**2.1. Bi**─**O**─**S superconductors**

The element composition of Bi4 O4 S3 is the same as Bi4 O4 (SO4 ) x Bi2 S4 (x = 0.5), and its parent Bi6 O8 S5 is an oxide insulator composed of alternatively stacked BiS2 and Bi2 O2 + SO4 + Bi2 O2 layers along the c-axis. It has a tetragonal structure with I4/mmm space group and its schematic crystal structure is shown in **Figure 1(c)**. Band calculations demonstrate that the half vacancy of SO4 layer generates electron carriers into BiS2 layer. The normal state of Bi4 O4 S3 is metallic and the superconductivity mainly originates from the Bi 6px and 6py orbitals in BiS2 layers. Therefore, the BiS2 layer is called the superconducting layer in this family.

Emerging Superconductivity and Topological States in Bismuth Chalcogenides http://dx.doi.org/10.5772/intechopen.73057 113

**Figure 1.** Crystal structures of (a) Bi2 OS2 , (b) Bi3 O2 S3 , and (c) Bi4 O4 S3 [21].

However, so far, only two kinds of unconventional superconducting systems have exceeded the Macmillan limit at ambient pressure, i.e., the cuprate and iron-based superconductors. In general, the correlation of structure and typical properties is always a useful guideline for effectively searching for special functional materials. In fact, the structure of both cuprate and iron-based superconductors can be characterized as a sandwiched "hamburger" model.

plane, Fe2

spacer layers, which stack alternatively along the c-axis [1, 2]. Superconductivity occurs when the charged carriers are generated by the defects or substitution in superconducting layers or more commonly provided by the space layers; namely, a new superconducting layer probably means a new superconducting system. The spacer layer can be easily tuned by doping, substitution, intercalation, and pressure, which could affect superconductivity [3]. Therefore, materials with layered structure have been regarded as the most promising playground for

cal superconductor candidate, as evidenced by the zero-bias conductance peak and quantum oscillation experiment [5, 6]. Very recently, superconductivity with topological states was

superconducting temperature is about 8 K for the samples annealed under high pressure [10]. As its structure is very similar to the iron-based superconductor LaOFeAs, this system has been intensively researched, and lots of isostructural superconductors have been syn-

(Re: Ce, Pr, Nd, Yb), Sr1−xRex

chapter, the crystal structure and superconducting properties of Bi─O─S superconductors,

is the same as Bi4

layers along the c-axis. It has a tetragonal structure with I4/mmm space group and its schematic crystal structure is shown in **Figure 1(c)**. Band calculations demonstrate that the half

[11–15]. These researches are focused on tuning the spacer layers. The attempts to

Bi2 Se3

M2

(M = As, P, S, Se, and Te) layer) and

Se3

Bi2 Se3

> Bi2 Se3

FBiS2

Fx BiSe2

single crystals are briefly reviewed.

O4 (SO4 )x Bi2 S4

layer is called the superconducting layer in this family.

O4 S3

and Nbx

was reported, whose structure is more definite and the zero-resistance

by Cu intercalation

is proposed as a topologi-

[7, 8]. In 2012, an exotic

(Re: La, Ce), EuBiS2

and Sr0.5La0.5FBiSe2

with zero-resistance


(Ch: S, Se). In this

(x = 0.5), and its parent

O2 + SO4 + Bi2

O2

O4 S3 is

orbitals in BiS2

and Bi2

layer. The normal state of Bi4

and 6py

F, and

[16–18].

It consists of superconducting layers (CuO2

superconductors.

was first reported [4]. It has drawn much attention since Cu<sup>x</sup>

BiS2

explore new superconducting layers only succeed in LaOx

**2. Crystal structure and superconducting properties**

O4 S3

is an oxide insulator composed of alternatively stacked BiS2

layer generates electron carriers into BiS2

metallic and the superconductivity mainly originates from the Bi 6px

single crystals, and Srx

also reported in its isostructural compounds, Srx

In 2010, superconductivity arising from the topological insulator Bi2

superconductivity was discovered in a new layered structure Bi4

superconducting temperature at about 4.5 K [9]. Soon, another new BiS2

So far, the superconducting layer of this system has been extended to BiCh2

Bi2 Se3

exploring new high-Tc

112 Superfluids and Superconductors

ductor LaO0.5F0.5BiS2

BiSe2

Eu3 Bi3 S4 F4

LaO1−xFx

Bi6 O8 S5

vacancy of SO4

layers. Therefore, the BiS2

thesized, including ReO1−xFx

**2.1. Bi**─**O**─**S superconductors**

The element composition of Bi4

However, the chemical composition studies show that it probably contains two new Bi─O─S phases, i.e., Bi2 OS2 and Bi3 O2 S3 . Their schematic structures can be seen in **Figure 1(a)** and **(b)**. Bi2 OS2 is an insulating phase and its content is less than 10%. Bi3 O2 S3 is the main phase and likely accounts for the 4.5 K superconductivity in Bi4 O4 S3 . And the superconductivity can be suppressed by the amount of Bi2 OS2 -like stacking faults [19]. Once the quality of Bi3 O2 S3 sample is improved, the superconducting volume fraction will be enhanced with its zeroresistance superconducting temperature increased up to 4.9 K [20].

The crystal structure of Bi3 O2 S3 is similar to Bi4 O4 S3 with the same I4/mmm space group, a = 3.9674 Å and b = 41.2825 Å. The electron carriers are believed to be generated from S2 2− layers replacing the vacancy of SO4 2− layers in Bi4 O4 S3 . The chemical composition of Bi2 OS2 can also be expressed as BiOBiS2 . Then we can see it is isostructural with LaOBiS2 with P4/nmm space group, a = b = 3.9744 Å and c = 13.7497 Å. BiOBiS2 has the simplest structure and composition, then it is probably the parent compound of this BiS2 -based family. Besides, superconductivity is likely to be induced by introducing carriers into spacer layer. In fact, F-doped Bi2 OS2 has been reported to exhibit bulk superconductivity below 5 K [21, 22].

