first-principle study of structural, electronic

First-principle study of structural, electronic, thermoelectric andvibrational properties of Co2-based Weyl semimetal VCo2Al

TAVNEET KAUR* and MURARI MOHAN SINHADepartment of Physics, Sant Longowal Institute of Engineering and Technology, Sangrur 148106, India

*Author for correspondence ([email protected])

MS received 9 July 2020; accepted 26 August 2020

Abstract. The class of semimetals has emerged as upcoming future devices due to their technological efficient

applications. The distinctive component in semimetals is the simultaneous manipulation of spin states along with elec-

tronic states that has prompted the discovery of spin ordering at Fermi level. The current investigation is first-principle

approach to compute structural, electronic, thermoelectric and vibrational properties of VCo2Al. The systematic and

detailed theoretical investigation based on density functional theory in combination with Boltzmann transport theory has

been done for the first time. The structural properties namely lattice constant, bulk modulus and pressure derivative of

bulk modulus have been calculated, revealing that VCo2Al gets stiffer on applying pressure. The plotted electronic band

structure shows band dispersion at two discrete points at Fermi level specifying VCo2Al to be Weyl semimetal. The joint

analysis of electronic band structure and plotted density of states affirms the band dispersion and presence of Weyl

electrons at Fermi level. The present investigation purposes VCo2Al as an excellent n-type high temperature thermo-

electric material having power factor of 184.3 9 1014 lW cm-1 K-2 s-1 at 800 K. The vibrational properties calculated

within the framework of density functional perturbation theory uncover the dynamic stability of VCo2Al. The computed

physical properties from these calculations would create new frontiers of experimental work for further realization of

innovative applications.

Keywords. Co-based Heusler; first-principle study; DFT; thermoelectric; electronic.

1. Introduction

The multifunctional properties of Weyl semimetals have the

potential to revolutionize the prevailing technology. This

class of compounds came into picture in the year 1929 when

Hermann Weyl speculated the presence of massless Weyl

Fermions in Dirac equation [1]. Weyl Fermions have not

been discovered for more than a century and their existence

has been recently reported in Weyl semimetals [2]. These

massless Fermions exist as low-energy excitations of the

Weyl semimetal, in which, singly degenerate band disperse

in the form of discrete points at Brillouin zone (BZ) called

Weyl points.

In this study, we list recently accounted Weyl

semimetals and acquaint VCo2Al to be a new candidate

under the category of Weyl semimetals. Since their dis-

covery, Weyl semimetals have pulled in incredible

exploration enthusiasm in the field of Material Physics. In

2015, Weyl signatures were accounted in TaAs [3–5],

TaP [6], NbAs, NbP [7,8] as well as in photonic crystals

[9] by a research team in Princeton by angle resolved

photoemission spectroscopy measurements. Iridates like

Y2Ir2O7 and HgCr2Se4 have likewise been anticipated as

Weyl semimetals [10]. The existence of Weyl nodes in

BZ has been reported on the inclusion of spin orbital

coupling in Co2TiX (X = Si, Ge or Sn) [11]. Chang et al[12] predicted Co2MnGa to be a candidate of Weyl

semimetal by first-principle band calculations and

observed the existence of w-shaped surface along mid-

point of U-M and V-shaped surface along U-X line.

Belopolski et al [13] experimentally demonstrated

Co2MnGa to be Weyl semimetal by photoemission

spectroscopy and quantum transport. Markou et al [14]conducted a systematic analysis of the structural and

magneto-transport properties of Co2MnGa films from thin

(20 nm) to bulk-like behaviour (80 nm) in order to

understand the underlying mechanisms and the role of

topology.

The Weyl semimetals are a rich family of materials

having exotic properties specifically ultra-high mobility

and the chiral anomaly [15–17]. The electrons in Weyl

semimetals are ten times faster than in conventional

semiconductor. They could replace silicon that is used in

transistors, diodes, integrated circuits, computer chips, cell

phones and in other electronic devices by operating at high

speeds with lower power requirements [18]. An expanding

interest in semimetals is due to upcoming optical and

electronic applications ranging from remote sensing to

Bull Mater Sci (2021) 44:27 � Indian Academy of Scienceshttps://doi.org/10.1007/s12034-020-02305-1Sadhana(0123456789().,-volV)FT3](0123456789().,-volV)

medicine [19]. To bring the class of high potential Weyl

semimetals into practical technological applications, a

total comprehension of physical properties is required. In

the present examination, systematic and detailed investi-

gation of structural, electronic, thermoelectric and vibra-

tional properties of VCo2Al has been carried out by

employing density functional theory-based simulation

code quantum espresso [20]. We present VCo2Al to be the

candidate of the class of Weyl semimetal with very

intersecting band crossing at Fermi level. The literature

reveals only the value of lattice constants, while other

physical properties are not available in the literature [21].

