Spontaneous Nernst effect in the iron-based superconductor ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{1-x}{\mathrm{Se}}_x$

We present a study of the Nernst effect in an iron-based superconductor with a nontrivial band topology ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{1-x}{\mathrm{Se}}_x$. A nonzero Nernst signal is observed in a narrow temperature region around the superconducting transition temperature $T_c$ at a zero field. This anomalous Nernst signal shows symmetric dependence on the external magnetic field and indicates an unconventional vortex contribution in an $s$-wave superconductor with a strong spin-orbit coupling, which is originated from the local magnetic moments of the interstitial Fe atoms. Our experiments also provide the first evidence of a locally broken time-reversal symmetry in bulk ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{1-x}{\mathrm{Se}}_x$ single crystals.

Figure 1

The zero-field thermoelectric responses of topological superconductor ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{1-x}{\mathrm{Se}}_x$. (a) Temperature $T$ dependence of the thermopower $kS$ (Seebeck signal) and the observed Nernst signal $e_N$ in sample 1. The thermopower signal $S$ was scaled by a factor $k=0.31$ to match the $T$ dependence of $S$ and $e_N$. (b) The same $T$ dependence of $S$ and $e_N$ for sample 4, which is in different batch and with different $T_c$. Similar to sample 1, sample 4 also shows that the observed Nernst signal $e_N$ matches the thermopower signal $S$ very well at $T>T_c$. However, a sharp peak appears around $T_c$. For both samples, the intrinsic spontaneous Nernst signal is extracted by subtracting the scaled thermopower signal $N_S\left(T\right)=e_N\left(T\right)-kS\left(T\right)$. (c), (d) Plot the intrinsic spontaneous Nernst signals $N_S$ vs $T$ in samples 1 and 4. The heater resistance is $1\mathrm{k}\mathrm{\Omega }$ for both samples.

Figure 2

Observed (a) Nernst signal $e_N$ and (b) Seebeck signal vs magnetic field $B$ at selected $T$ from 11 to 16 K in sample 1. (c) Ordinary Nernst signal $N_{AS}$ of sample 1 following the standard $B$ antisymmetrization to curves in (a). Arrows indicate the melting field $B_m$ of the vortex solid state. (d) Temperature dependence of the ordinary Nernst coefficient $\frac{N_{AS}}{B}$ at selected $B$ up to 13 T. The heater resistance is 1 $\mathrm{k}\mathrm{\Omega }$.

Figure 3

Magnetic field dependence of the intrinsic field-symmetrized Nernst signal. The Seebeck pickup has been subtracted [see Eq. (1)]. Arrows indicate the location of the shoulder trend $B_S$. Inset shows the temperature dependence of $B_S$, compared with the melting fields $B_m$. As expected for the characteristic field scales in superconductors, both fields converge to zero as the $T$ increases toward $T_c$. The heater resistance is 1 $\mathrm{k}\mathrm{\Omega }$.

Figure 4

(a) Fe concentration in ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{1-x}{\mathrm{Se}}_x$ samples 2, 3, 4, and 5. Error bars plot the standard deviation of Fe concentration on different sample spots. (b) The averaged peak values of the zero-field spontaneous Peltier Hall signal $|{\theta }^P|$, defined as the ratio of $|{\alpha }_{xy}|$ and ${\alpha }_{xx}$, in samples 6, 2, 3, 4, and 5, in the order that the nominal Fe concentration increases. As a comparison, iron concentration and $|{\theta }^P|$ in sample 1 are also plotted in (c). Samples 2, 3, 4, and 5 have a lower Te concentration compared to sample 1.

Figure 5

(a) Resistivity and (b) zero-field-cooled (ZFC) magnetic susceptibility in ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{1-x}{\mathrm{Se}}_x$ samples 1 to 6. The resistivity in sample 6 is multiplied by 10 for clarity and plotted in (a).