**Figure 2** shows the powder XRD patterns of Bi<sup>3</sup> O2 S3 , BiO1−xFx BiS2 , and Bi2 OS2 samples. We can see that samples of Bi─O─S compounds tend to contain impurities such as Bi2 O3 , Bi, and Bi2 S3 , because their synthesis temperature is relatively low (520°C for Bi4 O4 S3 and Bi3 O2 S3 , and 400°C for Bi2 (O,F)S2 ) [9, 19–21]. Besides, these samples can only be synthesized in a narrow temperature region. Another difficulty in detecting their actual composition and structure is that several strong diffraction peaks in the powder XRD patterns are very close to each other.

**Figure 2.** Powder XRD patterns of Bi<sup>3</sup> O2 S3 , Bi2 OS2 , and Bi2 O1−xFx S2 polycrystalline samples. The special characters (\*, #) represent the impurity phases.

Hence, bulk superconductivity is very important in this system. Up to now, high-quality samples, especially single crystals, are still needed to investigate the relationship of structure and properties, in view of the multiple competing low-energy crystal structures in this system.

The physical properties of Bi─O─S superconductors are introduced, taking Bi3 O2 S3 and F-doped Bi2 OS2 for instance [20, 21]. **Figure 3(a)** shows the temperature dependence of resistivity and magnetoresistivity under different applied magnetic fields for Bi<sup>3</sup> O2 S3 . Its normal state is metallic-like and a sharp drop in resistivity appears at 5.8 K and quickly down to zero at 4.9 K. The upper critical field is estimated from resistivity versus temperature curves under different applied magnetic fields perpendicular to the sample surface, as seen in the insets of **Figure 3(a)**. According to the Werthamer-Helfand-Hohenberg (WHH) formula, the upper critical field μ<sup>0</sup> Hc2(0) is evaluated to be about 4.84 T.

heat coefficient γ and phonon specific heat coefficient β for the normal state under 9 T are

O2 S3

of magnetic susceptibility at 2 K. (c) Hall resistivity versus magnetic field at different temperatures. (d) Curves of C/T

O2 S3

 in superconducting state (0 T) and normal state (9 T). The upper inset shows the data of normal state at low temperature region. The lower inset shows the temperature dependence of calculated electron specific heat in

external magnetic field, the electronic specific heat of superconducting state can be expressed

tions. However, we can see it is almost metallic from 300 K to 30 K, and a weak semiconductor behavior emerges below 30 K, which may be originating from the impurities. The F-doping can significantly decrease the normal state resistivity and increase the shielding volume fraction, as shown in **Figure 4**. The best doping ratio is about 0.24. From the temperature dependence of magnetic susceptibility, the best doped sample has a bulk type-II-like

. As the phononic contribution to the heat capacity is generally independent of the

(T) = C(T, H = 0) − C(T, H = 9T) + γT. (1)

is comparable to the BCS weak-coupling limit 1.43.

was predicted to be an insulating oxide by the band structure calcula-

), respectively, using linear fitting of C/T

. The lower inset shows the curves of resistivity versus

Emerging Superconductivity and Topological States in Bismuth Chalcogenides

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and the insets show the magnetic field dependence

onset and Tc

zero.

115

) and 2.6 mJ/(mol K4

temperature under different applied magnetic fields and the upper inset shows the field dependence of T<sup>c</sup>

/γT<sup>c</sup>

obtained as 1.65 mJ/(mol K2

superconducting state [20].

**Figure 3.** (a) Temperature dependence of resistivity for Bi3

(b) Temperature dependence of magnetic susceptibility for Bi3

Ce

The estimated value of ΔC<sup>e</sup>

OS2

versus T2

versus T2

by the equation

Undoped Bi2

The shielding volume fraction is about 100%, revealing bulk superconductivity, as seen in **Figure 3(b)**. The divergence in temperature dependence of magnetic susceptibility and the M-H curves characterize Bi3 O2 S3 as a type-II superconductor. The Hall effect shows a remarkable nonlinear magnetic field dependence of transverse resistivity, which means it is likely a multiband superconductor [23]. However, the Hall resistivity at different temperatures is all negative, indicating that the dominant charge carriers are electron-type. The evaluated charge carrier density is about 1.5 × 1019 cm−3. It is much lower than those of cuprate and iron-based superconductors, implying a low superfluid density. Chemical substitution effects seem to increase the charge carrier density, but ultimately inhibit the superconductivity [24–26].

A clear specific heat anomaly appears around the superconducting transition temperature, as seen in **Figure 3(d)**, confirming the bulk superconductivity in Bi<sup>3</sup> O2 S3 . The electronic specific

Emerging Superconductivity and Topological States in Bismuth Chalcogenides http://dx.doi.org/10.5772/intechopen.73057 115

**Figure 3.** (a) Temperature dependence of resistivity for Bi3 O2 S3 . The lower inset shows the curves of resistivity versus temperature under different applied magnetic fields and the upper inset shows the field dependence of T<sup>c</sup> onset and Tc zero. (b) Temperature dependence of magnetic susceptibility for Bi3 O2 S3 and the insets show the magnetic field dependence of magnetic susceptibility at 2 K. (c) Hall resistivity versus magnetic field at different temperatures. (d) Curves of C/T versus T2 in superconducting state (0 T) and normal state (9 T). The upper inset shows the data of normal state at low temperature region. The lower inset shows the temperature dependence of calculated electron specific heat in superconducting state [20].

