Apparatus, systems, and methods for generating thermopower
A thermoelectric device includes a thermoelectrode characterized by a band gap less than k B T, where k B is the Boltzmann constant and T is a temperature of the thermoelectrode. The device also includes a magnetic field source, operably coupled to the thermoelectrode, to apply a magnetic field B on the thermoelectrode along a first direction. The device also includes a voltage source, operably coupled to the thermoelectrode, to apply an electric field E on the thermoelectrode along a second direction substantially perpendicular to the first direction so as to generate a heat flow along the second direction.
1. A thermoelectric device, comprising:
a thermoelectrode characterized by a band gap less than k B T, where k B is the Boltzmann constant and T is a temperature of the thermoelectrode;
a magnetic field source, operably coupled to the thermoelectrode, to apply a magnetic field B on the thermoelectrode along a first direction; and
a voltage source, operably coupled to the thermoelectrode, to apply an electric field E on the thermoelectrode along a second direction substantially perpendicular to the first direction so as to generate a heat flow along the second direction.
2. The thermoelectric device of claim 1 , wherein the thermoelectrode comprises a semimetal.
3. The thermoelectric device of claim 1 , wherein the thermoelectrode comprises a Weyl semimetal.
4. The thermoelectric device of claim 1 , wherein the thermoelectrode comprises a three-dimensional (3D) Dirac metal.
5. The thermoelectric device of claim 1 , wherein the thermoelectrode comprises a doped semiconductor having a doping concentration of about 10 15 cm −3 to about 10 19 cm −3 .
6. The thermoelectric device of claim 1 , wherein the magnetic field source is configured to generate the magnetic field B such that ν/l B is greater than E F , where is the Planck constant, ν is a Dirac velocity of charge carriers in the thermoelectrode, E F is the Fermi energy of the thermoelectrode, l B =√{square root over (/eB)}, and e is unit electron charge.
7. The thermoelectric device of claim 1 , wherein the magnetic field source is configured to generate the magnetic field substantially equal to or greater than 1 T.
8. The thermoelectric device of claim 1 , wherein the thermoelectrode has a first resistivity longitudinal to the first direction and a second resistivity transverse to the first direction, and the second resistivity is at least 5 times greater than the first resistivity.
9. The thermoelectric device of claim 1 , wherein charge carriers in the thermoelectrode are characterized by a linear dispersion.
10. A thermoelectric device, comprising:
a thermoelectrode characterized by a band gap less than k B T, where k B is the Boltzmann constant and T is a temperature of the thermoelectrode;
a magnetic field source, operably coupled to the thermoelectrode, to apply a magnetic field B on the thermoelectrode along a first direction; and
a heat source, operably coupled to the thermoelectrode, to apply a heat flow on the thermoelectrode along a second direction substantially perpendicular to the first direction so as to generate an electric field along the second direction of the heat flow.
11. The thermoelectric device of claim 10 , wherein the thermoelectrode comprises a semimetal.
12. The thermoelectric device of claim 10 , wherein the thermoelectrode comprises a Weyl semimetal.
13. The thermoelectric device of claim 10 , wherein the thermoelectrode comprises a three-dimensional (3D) Dirac metal.
14. The thermoelectric device of claim 10 , wherein the thermoelectrode comprises a doped semiconductor.
15. The thermoelectric device of claim 10 , wherein the magnetic field source is configured to generate the magnetic field B such that ν/l B is greater than E F , where is the Planck constant, ν is a Dirac velocity of charge carriers in the thermoelectrode, E F is the Fermi energy of the thermoelectrode, l B =√{square root over (/eB)}, and e is unit electron charge.
16. The thermoelectric device of claim 10 , wherein the magnetic field source is configured to generate the magnetic field substantially equal to or greater than 1 T.
17. The thermoelectric device of claim 10 , wherein ω c τ is substantially equal to or greater than 1, where ω c =|q|B/m, wherein q is an electric charge of charge carriers in the thermoelectrode, m is the mass of charge carriers in the thermoelectrode, and τ is a momentum scattering time of the charge carriers in the thermoelectrode.
18. The thermoelectric device of claim 10 , wherein charge carriers in the thermoelectrode are characterized by a linear dispersion.