Figure 6

The Hall resistivity ${\rho }_{xy}$ measured at 14 K in ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{0.65}{\mathrm{Se}}_{0.34}$ sample 1. The inset shows the magnetoresistivity ${\rho }_{xx}$ measured at the same temperature. Red curve represents the field sweep up while blue curve represents the sweep down.

Figure 7

The Seebeck and Nernst signals measured with different cooling process in ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{1-x}{\mathrm{Se}}_x$ sample 4. Temperature $T$ dependence of the (a) thermopower $S$ (Seebeck signal) and (b) the observed Nernst signal $e_N$ in sample 4. (c) The intrinsic spontaneous Nernst signal is extracted by subtracting the scaled thermopower signal $N_S\left(T\right)=e_N\left(T\right)-kS\left(T\right)$. (d) Observed Nernst signal $e_N$ vs magnetic field $B$ at 11 K in sample 4. Black curves are taken with zero-field-cooled process. Red curves are taken with a 14-T field-cooled process. Green curves are taken with a $-14$-T field-cooled process. The field was applied at 350 K.

Figure 8

The zero-field Seebeck signal $S$ and Nernst signal $e_N$ measured in ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{1-x}{\mathrm{Se}}_x$ samples 1 to 6. For samples 1, 2, and 4, two Nernst channels are measured. For samples 3, 5, and 6, three Nernst channels are measured. The heater resistance is 1 $\mathrm{k}\mathrm{\Omega }$ for all the samples.

Figure 9

Observed (a) Nernst signal $e_{N2}$ and (b) Seebeck signal vs magnetic field $B$ at selected $T$ from 10 to 15 K in sample 2. (c) Ordinary Nernst signal $N_{AS}$ of sample 2 following the standard $B$ antisymmetrization to curves in (a). (d) Magnetic field dependence of the intrinsic field-symmetrized Nernst signal. Arrows indicate the location of the shoulder trend $B_S$. The Seebeck pickup has been subtracted. Inset shows the temperature dependence of $B_S$, compared with the melting fields $B_m$. As expected for the characteristic field scales in superconductors, both fields converge to zero as the $T$ increases toward $T_c$. The heater resistance is 1 $\mathrm{k}\mathrm{\Omega }$.

Figure 10

Observed (a) Nernst signal $e_{N2}$ and (b) Seebeck signal vs magnetic field $B$ at selected $T$ from 8 to 15 K in sample 3. (c) Ordinary Nernst signal $N_{AS}$ of sample 3 following the standard $B$ antisymmetrization to curves in (a). (d) Magnetic field dependence of the intrinsic field-symmetrized Nernst signal. Arrows indicate the location of the shoulder trend $B_S$. The Seebeck pickup has been subtracted. Inset shows the temperature dependence of $B_S$, compared with the melting fields $B_m$. As expected for the characteristic field scales in superconductors, both fields converge to zero as the $T$ increases toward $T_c$. The heater resistance is 1 $\mathrm{k}\mathrm{\Omega }$.

Figure 11

Observed (a) Nernst signal $e_{N1}$ and (b) Seebeck signal vs magnetic field $B$ at selected $T$ from 5 to 14 K in sample 4. (c) Ordinary Nernst signal $N_{AS}$ of sample 4 following the standard $B$ antisymmetrization to curves in (a). (d) Magnetic field dependence of the intrinsic field-symmetrized Nernst signal. Arrows indicate the location of the shoulder trend $B_S$. The Seebeck pickup has been subtracted. Inset shows the temperature dependence of $B_S$, compared with the melting fields $B_m$. As expected for the characteristic field scales in superconductors, both fields converge to zero as the $T$ increases toward $T_c$. The heater resistance is 1 $\mathrm{k}\mathrm{\Omega }$.