Hence, bulk superconductivity is very important in this system. Up to now, high-quality samples, especially single crystals, are still needed to investigate the relationship of structure and properties, in view of the multiple competing low-energy crystal structures in this system.

O1−xFx S2

state is metallic-like and a sharp drop in resistivity appears at 5.8 K and quickly down to zero at 4.9 K. The upper critical field is estimated from resistivity versus temperature curves under different applied magnetic fields perpendicular to the sample surface, as seen in the insets of **Figure 3(a)**. According to the Werthamer-Helfand-Hohenberg (WHH) formula, the upper

The shielding volume fraction is about 100%, revealing bulk superconductivity, as seen in **Figure 3(b)**. The divergence in temperature dependence of magnetic susceptibility and the

able nonlinear magnetic field dependence of transverse resistivity, which means it is likely a multiband superconductor [23]. However, the Hall resistivity at different temperatures is all negative, indicating that the dominant charge carriers are electron-type. The evaluated charge carrier density is about 1.5 × 1019 cm−3. It is much lower than those of cuprate and iron-based superconductors, implying a low superfluid density. Chemical substitution effects seem to increase the charge carrier density, but ultimately inhibit the superconductivity [24–26].

A clear specific heat anomaly appears around the superconducting transition temperature, as

for instance [20, 21]. **Figure 3(a)** shows the temperature dependence of resis-

as a type-II superconductor. The Hall effect shows a remark-

O2 S3 O2 S3 and

. Its normal

O2 S3

polycrystalline samples. The special characters (\*, #)

. The electronic specific

The physical properties of Bi─O─S superconductors are introduced, taking Bi3

tivity and magnetoresistivity under different applied magnetic fields for Bi<sup>3</sup>

Hc2(0) is evaluated to be about 4.84 T.

O2 S3 , Bi2 OS2 , and Bi2

seen in **Figure 3(d)**, confirming the bulk superconductivity in Bi<sup>3</sup>

O2 S3

F-doped Bi2

critical field μ<sup>0</sup>

OS2

**Figure 2.** Powder XRD patterns of Bi<sup>3</sup>

represent the impurity phases.

114 Superfluids and Superconductors

M-H curves characterize Bi3

heat coefficient γ and phonon specific heat coefficient β for the normal state under 9 T are obtained as 1.65 mJ/(mol K2 ) and 2.6 mJ/(mol K4 ), respectively, using linear fitting of C/T versus T2 . As the phononic contribution to the heat capacity is generally independent of the external magnetic field, the electronic specific heat of superconducting state can be expressed by the equation

$$\mathbf{C}\_{o}(\mathbf{T}) = \mathbf{C}(\mathbf{T}, \mathbf{H} = \mathbf{0}) - \mathbf{C}(\mathbf{T}, \mathbf{H} = \mathbf{9T}) + \gamma \mathbf{T}.\tag{1}$$

The estimated value of ΔC<sup>e</sup> /γT<sup>c</sup> is comparable to the BCS weak-coupling limit 1.43.

Undoped Bi2 OS2 was predicted to be an insulating oxide by the band structure calculations. However, we can see it is almost metallic from 300 K to 30 K, and a weak semiconductor behavior emerges below 30 K, which may be originating from the impurities. The F-doping can significantly decrease the normal state resistivity and increase the shielding volume fraction, as shown in **Figure 4**. The best doping ratio is about 0.24. From the temperature dependence of magnetic susceptibility, the best doped sample has a bulk type-II-like

**Figure 4.** (a) Temperature dependence of resistivity for BiO1−xFx BiS2 . The inset shows the variation of Tc with different F-doping content. (b) Temperature dependence of magnetic susceptibility for BiO1−xFx BiS2 under ZFC process. The inset presents the FC and ZFC data for x = 0.24 sample [21].

superconductivity. When doping content exceeds 0.27, superconductivity disappears and the resistivity increases quickly. Besides, the quality of samples (x > 0.27) synthesized by conventional solid state reaction method begins to deteriorate with increasing doping content [21]. In fact, the Bi2 (O,F)S2 samples synthesized by topotactic fluorination using XeF<sup>2</sup> also contain bismuth impurity [22]. It is difficult to get pure samples because the optimal synthesis temperature is only around 400°C.

#### **2.2. Re(O,F)BiCh2 (Ch: S, Se) superconductors**

Re(O,F)BiS2 (Re: La, Ce, Pr, Nd, Yb) superconductors have been intensively studied since the report of LaO0.5F0.5BiS2 . Their structure is more definite and similar to "1111" phase of iron-based superconductors. Single crystals of this structure have been successfully synthesized [27]. Structure tuning is mainly concentrated on the spacer layers rather than the superconducting layer. And only the electron-doping into the insulating parent can induce superconductivity [28]. Here, we introduce the crystal structure and various physical properties of LaO1−xFx BiSe2 single crystals, which also firstly extend the superconducting layer to BiSe2 layer.

The powder XRD pattern and crystal structure of LaO0.59F0.41BiSe2 superconducting single crystal are presented in **Figure 5**. No impurity phase is found and each peak is indexed. It has a P4/nmm tetragonal lattice with the refined lattice constants a = b = 4.1377 Å and c = 14.1566 Å, which are larger than those of LaO0.5F0.5BiS2 for the larger ionic radius of Se2−. **Figure 6** shows a comparison of the temperature dependence of resistivity for La(O,F)BiS2 and La(O,F)BiSe2 samples. LaOBiS2 can be described as an insulator while LaOBiSe2 is metallic. For LaO0.5F0.5BiS2 , it exhibits a semiconducting behavior before the superconducting transition begins. The transport property of LaO0.5F0.5BiSe2 is similar to Bi3 O2 S3 but with a lower residual resistivity. Other isostructural compounds such as LaO0.5F0.5BiTe2 and LaO0.5F0.5SbS2 are also reported, but no superconductivity can be observed down to 1.7 K [16].

