Sistem Fermi Ideal
Termodinamika dan Magnetisme Gas Elektron

Prof. Suminar Pratapa

Departemen Fisika, Institut Teknologi Sepuluh Nopember, Surabaya

Dari okupasi Fermi–Dirac menuju kalor jenis elektronik linear, lalu ke respons magnetik — paramagnetisme Pauli dan diamagnetisme Landau — pada gas elektron degenerat.

Derivation

Occupation & Emission

current T/T_F references emitted (E>ε_vac)

Temperature T/T_F0.10

Work function φ/ε_F0.50

μ/ε_F

1.000

ε_vac/ε_F

1.50

tail fraction

0.0%

Derivation

Thermodynamic Functions

exact (Fermi integrals) Sommerfeld low-T classical limit

Marker T/T_F0.30

μ/ε_F

—

C_V/Nk

—

U/Nε_F

—

Derivation

Spin Sub-bands

↑ moment ∥ B ↓ moment ∦ B

Field μ_B B / ε_F0.15

Temperature T/T_F0.05

M/Nμ_B

—

χ_P/χ_P(0)

—

(N↑−N↓)/N

—

Derivation

Landau Levels & dHvA

Landau levels ε_F

Field ℏω_c / ε_F0.10

levels ≤ ε_F

—

χ_L/χ_P

−0.33

The free-electron gas is weakly paramagnetic: spin (Pauli) and orbital (Landau) contributions partially cancel, leaving a net response set entirely by the density of states at the Fermi level.

Relative magnitudes (free electrons, m*=m)