Figure 12

Observed (a) Nernst signal $e_{N1}$ and (b) Seebeck signal vs magnetic field $B$ at selected $T$ from 9 to 16 K in sample 5. (c) Ordinary Nernst signal $N_{AS}$ of sample 5 following the standard $B$ antisymmetrization to curves in (a). (d) Magnetic field dependence of the intrinsic field-symmetrized Nernst signal. Arrows indicate the location of the shoulder trend $B_S$. The Seebeck pickup has been subtracted. Inset shows the temperature dependence of $B_S$, compared with the melting fields $B_m$. As expected for the characteristic field scales in superconductors, both fields converge to zero as the $T$ increases toward $T_c$. The heater resistance is 1 $\mathrm{k}\mathrm{\Omega }$.

Figure 13

Observed (a) Nernst signal $e_{N2}$ and (b) Seebeck signal vs magnetic field $B$ at selected $T$ from 10 to 15 K in sample 6. (c) Ordinary Nernst signal $N_{AS}$ of sample 6 following the standard $B$ antisymmetrization to curves in (a). (d) Magnetic field dependence of the intrinsic field-symmetrized Nernst signal. Arrows indicate the location of the shoulder trend $B_S$. The Seebeck pickup has been subtracted. Inset shows the temperature dependence of $B_S$, compared with the melting fields $B_m$. As expected for the characteristic field scales in superconductors, both fields converge to zero as the $T$ increases toward $T_c$. The heater resistance is 1 $\mathrm{k}\mathrm{\Omega }$.

Figure 14

(a) Observed Nernst signal $e_{N1}$, $e_{N3}$ and Seebeck signal $S$ vs $T$ at $B=0$ T for FeSe sample 1. Observed (b) Nernst signal $e_{N3}$ and (c) Seebeck signal $S$ vs magnetic field $B$ at selected $T$ from 4 to 21 K in FeSe sample 1. (d) Ordinary Nernst signal $N_{AS}$ of FeSe sample 1 following the standard $B$ antisymmetrization to curves in (b). The heater resistance is 1 $\mathrm{k}\mathrm{\Omega }$.

Figure 15

Thermal conductivity ${\kappa }_{xx}$ and thermal Hall conductivity ${\kappa }_{xy}$ measured in ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{0.65}{\mathrm{Se}}_{0.34}$ sample 1 at (a) $B$ = 1 T and (b) $B$ = 4 T. The thermal Hall angle ${\theta }_H$ is extracted from the ratio of the thermal Hall conductivity and thermal conductivity with $\tan {\theta }_H=\frac{{\kappa }_{xy}}{{\kappa }_{xx}}$.

Figure 16

(a) Experimental configuration of ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{1-x}{\mathrm{Se}}_x$ sample 1, which is the same as the ${\mathrm{Fe}}_{1+y}{\mathrm{Te}}_{1-x}{\mathrm{Se}}_x$ sample 1 configuration in the main text. Six contacts were remade to make sure they are well aligned. $S_x$ and $S_{x^{\prime }}$ are two Seebeck channels being measured simultaneously. Blue solid circles are electrical contacts. Dashed lines and arrows label the distance between the contacts. (b)–(d) Measured Seebeck coefficients for three pairs of Seebeck channels. The Seebeck coefficients of channel $S_1^{\prime }$ overlap with channel $S_1$ after multiplying by a factor of 0.94. The scaling factor between Seebeck channels $S_2$ and $S_2^{\prime }$, $S_3$ and $S_3^{\prime }$ are 0.84 and 0.87. Gray solid lines mark $S=0$ with their widths indicate the error bar of the Seebeck coefficient. The heater resistance is 1 $\mathrm{k}\mathrm{\Omega }$. The heater current is 0.4 mA. (e) Temperature dependence of the thermopower $kS$ (Seebeck signal) and the observed Nernst signal $e_N$ in sample 1. The thermopower signal $S$ was scaled by a factor $k=0.16$ to match the $T$ dependence of $S$ and $e_N$. (f) The intrinsic spontaneous Nernst signals $N_S$ vs $T$ in sample 1, which is extracted by subtracting the scaled thermopower signal $N_S\left(T\right)=e_N\left(T\right)-kS\left(T\right)$.