고급고체물리 II. Phonon. in solids. in metals. in magnetic materials. in ionic crystals. in dielectric materials

Transcription

1 고급고체물리 II oo. i dymi : oo mod. oo pifi. ml pio of yl Joogo o Qizd pil i Qm i Fmio oo i olid oo oo i ml Coop pi i mgi mil oo i ioi yl Fmio? i dili mil oo lo pi i CS oy i podig mil oo

2 ymi li modl Aom piodi odig olid i li li dymi li So omig of i li modl Fil o pli qilibim popi of olid Spifi, ml pio, lig Fil o pli po popi mp dpd iiviy : ig, lio, Spodiviy, ml odiviy, miio of olid Fil o pli iio of vio yp of diio Ili ig of lig : illoi d Rm, Sig of X- y d o i dymi vibio old b oidd! - mooomi li vibio - - [ ] ; Hmoi poil gy K [ ] : diplm d F && K[ [ ] [ ] ] iodi body odiio d [ ] ; N d vlig v olio fo q. ii i fom ω K ω i K i [ ] [ ] K o K ω i ipio lio : fio 4

3 ω K i p vloiy : v ω dω gop vloiy : vg d A lo fqy gio /λ, log vlg limi ± K K d ω ν p vloiy v v gop vloiy : ω ω g d : A ig fqy gio dω ν g ωm o d ± K ω ω m 5 - diomi li vibio C I : m m, b diff pig o : diplm && K d K d G [ ] [ [ ] ] Hmoi poil gy [ ] G [ ] d && K [ ] G [ ] [ ] [ ] d vlig v olio fo q. d ii ii i fom [ ω K G ] K G i K G ω K G d [ ] i [ ω K G ] K G Solv dmi of q. K G KG o K G K G ipio lio ω ± K G KG o d m K G i i 6

4 ipio lio K G ω ± If K G KG o ω d ω & m K G K G oi mod K G d opil mod If / ω G d ω K d oi mod opil mod C II : m pig o, b diff m i i ± && v&& [ ] C[ v ] [ v ] C [ v ] C v C ± ii ii & v ω C 7 o oo mod Aoi mod All om go i m diio. Compiv v o od v. Opil mod Oppoi ff o o om lomgi diio No ll fqi popg Oly di bd vilbl. om i pimiiv ll. oi b. - opil b Fo mpl, K i o om, A ogidil oi, A v oi O ogidil opil, O v opil 8

5 Qm oy of moi yl Qm oy of moi yl K p H H,, ϕ ϕ Hmiloi fo moi oillo [ ] i p i p m, ϕ,, ϕ ϕ ϕ K m m K m ip m m ip m dfi iilio d io opo m i p m m m m : mb opo N H gy lvl of moi yl ϕ ϕ ϕ ϕ ϕ N H Q, ω ½ ii gy ½ poil gy fo im vg 9 Gl fom of poo pifi Gl fom of poo pifi iio fio il gy diy piy gy qizio of li vibio pil ; oo gy Z l i i Z ol gy fo N oml mod i N io moi yl ω ol gy fo N oml mod i N-io moi yl i i Z 5 K Z l l l Z l Z l Il gy diy of moi yl q

6 Gl fom of poo pifi Gl fom of poo pifi d ig mp ppoimio ig mp ppoimio ig mp ppoimio ig mp ppoimio!! N d d lo mp ppoimio lo mp ppoimio oi mod oib o pifi If dipio lio i ppoimly d d d d d d d v Fo oi mod 4 5 v 5 o modl fo oo piy o modl fo oo piy C H piy o volm oom C N Fom pim lo ml o ilo oom. C C N C Fom pim, Rio of mb of moi oillo i o mb of i??,?, d C N N p, Avg iio qm mb of moi oillo olzm diibio p p p S S, Avg iio qm mb of moi oillo p d d d d S S S S < fo p d d S S ; l diibio

7 o modl fo oo piy iy of i -dimio p i 4, y, z, ±, ±, { y z } p i { y z } y z y z iy i -p iv i volm; N ± zz 8 4 N ρ dn d d dn 8 d d d d K y by ppoimio : dipio lio of oi poo / N N If poo filld p o d oly 6 N W d d d d d K K K X by ppo. Al d o modl fo oo piy 9 N 5 Θ d N Θ d C d lo mp d 4 5 d d Θ d Θ K 4 4 d N 5 5 C Nv Θ d Θ O o d, ii modl i Coid N oillo of m fqy v C N i N ig << C N log-i vl d N d lo >> v ol lo C 4