Fluorine doping effect on the superconductivity of LaO1−xFx

**Figure 6.** A comparison of the temperature dependence of resistivity between (a) La(O,F)BiS2

LaO0.59F0.41BiSe2

rectangle indicates the unit cell [17].

component of 0.9. The magnetic susceptibility measurement shows LaO1−xFx

29 T and 1 T for H∥ab and H⊥ab, respectively, which indicate large anisotropy.

in **Figure 7(a)** and **(b)**. F-doping can significantly decrease the resistivity of normal state and increase the superconducting transition temperature and shielding volume fraction. Unfortunately, the flux method can only grow single crystals with the largest F content of about 0.5. For example, the sample with F-doping amount of 0.52 was grown by a nominal

**Figure 5.** (a) Powder XRD pattern (black circles) with the Rietveld refinement (red curve) and Miller indices for

. The inset table summarizes the structural parameters. (b) Crystal structure of LaO0.59F0.41BiSe2

Emerging Superconductivity and Topological States in Bismuth Chalcogenides

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superconductivity and belongs to the type-II superconductors. Upper critical magnetic field can be evaluated from the resistivity versus temperature under various magnetic fields. As seen in **Figure 7(c)** and **(d)**, the upper critical fields at zero temperature are estimated to be

BiSe2

single crystals is shown

and (b) La(O,F)BiSe2

BiSe2

has a bulk

.

. The

117

Emerging Superconductivity and Topological States in Bismuth Chalcogenides http://dx.doi.org/10.5772/intechopen.73057 117

**Figure 5.** (a) Powder XRD pattern (black circles) with the Rietveld refinement (red curve) and Miller indices for LaO0.59F0.41BiSe2 . The inset table summarizes the structural parameters. (b) Crystal structure of LaO0.59F0.41BiSe2 . The rectangle indicates the unit cell [17].

superconductivity. When doping content exceeds 0.27, superconductivity disappears and the resistivity increases quickly. Besides, the quality of samples (x > 0.27) synthesized by conventional solid state reaction method begins to deteriorate with increasing doping content [21].

bismuth impurity [22]. It is difficult to get pure samples because the optimal synthesis tem-

iron-based superconductors. Single crystals of this structure have been successfully synthesized [27]. Structure tuning is mainly concentrated on the spacer layers rather than the superconducting layer. And only the electron-doping into the insulating parent can induce superconductivity [28]. Here, we introduce the crystal structure and various physical prop-

crystal are presented in **Figure 5**. No impurity phase is found and each peak is indexed. It has a P4/nmm tetragonal lattice with the refined lattice constants a = b = 4.1377 Å and

**Figure 6** shows a comparison of the temperature dependence of resistivity for La(O,F)BiS2

 **(Ch: S, Se) superconductors**

F-doping content. (b) Temperature dependence of magnetic susceptibility for BiO1−xFx

The powder XRD pattern and crystal structure of LaO0.59F0.41BiSe2

residual resistivity. Other isostructural compounds such as LaO0.5F0.5BiTe2

are also reported, but no superconductivity can be observed down to 1.7 K [16].

c = 14.1566 Å, which are larger than those of LaO0.5F0.5BiS2

samples. LaOBiS2

sition begins. The transport property of LaO0.5F0.5BiSe2

samples synthesized by topotactic fluorination using XeF<sup>2</sup>

BiS2

(Re: La, Ce, Pr, Nd, Yb) superconductors have been intensively studied since

. Their structure is more definite and similar to "1111" phase of

. The inset shows the variation of Tc

BiS2

single crystals, which also firstly extend the superconducting layer

can be described as an insulator while LaOBiSe2

is similar to Bi3

, it exhibits a semiconducting behavior before the superconducting tran-

also contain

with different

under ZFC process. The inset

superconducting single

is metal-

but with a lower

and LaO0.5F0.5SbS2

for the larger ionic radius of Se2−.

O2 S3

In fact, the Bi2

116 Superfluids and Superconductors

**2.2. Re(O,F)BiCh2**

erties of LaO1−xFx

and La(O,F)BiSe2

lic. For LaO0.5F0.5BiS2

layer.

to BiSe2

Re(O,F)BiS2

(O,F)S2

**Figure 4.** (a) Temperature dependence of resistivity for BiO1−xFx

presents the FC and ZFC data for x = 0.24 sample [21].

BiSe2

perature is only around 400°C.

the report of LaO0.5F0.5BiS2

**Figure 6.** A comparison of the temperature dependence of resistivity between (a) La(O,F)BiS2 and (b) La(O,F)BiSe2 .

Fluorine doping effect on the superconductivity of LaO1−xFx BiSe2 single crystals is shown in **Figure 7(a)** and **(b)**. F-doping can significantly decrease the resistivity of normal state and increase the superconducting transition temperature and shielding volume fraction. Unfortunately, the flux method can only grow single crystals with the largest F content of about 0.5. For example, the sample with F-doping amount of 0.52 was grown by a nominal component of 0.9. The magnetic susceptibility measurement shows LaO1−xFx BiSe2 has a bulk superconductivity and belongs to the type-II superconductors. Upper critical magnetic field can be evaluated from the resistivity versus temperature under various magnetic fields. As seen in **Figure 7(c)** and **(d)**, the upper critical fields at zero temperature are estimated to be 29 T and 1 T for H∥ab and H⊥ab, respectively, which indicate large anisotropy.

