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Unconventional longitudinal resistance and
magnetoresistance in Single Crystalline Bismuth Thin Film
Kai Zhu, Shunhao Xiao, Xiaofeng Jin
Department of Physics, Fudan University, Shanghai 200433
Bismuth, a prototype semimetal, has unique electronic properties. A semimetal-semiconductor(SMSC) transition is
predicted to exist, even after decades of theoretical and experimental works on this still remains a controversial issue.
In the present work, the non-monotonic resistivity(conductance) – temperature curve of single crystalline Bismuth
epitaxial grown on Si(111)-7*7 shows the nature of competition between metallic surface state and bulk
semiconductor. Magneto resistivity of Bismuth ultrathin film at low temperature give support for the two
dimensional nature of the surface states.
Semiconductor-to-Semimetal transition
It was predicted that with the decreasing thickness of
Bismuth film, a band gap would develop due to the
quantum size effect, which lead to semimetalsemiconductor (SMSC) transition[1].
[1] V. N. Lutskii, JETP Lett. 2, 245 (1965), V.B. Sandomirsjii, JETP 25,
101 (1967)
Epitaxial Bismuth thin film on Si (111) substrate
d
The RHEED pattern and Grazing angel XRD result of
Bismuth of different thickness confirms the phase
transition from pseudocubic phase (PC) to hexagonal
phase (HEX) [2].
[2] T. Nagao, J.T. Sadowski, T. Sakurai PhysRevLett_93_105501(2004)
Weak Antilocalization in ultrathin bismuth films
RHEED of Si(111)-7×7 and Bismuth film of different thickness
886
5
10
884
Bi1-10
6
10
Si 2-20
2K
3K
4K
5K
7K
9K
11K
Si2-20
4
10
882
5
3
2
10
880
4
10
MR (Ω)
10
Intensity/a.u.
Intensity/a.u.
10
3
10
878
2
1
10
10
876
1
10
0
10
0
20
40
60
80
100
874
120
0
2θ
15
30
45
60
75
90
105
120
2θ
872
-1.5
Grazing angle XRD of Bismuth with thickness 1.5nm(left) 6nm(right)
4nm
7.0x10
-3
6.0x10
-3
1.0
1.5
5.0x10
-3
4.0x10
-3
3.0x10
-3
2.0x10
-3
1.0x10
-3
𝟏
,
𝟐
𝜳 is the digamma function 𝜶 =
𝑩𝝋 = h/(8𝝅𝑫𝒆𝝉𝝋 )
a characteristic field related to the dephasing time D is
the diffusion constant. Below gives the fitting to the
experiment data.
500
6nm
8nm
--1
10nm
300
σ (Ω )
ρ xx (Ω)
0.5
𝑩𝝋
𝒆𝟐
𝟏 𝑩𝝋
∆𝝈 = −𝜶 ∙
𝚿
+
− 𝑳𝒏
𝟐𝝅𝒉
𝟐 𝑩
𝑩
600
15nm
5K
Linear Fit of σ
25nm
100
0.0
Weak Antilocalization effect of 3nm Bismuth
In the limit of very strong spin-orbit coupling , The
Hikami-Larkin-Nagaoka (HLN) equation to account for
the magnetoconductivity is reduce to
700
200
-0.5
B (T)
Transport properties of bismuth thin film
400
-1.0
B (T)
𝟏𝟎−𝟑 𝜴 −𝟏
40nm
0
0
50
100
150
200
T (K)
250
300
350
400
0.0
0
10
20
30
40
50
∆𝝈(𝝁𝑺)
d (nm)
The competition between metallic surface state and bulk semiconductor give rise a non-monotonic
resistance – temperature curve. From the dependence of the sheet conductance on the film thickness
the conductance of the surface states is about 𝟏𝟎−𝟑 𝜴 −𝟏 .
Summary
 The predicted semimetal-semiconductor(SMSC) transition in Bismuth thin film does exist. The unconventional transport behavior of Bismuth thin
film is due to the competition of semiconductor bulk and metallic surface state.
 Weak antilocalization in ultrathin bismuth films give support for the two dimensional nature of the surface states.