2. Methodology

This study focuses at the computation of structural,

electronic, thermoelectric and vibrational properties of

cobalt-based Weyl semimetal VCo2Al by employing the

plane wave basis set, which has been carried out using

quantum espresso [20]. The exchange correlation func-

tional of Perdew–Zunger (PZ) [22] is used within local

density approximation to depict the interaction between

the nuclei and valence shell electrons. The use of full

relativistic pseudopotential includes the effect of spin

orbital coupling.

The structure has been relaxed by varying the kinetic

energy cut off for plane wave basis set, k-points mesh

density, degauss and lattice cell constant for the least

possible value of total energy. To achieve excellent

convergence, the kinetic energy cut off of 100 Ry has

been selected for the expansion of plane wave basis set.

Monkhorst and Pack [23] matrix of 69696 k-points has

been used for meshing the BZ to compute structural and

electronic properties. The k-mesh of 25925925 has been

utilized for the computation of thermoelectric properties.

The value of degauss has been selected to be 0.02. The

iterative procedure of self-consistent SCF calculations is

employed until the total energy of the system is

stable within 10-8 Ry. The thermoelectric properties of

VCo2Al have been computed using BoltzTraP [24],

which is based on semi-classical Boltzmann transport

equation (BTE). The force constants for phonon disper-

sion calculations have been derived from 49494 q-mesh

in the BZ of U-X-K-U-L using density functional per-

turbation theory [25].

The full Heusler VCo2Al having face-centred cubic

crystal structure with space group Fm�3m (No 225) has

been studied. The Wyckoff positions of VCo2Al with Al

at 4a (0, 0, 0), V at 4b (0.5, 0.5, 0.5), Co at 4c (0.25, 0.25,

0.25) and 4d (0.75, 0.75, 0.75) are shown in figure 1. The

three-dimensional view of crystal structure is displayed

using XcrySDen [26] (X-Window) Crystalline Structure

& Densities, as illustrated in figure 1. It visualizes crys-

talline and molecular structures and unveils contours and

isostructures.

3. Results and discussion

3.1 Structural properties

The geometrical optimization involves the calculation of

cell volume at minimum value of energy, which gives the

ground state energy, as shown in figure 2. The calculated

value of energy as a function of unit cell volume is fitted to

third-order Birch–Murnaghan equation of state [27] in order

to obtain equilibrium lattice constant (a0), bulk modulus (B)and the first-order derivative of bulk modulus (B0) at zeroGiga Pascal pressure and zero Kelvin temperature as stated

below:

E ðVÞ ¼ E0 þ9BV0

16� V0

V

� �23

�1

" #3

B0

8<:

þ V0

V

� �23

�1

" #2

6� 4V0

V

� �23

" #9=;; ð1Þ

where E0 is minimum energy, V0 is optimized volume, V is

deformed volume. P is the pressure, B the bulk modulus and

B0 is pressure derivative of bulk modulus given by:

P ¼ dE

dV; B ¼ V

dP

dV¼ d2E

dV2; B0 ¼ dB

dP: ð2Þ

The obtained converged value of equilibrium lattice

constant is 5.691 A, which is consistent with the experi-

mental value of 5.779 A [21] of VCo2Al as tabulated in

table 1. The large value of bulk modulus (273.3 GPa)

indicates that VCo2Al is hard and the positive value of

pressure derivative of bulk modulus (4.34) specifies the

rigidity of crystal on applying pressure [28].

3.2 Electronic properties

The electronic properties compute the band structure, which

indicates the nature of bonding within the atoms and

determines the nature of material. The electronic band

structure has been plotted for the high symmetry directions

W-L-U-X-W-K. To obtain electronic band structure, the

Fermi energy is shifted at origin by subtracting (EF)

17.4296 eV from computed energies of VCo2Al. It is clear

from the zoomed and focused low-energy window at Fermi

level in electronic band structure (shown in figure 3a) that

there is dispersion of lowest lying conduction band (CB)

and the upper lying valence band (VB) at two discrete

points specifying VCo2Al to be Weyl semimetal. The

plotted band structure from first-principle study reveals the

formation of two Weyl points when going from U-X and

X-W across the BZ. The incorporation of spin orbital cou-

pling reports VCo2Al to be Weyl semimetal specified by

band dispersion of the VB and CBs at two discrete points

called Weyl nodes. Our result is consistent as earlier Weyl

27 of 8 Bull Mater Sci (2021) 44:27

Figure 1. The crystal structure of VCo2Al.