**Figure 7.** Superconducting properties of LaO1−xFx BiSe2 single crystals with different F-doping contents. (a) Temperature dependence of resistivity and an enlarged view near the superconducting transition temperature for all samples. (b) ZFC and FC magnetic susceptibility versus temperature with magnetic field applied parallel to ab-plane for all samples. (c) and (d) Resistivity versus temperature with magnetic field applied perpendicular to and parallel to ab-plane, respectively, for the x = 0.52 sample [17].

The anisotropy parameter γ<sup>s</sup> of the LaO1−xFx BiSe2 superconducting single crystal is investigated by measuring the angular dependence of resistivity under various magnetic fields at 3 K (see **Figure 8**). Note that the angle θ describes the deviation of magnetic field with respect to the ab-plane of single crystal. Only the data with magnetic field below 1 T are selected for the reduced magnetic field, because the HC2(0) for H⊥ab is about 1 T. The reduced magnetic field is calculated by the equation <sup>−</sup><sup>2</sup> cos2 <sup>θ</sup> . (2)

$$\mathbf{H}\_{\rm nd} = \mathbf{H}\sqrt{\sin^2\Theta + \chi\_s^{-2}\cos^2\Theta}.\tag{2}$$

is expected for LaO0.5F0.5BiSe2

single crystal samples of LaO0.5F0.5BiSe2

**Figure 8.** Anisotropy of LaO1−xFx

magnetic field Hred [17].

BiSe2

very different from the BiS<sup>2</sup>

**2.3. Mx**

**Bi2 Ch2**

phase emerges at about 1.2 GPa and Tc

under external pressure since its zero-resistance temperature

superconducting single crystal. (a) Angular dependence of resistivity taken under

Emerging Superconductivity and Topological States in Bismuth Chalcogenides

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119

reaches about 6.5 K at 2.17 GPa [31]. Accompanied

single crystal. (a) High-pressure effect on the


is about 3.5 K. However, we find that its superconductivity and shielding volume fraction decrease unexpectedly with increasing pressure below 1 GPa hydrostatic pressure, as seen in **Figure 9(a)**. Another experiment with higher pressure shows that a new superconducting

temperature dependence of magnetic susceptibility. (b) and (c) High-pressure effect on the transport properties of two

magnetic fields from 0.1 T to 6 T at 3 K for LaO0.48F0.52BiSe1.93 single crystal. (b) Scaling of the resistivity vs. the reduced

by this crossover, the normal state is switched from that with a low temperature resistivity upturning to a metallic one. Accordingly, the normal state resistivity also shows a nonmono-

Topological insulator has linearly dispersive band structures and its topological surface state exhibits metallic properties while the bulk state is insulating. If its spin-momentum locking effect combines with superconductivity, Majorana fermion may exist, which is useful for quantum computing. At first, the topological superconductors were mostly focused on the proximity-induced

tonic change with the external pressure. These facts suggest that the BiSe2


 **(Ch: Se, Te) superconductors**

**Figure 9.** High-pressure effect on the superconductivity of LaO0.5F0.5BiSe2

[31].

According to the Ginzburg-Landau theory [29], the curves of resistivity versus reduced magnetic field under different magnetic fields should merge into one. The resultant anisotropy parameter at 3 K is about 30 (see **Figure 8(b)**), which is close to the result of upper critical field within the ab-plane.

Considering that the Tc of LaO0.5F0.5BiS2 is increased from 2.7K to 10.6K under a hydrostatic pressure of 1.68 GPa [30], the highest Tc among the BiS2 -based superconductors, higher Tc , above 10.6 K

Emerging Superconductivity and Topological States in Bismuth Chalcogenides http://dx.doi.org/10.5772/intechopen.73057 119

**Figure 8.** Anisotropy of LaO1−xFx BiSe2 superconducting single crystal. (a) Angular dependence of resistivity taken under magnetic fields from 0.1 T to 6 T at 3 K for LaO0.48F0.52BiSe1.93 single crystal. (b) Scaling of the resistivity vs. the reduced magnetic field Hred [17].

**Figure 9.** High-pressure effect on the superconductivity of LaO0.5F0.5BiSe2 single crystal. (a) High-pressure effect on the temperature dependence of magnetic susceptibility. (b) and (c) High-pressure effect on the transport properties of two single crystal samples of LaO0.5F0.5BiSe2 [31].

is expected for LaO0.5F0.5BiSe2 under external pressure since its zero-resistance temperature is about 3.5 K. However, we find that its superconductivity and shielding volume fraction decrease unexpectedly with increasing pressure below 1 GPa hydrostatic pressure, as seen in **Figure 9(a)**. Another experiment with higher pressure shows that a new superconducting phase emerges at about 1.2 GPa and Tc reaches about 6.5 K at 2.17 GPa [31]. Accompanied by this crossover, the normal state is switched from that with a low temperature resistivity upturning to a metallic one. Accordingly, the normal state resistivity also shows a nonmonotonic change with the external pressure. These facts suggest that the BiSe2 -based system is very different from the BiS<sup>2</sup> -based system.

#### **2.3. Mx Bi2 Ch2 (Ch: Se, Te) superconductors**

The anisotropy parameter γ<sup>s</sup>

respectively, for the x = 0.52 sample [17].

118 Superfluids and Superconductors

**Figure 7.** Superconducting properties of LaO1−xFx

field is calculated by the equation

within the ab-plane.

