms (10 emu)
Magnetic
t
2
-10
-6
Strange Magnet?
the area of to
largest
magn
that the-2 magnetic signal is not correlated
the
t
No. 4). We note that meas
samples indicate that
phy in -3any irradiation stage. For comparison,
in #Fd
ties of the measured surf
show a -10topography
line moment
scans
magnetic
fromoM
-5
0 and 5 magnetic
10
rough estimate only [17
Field (kOe)
normal to theMagnetic
magnetic
domain structure
at stag
moment measured
by M
The MFM(b)pictures shown in Fig. 3 were obtain
distance of 50 nm between tip and surface. Bec
1
the small
coercive field of the magnetic surface
influence of the magnetic tip we have observed
magnetic domain distribution depends on the d
0.1
between
tip and surface. Theoretically, the pha
1
10by MFM
100
1000
!" measured
should
be proportional
Irradiated Total Charge C (µC)
magnetic force gradient, which should depend
FIG. 2. (a) Magnetic moment (in units of 10 emu) measured at T & 300
K as a function
of thetip
magnetic
field asand
in
distance
between
the
apex
sample
surfa
FIG.
3. Top: Phase
gradie
Fig. 1(b), %5
for sample 2 before (!) and after (") proton
perature from MFM at thre
magnetic
moment as between
a
"hirradiation.
' ## (b) ,Measured
beingsaturation
# the
distance
the tip
a
ing to the irradiation
stages
function of the total irradiated charge C for sample 1 (")
at the bottom left of the fig
for sample 2 (!).position
The dashed lineof
is the
function
m &
theandeffective
the
magnetic
inof
phase moment
gradient line scans
0:22)10 emu=!C *C .
at stage No. 2.
Measuring
!" as a function of h we estimate # !
227201-3
100# nm. With this value we estimate the maximu
netic moment observed by the tip m ! 3 $ 10%15
the area of largest magnetic moment (stages No
No. 4). We note that measurements on different m
samples indicate that # depends on the magnetic
ties of the measured surface and therefore the ca
magnetic moment from MFM data should be tak
rough estimate only [17]. Assuming that the m
moment measured by MFM corresponds to a re
Saturation Moment ms (10 emu)
Ct , our results indicate a relation of the type ms / Ct ;
see Fig. 2(b). It is interesting to note that after the No. 4
irradiation the magnetic moment of sample 1 decreases
[see Fig. 1(a)] indicating that there might be a competition
between the produced disorder and the implanted charge,
which determines the total magnetic ordering.
Hysteresis loops were measured at 5, 300, and 380 K. In
this temperature range there is no significant change of
the ferromagnetic loops with temperature. This result is
1
21
Zigzag Domain Wall
在石墨平原上的奈米懸崖
22
Edge State
活在奈米懸崖邊的電子們
23
Have Some Calcium...
y used to write or draw
ept indefinitely or erased
perty that encourages
different kind has led Weller
scovery of superconducting
operties, as reported on page
ipulated the material to
r with a critical temperature
mply adding the common
the less-common element
onding Tc of 6.5 K). In
assium and sodium as
erature did not exceed 1 K,
techniques that yielded an
The new results1 have been
d quickly4 and theoretical
l of explanations (see, for
2,000
Graphite (002)
C6Yb
(004)
C6Yb
(002)
0
10
C6Yb
(004)
Graphite (004)
20
Graphite (004)
FC
–4
Graphite (006)
–6
C6Yb
(006)
Yb2O3
(111)
–8
30
–10
0
40
ZFC
50
θ (°)
2θ
60
C6Yb
70
C6Yb
(008)
80
4
6
8 10 12
Figure 1 X-ray diffraction pattern of highly
oriented pyrolytic
Temperature
(K) graphite
90
2
intercalated with ytterbium. These data were taken using a Bragg–Brentano
geometry with Cu Kα radiation. As a consequence of this, only the (00l) peaks may
be sampled. Top: The
modelled10 using a stage-1 graphite
c derived structure
d
intercalation compounds with a c∗ axis sandwich depth (C–Yb–C) of 4.57 Å.
100
Measurements for C6 Ca have a sandwich depth (C–Ca–C) of 4.51± 0.02 Å, in
reasonable agreement with the study in ref. 11, which determines a value of
4.524 Å. In the structure of80
C6 Yb the graphite sheets have an A–A registration
whereas the ytterbium have an α–β registration. Calculations based on peak
intensities reveal that 13% of the sample volume fraction is made up of C6 Yb. From
our analysis we find that the
60contamination of Yb2 O3 is less than 1% after
surface abrasion.