8 by ppoimio v. ii ppoimio Fo oi poo, dipio lio i. Θ : by mp 4 Θ, N Fo opil poo, dipio lio i o 5 by mp by mp i m of mp bov i ll mod bgi o b id, blo i mod bgi o b foz o Θ 4, N I ml, Z i Z; ioi vl :odio lo diy i :io diy 4 F N Z F F :Fmi f 6

9 iy of S fo poo mod : mb of p i fqy g Nmb of llod vl of fo i poo fqy i b d d d d dsd ds ; o o fqy f i -p d ig v g : gop vloiy d d ds d ds d d d v ds vg d C g ds d ds d by ppo. by olid A l olid d ds Al 7 d iy of S i NCl yl ii modl fo Fo, ds? by modl fo by ii modl fo 8

10 mpl : Qizd poo mod i Cbo Nod mpl : Qizd poo mod i Cbo Nod Ho l. Si 89, 7-7 d C ypilly d C d di i li ypilly, d C lo, A d : dimioliy fo li dipig mod C Fo, 9 ml pio of yl ml pio of yl m q Ioi iio gy ; qilibim gy moi m moi m Hlmolz f gy F ; q gy S F S :opy S S S F p F p q Fo moi yl q

11 ml pio offii ml pio offii l l ig dfi li ml pio offii fo l Q ; l modl q ig l dfi l,,, dfi Güi pm ; ml pio offii ml pio offii fi Güi pm,,, fo o fo >> Θ o. o. &. ~ Q Q Θ I ml, l R fo f lo g.. l l. l io Ildig loi oibio

12 oo ig. oo bopio d miio. Rm ig. Ifd Spoopy 4. olio poo poo oplig Sig of -y, o, d lig by poo A ypil poo gy ; q ~ X-y ig ~ 4 I gl, olio of mll poo fqy if i o diffil o oly m ol d diio of ll fqi i diff bgod of diio fod gl y fom o ifyig gg odiio. ig ig ~ poo v vo ~ 5 m - mll ompd i illoi zo dimio~ 8 m -, ifomio i povidd oly bo poo q. Rf. v mb m - ~ ν ν λ po i illoi ig poo mid o bobd i oi, Rm ig poo i opil. No ig ~ - - fo ml o o m poo i p o gy d v vo, o o o ig llo di mm of dipio lio. Hov, o didvg i livly poo gy d v vo olio d o lo iiy of vilbl o bm 4

13 Sig of -y, o, d lig by poo gy momm lio poo p Sig by poo o p 4.67 gy ovio q q q omm ovio p p q G Iid bm;, p Sd bm;, p Ripol li vo ; G : poo o opio o mb g oo fqy & v mb ; g q, q oo miio oo bopio 5 oo ig Zo poo ig : li ig G gg diffio odiio O-poo ig ± : ili ig ± ± q G oo; q, q q o-poo ig ± : ili ig q q q q G oo;, q & q, q q 6

14 Rm Sig oo miio oo bopio Iid poo Iid poo q ± ± q j d poo d poo I mil i fiv id,, Q λ λ I fi-od Rm ig, 7 Wv lg >> li pm ; λ >>, q << oly q opil poo b id. Rm ig p.. ooomo. oliz Smpl Alyz 8

15 olizd lig Rm poopy Iid lig i/o polizio diio d lig v mb m - ~ ν ν λ 9 Clil oy of Rm ff A im dpd dipol mom i i --- dipol mom idd by lig li fild --- : loi polizbiliy d o, : yppolizbiliy d o If i plll o i of diomi moll, o ill g lily i oml oodi Q fo of m Q µ µ :dd m --- I o-qilibim, polizbiliy i pd by ylo i Q Q Q Q od Rm ff d od Rm ff ---4 If moll l vib i fqy, oml oodi i pd by Q Q o ---5