Considering that the Tc

sure of 1.68 GPa [30], the highest Tc

Hred = H √

of LaO0.5F0.5BiS2

of the LaO1−xFx

BiSe2

BiSe2

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ sin2 θ + γ<sup>s</sup>

gated by measuring the angular dependence of resistivity under various magnetic fields at 3 K (see **Figure 8**). Note that the angle θ describes the deviation of magnetic field with respect to the ab-plane of single crystal. Only the data with magnetic field below 1 T are selected for the reduced magnetic field, because the HC2(0) for H⊥ab is about 1 T. The reduced magnetic

dependence of resistivity and an enlarged view near the superconducting transition temperature for all samples. (b) ZFC and FC magnetic susceptibility versus temperature with magnetic field applied parallel to ab-plane for all samples. (c) and (d) Resistivity versus temperature with magnetic field applied perpendicular to and parallel to ab-plane,

According to the Ginzburg-Landau theory [29], the curves of resistivity versus reduced magnetic field under different magnetic fields should merge into one. The resultant anisotropy parameter at 3 K is about 30 (see **Figure 8(b)**), which is close to the result of upper critical field

among the BiS2

superconducting single crystal is investi-

single crystals with different F-doping contents. (a) Temperature

<sup>−</sup><sup>2</sup> cos2 <sup>θ</sup> . (2)

, above 10.6 K

is increased from 2.7K to 10.6K under a hydrostatic pres-


Topological insulator has linearly dispersive band structures and its topological surface state exhibits metallic properties while the bulk state is insulating. If its spin-momentum locking effect combines with superconductivity, Majorana fermion may exist, which is useful for quantum computing. At first, the topological superconductors were mostly focused on the proximity-induced superconductivity. The discovery of Cux Bi2 Se3 superconductor opens a new gate to topological superconductors, i.e., superconductors induced by doping into topological insulators, which are expected to be the candidate of three-dimensional topological superconductors. Recently, a series of superconductors based on the topological insulators have been reported, such as Cux (PbSe)5 (Bi2 Se3 ) 6 [32], Srx Bi2 Se3 [7], Nbx Bi2 Se3 [8], and Tlx Bi2 Te3 [33]. Here, we put emphasis on the crystal structure and physical properties of Srx Bi2 Se3 single crystals.

The structure of Srx Bi2 Se3 is similar to that of Cux Bi2 Se3 and isomorphic to the parent Bi2 Se3 . Sr atoms may act as a bipolar dopant that can be embedded in the van der Waals space or randomly substitute for Bi. The actual Sr doping content of Srx Bi2 Se3 is very little so that it is hard to define its precise position. Nevertheless, the lattice constants of Sr<sup>x</sup> Bi2 Se3 are a little larger than those of Bi2 Se3 , while the lattice constants of Bi2−xSrx Se3 are smaller. The c-axis lattice constant of Bi2−xSrx Se3 decreases slightly with increasing doping content (see **Figure 10(b)**). In addition, all samples grown in Bi2−xSrx Se3 ratio show no signs of superconductivity at 1.8 K, as seen in **Figure 11(a)**. Therefore, we could use **Figure 10(a)** as the schematic structure diagram.

The linear curves of Hall resistivity versus magnetic field indicate that Sr<sup>x</sup> Bi2 Se3 has only one electron-like bulk carrier. The carrier density increases slightly with decreasing temperature. Its average is around 2.3 × 1019 cm−3, about 1–2 orders of magnitude lower than Cux Bi2 Se3 . **Figure 11(d)** and **(e)** shows that the Tc of superconducting samples changes little with different Sr contents, but the shielding volume fraction is very different. Only those samples with Sr content above 0.06 have a large shielding volume fraction. Moreover, the superconductivity is very stable in air, as evidenced by the almost unchanged shielding volume fraction for the sample placed in air even for a month. This provides great convenience for experimental research.

The topological surface state of Srx Bi2 Se3 single crystal has been investigated through Shubnikov-de Haas oscillation measurements. Clear oscillations in resistivity and Hall resistivity can be observed under high magnetic field at different temperatures, as shown in **Figure 12(a)** and **(c)**. The oscillation amplitudes become more pronounced for higher magnetic field and lower temperature. However, the oscillatory periods measured at different temperatures remain constant, so only the data at 0.35 K with the most noticeable oscillations are selected to deduce the Landau level

indices. In fact, the measured resistivity and Hall resistivity actually contain contributions from both the surface and bulk conductance when a large parallel bulk conduction channel is present. Therefore, the least confusing method is to convert resistivity into conductance to determine the Landau index because its components are additive [34]. The following equations are used to cal-

. (b) Hall resistivity versus magnetic field curves measured at different temperatures. (c) Temperature dependence of estimated Hall coefficient and charge carrier density. (d) Temperature dependence of susceptibility for samples with

After removing the nonoscillatory background, the oscillatory components are obtained and plotted as a function of 1/B. The frequencies are 146 T for longitudinal conductance

ΔGxy are assigned to n + 1/4 [see **Figure 13(a)** and **(c)**]. The 1/4 shift arises to match the valleys in dΔGxy/dB with the valleys in ΔGxx [34]. The obtained intercepts of the linear fittings for n versus 1/B are both close to the value for an ideal Dirac system, i.e., −0.5 rather than 0 or 1 (see **Figure 13(b)** and **(d)**). Thus, it provides transport evidence for the existence of Dirac fermions

<sup>2</sup> , Gxy <sup>=</sup> <sup>R</sup> \_\_\_\_\_\_ xy Rxx <sup>2</sup> + Rxy

. (a) Temperature dependence of resistivity for Srx

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zero, and shielding volume fraction as a function of Sr content [7].

. The integer Landau index n corresponds to the valleys in ΔGxx, while the valleys in

<sup>2</sup> . (3)

Se3

but smaller than

Bi2 Se3 and Bi2−

Rxx <sup>2</sup> + Rxy

Bi2 Se3

onset, Tc

and 144.8 T for Hall conductance, which are comparable to those of Bi2

culate conductance

Cux Bi2 Se3

x Srx Se3

in Srx Bi2 Se3

Gxx <sup>=</sup> <sup>R</sup> \_\_\_\_\_\_ xx

**Figure 11.** Superconducting properties of Srx

different Sr contents. (e) Plot of T<sup>c</sup>

superconductor.