補充點鈣質，
有益身心健康！
17
40
40
0.00
–2
–12
60
0.02
Moment (e.m.u. cm–3)
1,000
stivity (µΩ cm)
(002)
2
80
b
2
Moment (e.m.u. cm–3)
Intensity (counts)
Ca
0
100
0
500
Ma
ZFC
c
Ca
1,500
Ca
–8
Ma
a
Mb
–6
–12
20
–0.02
0
–0.04 0FC 20
–0.06
Figure 2 The te
–0.08
resistivity for C
C6 Ca (b). These
–0.10
ZFfi
c∗ axis. These
measurement an
–0.12
There is0a clear 5
d, The supercon
results of the ma
type-II supercon
whereas there is
2.5
is approxim
2.0 critica
upper
parameter of
2 across the
1.5 theo
Landau
electron mas
of1.0
the24ratio
Field (kOe)
ETTERS
–4
–10
Resistivity (µΩ cm)
Figure 1 Crystal structure
of C6Ca. The unit cell is
rhombohedral with the calcium
atoms in green and graphene
sheet in red.
noscience Delft, Delft University
, 2628 CJ Delft, The Netherlands.
mail: t.m.klapwijk@tnw.tudelft.nl
R 2005 | www.nature.com/naturephysics
Mb
Ca
K
ays a fascinating playground
s to explain the world in
orld is not a static entity. It
e ideas and materials that
lenges. Most people would
ent in architecture or on the
nsed-matter physics has a
th advances in materials and
are sometimes part of the
etimes more hidden.
y, which has brought us
o brought us the quantum
matter has become a very
perimental
2,000 physics to create
conditions. Where would
Graphite
ystems of two-dimensional
for semiconductor
chers go one step further
y changing the boundary
n a judicious manner
veries
in such untrodden
1,500
Moment (e.m.u. cm–
The discovery of a superconductor is always exciting, but particularly so
when the material is a common stationery item and the superconductivity is
possibly unconventional.
FC
–2
006)
0
2
4
6
8 10
Temperature (K)
12
0
5
Superconducting!!
d
100
2.5
80
2.0
吃鈣的鉛筆，
1.5
超導！
60
Field (kOe)
Resistivity (µΩ cm)
c
10
Temp
40
1.0
C6Yb
20
0.5
0
0.0
0
20
40
60
80
Temperature (K)
100
2
3
4
Temp
25
0
Moment (e.m.
Moment (e.m.
–4
–6
–0.04 FC
–0.06
C Yb
–8
–0.08
Diamagnetic
Response
6
–10
–12
–0.10
ZFC
0
2
4
6
8 10
Temperature (K)
–0.12
12
C6Ca
ZFC
0
5
10
15
20
Temperature (K)
25
漢賊不兩立 — 不喜歡磁場的超導體
bc
d
HC1 || ab
0.00
80
–0.02
2.0
FC
60
–0.04
1.5
–0.06
40
–0.08
20
–0.10
–0.12
0 0
0
12
2.5
06)
d
2.5
6Ca
C6CYb
ZFC
25
205 4010 6015 8020 100
Temperature(K)(K)
Temperature
Field (kOe)
Resistivity
(µΩ cm
cm)–3)
Moment
(e.m.u.
0.02
100
HC2 || ab
HC1 || c
HC2 || c
1.0
C6Yb
0.5
0.0
2
3
4
5
6
7
Temperature (K)
8
26
Where are the electrons?
LETTERS
Mb
Ca
Ma
Ca
2,000
Graphite (002)
C6Yb
(004)
作媒的電子雲
1,500
nts)
Graphite (004)
27
你了解 電子的自旋嗎？
Charge and Spin
電荷︰運用半導體
處理資訊
自旋︰運用磁性材料
儲存資訊
29
What is “spintronics” ?
Spintronics
=
Spin + Electronics
如何在複雜的凝態系統中，
隨心所欲地操控自旋。
30
Spin Valve
G. Prinz, Science 282, 1661 (1998)
自旋不同，物性不同。
metal
insulator
31
Spin Valve
用自旋來當開關。
32
Moving Electric Field...
複習一下電磁學…
1 ∂E
∇ × B = µ0 J + 2
c ∂t
∇
電動生磁
1
!
−µ
v
×
E
×BB==
J
+
c2 0
1
!