Figure 2. The variation of total energy of systemwith respect to volume in Birch–Murnaghan fit.

Bull Mater Sci (2021) 44:27 of 8 27

nodes have been reported for Co2TiX (X = Si, Ge or Sn)

[11] and Co2MnGa [12] along high symmetry BZ.

In addition to this, total and partial density of states have

been plotted as shown in figure 3b. The plotted partial

density of states illustrate the contribution of each orbital

responsible for electronic properties. The band dispersion is

also affirmed by the plot of total and partial density of

states. It is evident from figure 3b that low energy region

from -100 to -20 eV originates mainly from s and p

orbitals of cobalt and vanadium. In high energy region of

VB from -20 to 0 eV, d orbitals of cobalt has major con-

tribution, while d orbitals of vanadium has little contribu-

tion. In region of positive energy from 0 to 20 eV of CB

originates mainly from d orbitals of vanadium and cobalt.

The hybridization of p orbitals of aluminium, d orbitals of

cobalt and vanadium is responsible for the dispersion of

bands and presence of Weyl electrons at Fermi level. The

availability of Weyl electrons at two discrete Weyl points

would lead to enhanced carrier mobility.

3.3 Thermoelectric properties

The Boltzmann transport theory has been employed using

BoltzTraP code [24] to compute electronic transport prop-

erties of VCo2Al, namely Seebeck coefficient, electrical

Table 1. The lattice constant (a0), bulk modulus (B) and the

pressure derivative of bulk modulus (B0) of VCo2Al.

Reference a0 (A) B (GPa) B0

VCo2Al Present 5.691 237.3 4.34

Experimental [21] 5.779 — —

Figure 3. (a) The plot of electronic band structure and (b) the plot of total and partial

density of states (DOS).


conductivity, thermal conductivity and thermoelectric

power factor as a function of chemical potential (l) for 300,600 and 800 K and also as a function of temperature over

the range from 50 to 800 K.

3.3a Seebeck coefficient (S): The graph of Seebeck

coefficient plotted as function of chemical potential shows

the maxima and minima at 0 eV for 300, 600 and 800 K. At

300 K, the maximum positive attainable value of Seebeck

Figure 4. The variation of Seebeck coefficient with (a) chemical potential and (b) temperature. The variation of

electrical conductivity with (c) chemical potential and (d) temperature. The variation of electronic thermal

conductivity with (e) chemical potential and (f) temperature. The variation of thermoelectric power with (g) chemical

potential and (h) temperature.


coefficient is 303 lV K-1 for the zero value of chemical

potential as shown in figure 4a. The maximum negative

value of Seebeck coefficient is -441 lV K-1, which is

comparable to obtained -592.02 lV K-1 value for Sc2FeSi

[29].

The curve of Seebeck coefficient attains higher value of

negative maxima in comparison to positive maxima at zero

chemical potential clearly, specifying that n-type doping

will be fruitful in improving the thermoelectric perfor-

mance. We thereby purpose that doping of Al with Si will

certainly plunge the thermoelectric performance to great

heights. The value of Seebeck coefficient is found to

decrease with the corresponding increase in temperature

and the value is highest at room temperature. The line graph

showing the variation of Seebeck coefficient with temper-

ature attains maxima at room temperature, also shown in

figure 4b.

3.3b Electrical conductivity (r/s): The value of

electrical conductivity divided by relaxation time

experiences increase with the subsequent rise in the value

of chemical potential. Across the positive side of chemical

potential, the value of r/s undergoes a significant rise after

the value of 1 eV. The maximum attained value of electric

conductivity is 12.69 9 1020 X-1 m-1 s-1 for 2 eV value of

chemical potential, as shown in figure 4c. The maxima for

positive value of chemical potential indicates that n-type-doped impurity will lead to high thermoelectric power.

Figure 4d shows a slight increase in the value of electrical

conductivity with the corresponding increase in

temperature.