**Figure 10.** Crystal structure of Srx Bi2 Se3 superconductors. (a) Schematic diagram of Srx Bi2 Se3 crystal structure. (b) Powder XRD patterns of Sr<sup>x</sup> Bi2 Se3 , Bi2 Se3 , and Bi2−xSrx Se3 [7].

Emerging Superconductivity and Topological States in Bismuth Chalcogenides http://dx.doi.org/10.5772/intechopen.73057 121

superconductivity. The discovery of Cux

Bi2 Se3

Bi2 Se3

Se3

addition, all samples grown in Bi2−xSrx

**11(d)** and **(e)** shows that the Tc

The topological surface state of Srx

**Figure 10.** Crystal structure of Srx

Bi2 Se3 , Bi2 Se3

XRD patterns of Sr<sup>x</sup>

Bi2 Se3

, and Bi2−xSrx

Se3 [7].

Se3

Bi2 Se3

[8], and Tlx

domly substitute for Bi. The actual Sr doping content of Srx

[7], Nbx

[32], Srx

Bi2 Se3

The structure of Srx

than those of Bi2

constant of Bi2−xSrx

physical properties of Srx

120 Superfluids and Superconductors

Bi2 Se3

superconductors based on the topological insulators have been reported, such as Cux

, while the lattice constants of Bi2−xSrx

Se3

average is around 2.3 × 1019 cm−3, about 1–2 orders of magnitude lower than Cux

The linear curves of Hall resistivity versus magnetic field indicate that Sr<sup>x</sup>

Bi2 Se3

Bi2 Te3

is similar to that of Cux

to define its precise position. Nevertheless, the lattice constants of Sr<sup>x</sup>

single crystals.

superconductors, i.e., superconductors induced by doping into topological insulators, which are expected to be the candidate of three-dimensional topological superconductors. Recently, a series of

> Bi2 Se3

atoms may act as a bipolar dopant that can be embedded in the van der Waals space or ran-

seen in **Figure 11(a)**. Therefore, we could use **Figure 10(a)** as the schematic structure diagram.

electron-like bulk carrier. The carrier density increases slightly with decreasing temperature. Its

tents, but the shielding volume fraction is very different. Only those samples with Sr content above 0.06 have a large shielding volume fraction. Moreover, the superconductivity is very stable in air, as evidenced by the almost unchanged shielding volume fraction for the sample placed in air even for a month. This provides great convenience for experimental research.

Haas oscillation measurements. Clear oscillations in resistivity and Hall resistivity can be observed under high magnetic field at different temperatures, as shown in **Figure 12(a)** and **(c)**. The oscillation amplitudes become more pronounced for higher magnetic field and lower temperature. However, the oscillatory periods measured at different temperatures remain constant, so only the data at 0.35 K with the most noticeable oscillations are selected to deduce the Landau level

superconductors. (a) Schematic diagram of Srx

superconductor opens a new gate to topological

[33]. Here, we put emphasis on the crystal structure and

ratio show no signs of superconductivity at 1.8 K, as

Bi2 Se3

Se3

of superconducting samples changes little with different Sr con-

single crystal has been investigated through Shubnikov-de

Bi2 Se3

crystal structure. (b) Powder

decreases slightly with increasing doping content (see **Figure 10(b)**). In

and isomorphic to the parent Bi2

Bi2 Se3 (PbSe)5

is very little so that it is hard

are smaller. The c-axis lattice

Bi2 Se3 (Bi2 Se3 ) 6

> Se3 . Sr

are a little larger

has only one

. **Figure** 

Bi2 Se3

**Figure 11.** Superconducting properties of Srx Bi2 Se3 . (a) Temperature dependence of resistivity for Srx Bi2 Se3 and Bi2− x Srx Se3 . (b) Hall resistivity versus magnetic field curves measured at different temperatures. (c) Temperature dependence of estimated Hall coefficient and charge carrier density. (d) Temperature dependence of susceptibility for samples with different Sr contents. (e) Plot of T<sup>c</sup> onset, Tc zero, and shielding volume fraction as a function of Sr content [7].

indices. In fact, the measured resistivity and Hall resistivity actually contain contributions from both the surface and bulk conductance when a large parallel bulk conduction channel is present. Therefore, the least confusing method is to convert resistivity into conductance to determine the Landau index because its components are additive [34]. The following equations are used to calculate conductance

$$\mathbf{G}\_{\text{x}\prime} = \frac{\mathbf{R}\_{\text{xx}}}{\mathbf{R}\_{\text{xx}}^2 + \mathbf{R}\_{\text{xy}}^2}, \quad \mathbf{G}\_{\text{xy}} = \frac{\mathbf{R}\_{\text{xy}}}{\mathbf{R}\_{\text{xx}}^2 + \mathbf{R}\_{\text{xy}}^2}. \tag{3}$$

After removing the nonoscillatory background, the oscillatory components are obtained and plotted as a function of 1/B. The frequencies are 146 T for longitudinal conductance and 144.8 T for Hall conductance, which are comparable to those of Bi2 Se3 but smaller than Cux Bi2 Se3 . The integer Landau index n corresponds to the valleys in ΔGxx, while the valleys in ΔGxy are assigned to n + 1/4 [see **Figure 13(a)** and **(c)**]. The 1/4 shift arises to match the valleys in dΔGxy/dB with the valleys in ΔGxx [34]. The obtained intercepts of the linear fittings for n versus 1/B are both close to the value for an ideal Dirac system, i.e., −0.5 rather than 0 or 1 (see **Figure 13(b)** and **(d)**). Thus, it provides transport evidence for the existence of Dirac fermions in Srx Bi2 Se3 superconductor.