B =− 2
c
1 ∂E
c2 ∂t
v×E
33
Rashba Interaction
自旋–軌道
交互作用
34
Datta-Das Transistor
用電場來控制自旋
用自旋來控制電流
35
(Ga,Mn) As
半導體摻點磁性
雜質，如何？
36
Ferromagnetic Semiconductor
於是，磁性半導體
就誕生了。
37
Curie Temperature
Hso = αR (k × n̂) ·
= Ωk · S
Curie 溫度與電洞密
度1/3次方成正比。
1/3
Tc ∼ nh
38
Field Effect
) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 33345)61''-7"8,1#09):1709-,.%9#-'$)
1#1'-$#'%9#%'1$)
08+#40''".0"#0-,)
"22=)'1.%91.)D=)
+1).-7"0,)?"22)
FO"(!,IA$) D=)
"2$-) -D$1'E1.)
VG < 0
0.04
0.02
RHall (k$ )
1
1.5 K
5K
10 K
0
20 K
-1
R Hall (k$)
+1)'1"$-,)?+=)
=) -,2=) ") $208+#)
.'"7"#09)1>>19#@)
)0$)-D$1'E1.)0,)
M","7%'")1#)"2@)
) 2-?1') B+-#-,)
A$)9"$1@)*,)#+1)
0-,) 1>>19#$) 0,)
1.)#-)#+1)$7"22)
-0.5
0.00
0.0
VG > 0
0.5
B (T)
22.5 K
VG
0V
+125 V
-125 V
0V
-0.02
-0.04
-1.0
-0.5
0.0
0.5
1.0
B (mT)
Fig. 38.) V"22) '1$0$#",91) RV"22) ->) ",) 0,$%2"#1.) 8"#1) F3,(!,IA$)
>012.41>>19#)#'",$0$#-')"#)KK@<)M)"$)")>%,9#0-,) ->)#+1) 7"8,1#09)
>012.) >-') #+'11) .0>>1'1,#) 8"#1) E-2#"81$@) RV"22) 0$) B'-B-'#0-,"2) #-)
#+1)7"8,1#0C"#0-,)->)#+1)F3,(!,IA$)9+",,12@)cBB1')'08+#)0,$1#)
$+-?$) #+1) #17B1'"#%'1) .1B1,.1,91) ->) RV"22@) \1>#) 0,$1#) $+-?$)
用電場可以讓磁性消失或存在
39
Transport and Magnetism
REVIEW ARTICLE
cular,
k
agnetism
ty of
allows
ally.
omagnetism
netically
T 3/2 dependence expected for
a homogeneous ferromagnet
Magnetization (e.m.u. cm–3)
30
25
20
15
10
5
磁性與電阻有很強的
關連性，為什麼？
0
8
Resistivity (mΩ cm)
key
umerous
f
py40,41, d.c.
re45,46 and
thorough
sible
ush TC still
e include
the free
ing in
ectiveness
rom certain,
magnetism
ns,
rials
Figure 2 The temperature
dependence of the
magnetization and resistivity
of Ga0.083Mn0.917As (ref. 36).
The two curves in each are for
non-annealed (as grown) and
annealed samples, and they
reveal the striking physical
changes wrought by annealing
(increased TC and conductivity,
and conventional behaviour of
the temperature-dependent
magnetization).
35
7
As-grown
6
Two-hour anneal
5
4
3
2
0
50
100
150
Temperature (K)
Mn ion. The valence-band hole will then tend to align
40
Magnetism vs Optics
這下子，磁性和光學性質也扯在一起了
41
Carrier-Mediated Ferromagnetism
老師不在，
亂亂亂…
一位好老師，
幾個好學生。
一群好老師，
春風化雨。
42
你了解 奈米傳輸嗎？
Quantum Wire
需要量子線來連接
奈米元件
水管流量和截
面積成正比，
那量子線呢？
44
Nano MRT I
量子線的傳導與截面積
並不成正比，而有量子
化現象。
量子線的傳導像捷運系
統一般，分成淡水線、
板南線、木柵線等等。
45
Nano MRT II
每一條捷運線標誌不同
46
Nano MRT III
破壞一下，哪條捷運線斷掉了？
47
DNA Nanowire?
連 DNA 都可以拿
來當電線
• 導體 ？
• 絕緣體 ？
• 半導體 ？
• 超導體？
48
Share
Solve
Find the
the Problem
Problem
Solution
Thank You!!