3.3c Electronic thermal conductivity (je/s): The value

of electronic thermal conductivity divided by relaxation

time rises with the corresponding increase in chemical

potential for 300, 600 and 800 K. For 2 eV value of

chemical potential, the attained maximum for 800 K is at

24.15 9 1015 W m-1 K-1 s-1, for 600 K the maxima is at

18.07 9 1015 W m-1 K-1 s-1 and for 300 K maxima is at

9.292 9 1015 W m-1 K-1 s-1, as shown in figure 4e. As the

value of temperature is increased from 300 to 600 K and

then to 800 K, the value of je/s showed significant rise due

to the subsequent enhancement of carrier concentration, as

shown in figure 4f.

3.3d Thermoelectric power factor (S2r/s): The higher

value of Seebeck coefficient and electrical conductivity

leads to high power factor and consequently to good

thermoelectric material [30]. The positive values of

chemical potential represent electron doping, while the

negative values represent hole doping. It is clearly stated in

figure 4g that the peak values of the power factor are for the

positive values of chemical potential over the mentioned

range of temperature for 300, 600 and 800 K. The obtained

maximas for the positive value of chemical potential

indicate that n-type electrons act as majority carriers.

Power factor could be further enhanced by electron doping

rather than hole doping for the same values of chemical

potential, clearly indicating that thermoelectric performance

can be enriched by doping of n-type composition. The peak

values for the positive value of chemical potential

are at 42.27 9 1014, 122.8 9 1014 and 184.3 9

1014 lW cm-1 K-2 s-1 for 300, 600 and 800 K,

respectively. At 300 K, power factor maxima is at 42.27

9 1014 lW cm-1 K-2 s-1 comparable to that for Bi2Te3[31], which is one of the well-established thermoelectric

material. Figure 4h illustrates that with the rise in

temperature; the value of power factor arouses

significantly and attains maxima at 800 K. The present

figured outcomes reveal that VCo2Al is the best

thermoelectric material at high temperature.

3.4 Vibrational properties

The dynamical vibrational properties have been computed

within the framework of density functional perturbation

theory [25], as phonon frequencies are second-order

derivatives of energy subjected to atomic displacements.

The phonon dispersion curve (PDC) is plotted without

incorporating the spin orbital coupling along the high

symmetry directions of C-X-K-C-L for the cubic phase of

VCo2Al. There are four atoms in the primitive unit cell of

VCo2Al. Consequently, a total of twelve phonon modes are

observed, as shown in figure 5. Out of which three phonon

modes with zero frequency at zone centre are acoustic

modes and the rest nine with higher frequency at zone

centre are optical branches. The computed phonon fre-

quencies for all the twelve modes are positive, specifying

the dynamic stability of VCo2Al.

The computed total and partial density of states (PDOS)

indicate the contribution of each atom in the obtained

phonon modes. The plot of PDOS as shown in figure 6

clearly signifies that the lower mass aluminium contributes

to the higher optical phonon modes, while higher mass

atoms cobalt and vanadium contribute to the acoustic and

lower optical modes. In terms of frequency, PDC (as shown

Figure 5. The phonon dispersion curve of VCo2Al.


in figure 5) has been classified into two zones, namely the

upper frequency zone (UFZ) and lower frequency zone

(LFZ). The LFZ consist of nine phonon modes, varying

frequency from 0 to 283.4 cm-1 due to higher mass atoms

cobalt and vanadium. The UPZ attributes to three phonon

modes in frequency range 334.4 to 365 cm-1 due to lower

mass aluminium atom. It is evident from the PDC and plot

of density of states that band gap of 51 cm-1 exists between

UFZ and LFZ, arising from the difference in mass of alu-

minium in comparison to the mass of cobalt and vanadium.

Thereby, it has been concluded that higher frequency mode

arises from lighter atoms, while the lower frequency mode

arises from heavier atoms.

4. Conclusion

Weyl semimetals have emerged as a rich family of materials

having upcoming applications in spintronics and electronics

[32]. The structural properties reveal that VCo2Al gets

stiffer on applying pressure. The electronic band structure

plotted from first-principle calculations specifies VCo2Al to

be Weyl semimetal. The dispersion of bands at Fermi level

in electronic band structure and plotted density of states

indicate the presence of Weyl electrons with enhanced

electron mobility. This study concludes VCo2Al to be an

excellent thermoelectric material having high thermoelec-

tric power of 184.3 9 1014 lW cm-1 K-2 s-1 at 800 K,

comparable to that of Bi2Te3 [31]. Our calculations further

reveal that n-type-doped Si in place of Al will enhance the

thermoelectric performance. As far as the stability of crystal

is concerned, it is clearly stated by the calculated positive

phonon frequencies. The predictions of physical properties

from these calculations would create future scope of

experimental work for further acknowledgement of fasci-

nating applications of VCo2Al.

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