16 Clil oy of Rm ff 5 4 Q o ---6 Q 6 o Q Q o b Q o o [ o o ],, b Q Q ---7 Fom lil diio oy of oillig dipol, iiy of diio mid by io olid gl dωiθ dθ dφφ dω di & 4 i θ I A & ---8 Rylig po pm i fqy domi : q of Foi fom of 7 9 τ && τ A lim τ τ i d ---9 I d { δ δ [ ] [ ]} A δ Rylig So Ai-o --- Gl ppo : polizbiliy o z z A o pio of polizio i oml oodi y z y z y yy yz --- y z zy zz z If oodi,y,z i fomd o piipl p i,y,z, i digol polizio y yy y z zz z --- R b fom mi fom ym,y,z o piipl ym,y,z R R δ, --- polizio i qilibim ofigio ρσ ρσ ρσ yy zz ---4 R R R I o-qilibim, polizbiliy i pd by ylo i ρσ ρσ ρσ, Q ρσ,, Q, ---5, oogol mi R y R R R ρσ, ρσ Q y

17 olizbiliy o ig lig li fild d oml oodi y 5, polizio i σ o, Q Q o σ [ o o ] ρ ρ o b ρ,, b Q ρ ρσ σ ρ ρσ, σ σ I diomi moll Q δ ρσ, yy, Q, yy, zz, zz, i mod i Rm iv i g diibio d ill b diff fo oppoily dipld poiio Cv I. Hov, diplm li v II d III iiv Rm iv d iiv mod yp of polizbiliy i diplm I H O I XY moll iv Cv I iiv Cv II,III Cv I, iv δ ρσ Cv II,III fo ρρ,, b iv fo d b δ ρσ d iiv Cv II,III, δ ρσ 4

18 Rm iv d iiv mod Fo Ivio ymmy i i ; If iq Q I gl, Rm iiv ifd iv NCl CCl b : Ivio ymmy y i o lod om. Fo Ivio ymmy i If iq Q Rm iv imod o f li dipld fom o by ¼ of body digol. Ivio ymmy i o lod om. ZS No ivio ymmy: vio Rm iv mod 5 Rm iv d iiv mod Il ymmy oly C i dipld l ymmy C vib gi C C C O g-mod : iq Q mod : iq Q R : fo Rm iv IR : fo Ifd iv 6

19 Rl fom Rm pim Appliio : dmiio, mliompo qliiv lyi, d qiiv lyi R, 5, Ifd poopy p ilo ifom I opil pim I I I I R Iid iiy : I Rflio iiy : I R miio i iiy i : I Abopio iiy : I A A. Rdiio o ifd-viibl-lviol 4 m - λ -5 µm. io 4. m pli 8. mpl 7,9.. oo do. o-i mp. / A ov 8

20 Opil popy of mil Compl dili fio of mil i Compl fiv id i Rfliviy R Rflio offii R ~~, ~ ~ --- R, R R oφ iφ miio i i R iφ R R oφ I I Abopio offii K --- φ : p if of lig v ---4 ipio lio φ fo follo fom gl Km-Koig lio l R l R d φ K Compio mod of dili o fom piml l, m R ll φ by q. 5 ll, by q. 4 omp, by q. Km-Koig lio d, d oo mod i m fliviy R ll φ ll, omp, 4

21 Opil popy by poo Opil popy by poo [ ] W lig li fild i pplid o diomi yl --- ; ffiv g [ ] [ ] --- i q i Coid fo vibio of li by lig li fild iplm of /- io i dy pd by i i, Fo ifii vlg limi q,, [ ] [ ] ,4 iplm of /- io i l f / i Opil popy by poo Opil popy by poo [ ] [ ], ---7 iplm of /- io v fqy i Ioi polizio i p i volm : mb of moll ---8 li diplm dili o v fqy i li diplm, dili o : loi polizio ---9 [ ] [ ] µ µ, --- Rliv dili o [ ] µ --- Rliv dili o µ fo limi Rliv dili o --- 4

22 Opil popy by poo Rliv dili o ogidil fqy --- l fo l l Opil popy of mil i : opil id of fio : iio offii Rfliviy of mil R ol flio R fo < < l 4 olio poo poo oplig q ipio lio fo poo i vm, i mil olio : poo poo opld mod q q Rf. ili lio by poo 44

23 Rm & Ifd p. 45 R, 56,