**Figure 12.** SdH oscillations under high magnetic field for Sr<sup>x</sup> Bi2 Se3 single crystal. (a) and (c) Magnetic field dependence of resistivity and Hall resistivity at different temperatures. (b) and (d) Magnetic field dependence of the fitted longitudinal and Hall conductivity at 0.35 K [7].

attributed to the reduction of charge carrier density, which is apparent from the normal state resistivity. However, if the pressure continues to increase, the normal state resistivity begins

**Figure 14.** (a) Temperature dependence of magnetic susceptibility under different pressures. (b) and (c) Temperature

charge carrier density estimated from the normal state resistivity gradually increase with the

remains almost constant for the pressure up to 40 GPa, although the normal state resistivity

little under 80 GPa [35]. In fact, the whole process contains three structural phases, i.e., R-3 m, C2/m, and I4/mmm, as seen in **Figure 14(d)**. The structural transitions and pressure-invariant Tc

for selective systems. Hall effect and specific heat suggest that they are probably multiband

Se3

onset reaches around 8 K when P > 14 GPa. But unfortunately, the Tc

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123

. The crystal structure and various superconducting properties are reviewed

, which needs further investigations.

O4 S3 onset and the

Bi2 Se3 [35].

onset still changes

brings in a new BiS2

layer in LaO1−xFx

, and MFBiS2

BiSe2

onset


and

to decrease and a sign of superconducting transition occurs at 6 GPa. Then, the Tc

dependence of resistance under high pressure. (d) The structural phase diagram on pressure for Srx

keeps decreasing. The reemerging superconductivity is very robust and the Tc

based superconducting family, including the Bi─O─S compounds, Re(O,F)BiS2

The discovery of superconductivity in layered compound Bi4

superconductors. The superconducting layer is extended to BiSe2

increasing pressure, and Tc

**3. Conclusions**

FBiSe2

Sr1−xLax

are very similar to the parent compound Bi2

**Figure 13.** (a) and (c) Oscillatory component of the longitudinal and Hall conductivity at 0.35 K plotted against 1/B. (b) The Landau index n versus 1/B, where n and n + 1/2 correspond to the valleys and peaks of ΔGxx. (d) n versus 1/B derived from (c), where n + 1/4 corresponds to the valleys of ΔGxy [7].

The superconductivity of Srx Bi2 Se3 is very sensitive to external pressure below 1 GPa, as seen in **Figure 14(a)** and **(b)**. With the increasing applied pressure, the Tc and shielding volume fraction decrease but the normal state resistivity increases. This depression of superconductivity can be

Emerging Superconductivity and Topological States in Bismuth Chalcogenides http://dx.doi.org/10.5772/intechopen.73057 123

**Figure 14.** (a) Temperature dependence of magnetic susceptibility under different pressures. (b) and (c) Temperature dependence of resistance under high pressure. (d) The structural phase diagram on pressure for Srx Bi2 Se3 [35].

attributed to the reduction of charge carrier density, which is apparent from the normal state resistivity. However, if the pressure continues to increase, the normal state resistivity begins to decrease and a sign of superconducting transition occurs at 6 GPa. Then, the Tc onset and the charge carrier density estimated from the normal state resistivity gradually increase with the increasing pressure, and Tc onset reaches around 8 K when P > 14 GPa. But unfortunately, the Tc onset remains almost constant for the pressure up to 40 GPa, although the normal state resistivity keeps decreasing. The reemerging superconductivity is very robust and the Tc onset still changes little under 80 GPa [35]. In fact, the whole process contains three structural phases, i.e., R-3 m, C2/m, and I4/mmm, as seen in **Figure 14(d)**. The structural transitions and pressure-invariant Tc are very similar to the parent compound Bi2 Se3 , which needs further investigations.

## **3. Conclusions**

The superconductivity of Srx

Bi2 Se3

from (c), where n + 1/4 corresponds to the valleys of ΔGxy [7].

**Figure 12.** SdH oscillations under high magnetic field for Sr<sup>x</sup>

and Hall conductivity at 0.35 K [7].

122 Superfluids and Superconductors

**Figure 14(a)** and **(b)**. With the increasing applied pressure, the Tc

decrease but the normal state resistivity increases. This depression of superconductivity can be

**Figure 13.** (a) and (c) Oscillatory component of the longitudinal and Hall conductivity at 0.35 K plotted against 1/B. (b) The Landau index n versus 1/B, where n and n + 1/2 correspond to the valleys and peaks of ΔGxx. (d) n versus 1/B derived

Bi2 Se3

resistivity and Hall resistivity at different temperatures. (b) and (d) Magnetic field dependence of the fitted longitudinal

is very sensitive to external pressure below 1 GPa, as seen in

and shielding volume fraction

single crystal. (a) and (c) Magnetic field dependence of

The discovery of superconductivity in layered compound Bi4 O4 S3 brings in a new BiS2 based superconducting family, including the Bi─O─S compounds, Re(O,F)BiS2 , and MFBiS2 superconductors. The superconducting layer is extended to BiSe2 layer in LaO1−xFx BiSe2 and Sr1−xLax FBiSe2 . The crystal structure and various superconducting properties are reviewed for selective systems. Hall effect and specific heat suggest that they are probably multiband superconductors and can be described by BCS weak-coupling theory. Moreover, bismuth chalcogenide topological insulators can be turned into superconductors by doping, which are potential candidates for 3D topological superconductors. For example, the topological surface state of Srx Bi2 Se3 is well supported by SdH oscillations under high magnetic field. The intermediate external pressure can efficiently suppress the superconductivity, which reemerges when pressure is further increased, while Tc is nearly invariant in high-pressure region, indicating an unconventional pairing state.

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