Theory of Magnetoresistance in Three-Dimensional Dirac Materials - PowerPoint PPT Presentation

Theory of Magnetoresistance in Three-Dimensional Dirac Materials

<latexit sha1_base64="7WQLI25XV1F3tBd3haFE2R5xPE=">ACGHicbZBNS8MwGMfT+TbnW9Wjl+AQtoOzFUEvgzEvHie4F1jLSN0C0vTkqTCKPsYXvwqXjwo4nU3v43pVlA3Hwj58f8/D8nz92JGpbKsL6Owtr6xuVXcLu3s7u0fmIdHRklApM2jlgkeh6ShFO2oqRnqxICj0GOl649vM7z4SIWnEH9QkJm6IhpwGFCOlpYF54fiEKeSIUVR3AoFwmGlWT1f3HWrOk1/sDQwy1bNmhdcBTuHMsirNTBnjh/hJCRcYak7NtWrNwUCUxI9OSk0gSIzxGQ9LXyFIpJvOF5vCM634MIiEPlzBufp7IkWhlJPQ050hUiO57GXif14/UcGNm1IeJ4pwvHgoSBhUEcxSgj4VBCs20YCwoPqvEI+QjkfpLMQ7OWV6FzWbOtmn1/VW408ziK4AScgqwTVogDvQAm2AwRN4AW/g3Xg2Xo0P43PRWjDymWPwp4zZN/65nmo=</latexit> <latexit sha1_base64="7WQLI25XV1F3tBd3haFE2R5xPE=">ACGHicbZBNS8MwGMfT+TbnW9Wjl+AQtoOzFUEvgzEvHie4F1jLSN0C0vTkqTCKPsYXvwqXjwo4nU3v43pVlA3Hwj58f8/D8nz92JGpbKsL6Owtr6xuVXcLu3s7u0fmIdHRklApM2jlgkeh6ShFO2oqRnqxICj0GOl649vM7z4SIWnEH9QkJm6IhpwGFCOlpYF54fiEKeSIUVR3AoFwmGlWT1f3HWrOk1/sDQwy1bNmhdcBTuHMsirNTBnjh/hJCRcYak7NtWrNwUCUxI9OSk0gSIzxGQ9LXyFIpJvOF5vCM634MIiEPlzBufp7IkWhlJPQ050hUiO57GXif14/UcGNm1IeJ4pwvHgoSBhUEcxSgj4VBCs20YCwoPqvEI+QjkfpLMQ7OWV6FzWbOtmn1/VW408ziK4AScgqwTVogDvQAm2AwRN4AW/g3Xg2Xo0P43PRWjDymWPwp4zZN/65nmo=</latexit> <latexit sha1_base64="7WQLI25XV1F3tBd3haFE2R5xPE=">ACGHicbZBNS8MwGMfT+TbnW9Wjl+AQtoOzFUEvgzEvHie4F1jLSN0C0vTkqTCKPsYXvwqXjwo4nU3v43pVlA3Hwj58f8/D8nz92JGpbKsL6Owtr6xuVXcLu3s7u0fmIdHRklApM2jlgkeh6ShFO2oqRnqxICj0GOl649vM7z4SIWnEH9QkJm6IhpwGFCOlpYF54fiEKeSIUVR3AoFwmGlWT1f3HWrOk1/sDQwy1bNmhdcBTuHMsirNTBnjh/hJCRcYak7NtWrNwUCUxI9OSk0gSIzxGQ9LXyFIpJvOF5vCM634MIiEPlzBufp7IkWhlJPQ050hUiO57GXif14/UcGNm1IeJ4pwvHgoSBhUEcxSgj4VBCs20YCwoPqvEI+QjkfpLMQ7OWV6FzWbOtmn1/VW408ziK4AScgqwTVogDvQAm2AwRN4AW/g3Xg2Xo0P43PRWjDymWPwp4zZN/65nmo=</latexit> <latexit sha1_base64="7WQLI25XV1F3tBd3haFE2R5xPE=">ACGHicbZBNS8MwGMfT+TbnW9Wjl+AQtoOzFUEvgzEvHie4F1jLSN0C0vTkqTCKPsYXvwqXjwo4nU3v43pVlA3Hwj58f8/D8nz92JGpbKsL6Owtr6xuVXcLu3s7u0fmIdHRklApM2jlgkeh6ShFO2oqRnqxICj0GOl649vM7z4SIWnEH9QkJm6IhpwGFCOlpYF54fiEKeSIUVR3AoFwmGlWT1f3HWrOk1/sDQwy1bNmhdcBTuHMsirNTBnjh/hJCRcYak7NtWrNwUCUxI9OSk0gSIzxGQ9LXyFIpJvOF5vCM634MIiEPlzBufp7IkWhlJPQ050hUiO57GXif14/UcGNm1IeJ4pwvHgoSBhUEcxSgj4VBCs20YCwoPqvEI+QjkfpLMQ7OWV6FzWbOtmn1/VW408ziK4AScgqwTVogDvQAm2AwRN4AW/g3Xg2Xo0P43PRWjDymWPwp4zZN/65nmo=</latexit> Magnetoresistance Magnetoresistance is the tendency of a material to change the value of its electrical resistance in an externally-applied magnetic field. -- Wikipedia • Geometrical magnetoresistance • Shubnikov de Haas oscillations • Anisotropic magnetoresistance (AMR) • Giant magnetoresistance (GMR) Tunnel magnetoresistance (TMR) • • Colossal magnetoresistance (CMR) in manganites Negative longitudinal magnetoresistance in Weyl/Dirac semimetals • • ….............. δρ = ρ ( B ) − ρ ( B = 0) ρ ( B = 0) Magnetoresistance/Aug 22, 2019, Seoul

Lorentz Force Induced MC Relaxation time approximation md v dt = q ( E + v × B ) d v dt → v en e v → j τ j = σ E + µ j × B ρ = 1 μ is the electric mobility. E = 1 σ j − µ σ j × B No magnetoresistance σ µ 2 σ µ σ σ j = 1 + µ 2 B 2 E + 1 + µ 2 B 2 ( E · B ) B + 1 + µ 2 B 2 E × B E perpendicular to B: E parallel with B: σ j = σ E j = 1 + µ 2 B 2 E Usually the transverse magnetoconductivity is negative. Magnetoresistance/Aug 22, 2019, Seoul

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c ⌧ + ! c ⌧ 1 1 + ( ! c ⌧ ) 2 m ∗ Perpendicular magnetoresistivity tensor Several mechanisms to produce MR: • Energy dependence of the relaxation time ✓ ◆ ⇢ ( B ) = m ∗ 1 • Anisotropy of the band structure ! c ⌧ 1 % e 2 ⌧ Multiple bands • − ! c ⌧ ……….. • In the spherical one-band model with a Two-band model: one charge carrier is of single relaxation time, the diagonal electron while the other is of hole magnetoresistivity turns out to be independent from the magnetic field The Hall coefficient is independent both from the effective mass and the relaxation time. Magnetoresistance/Aug 22, 2019, Seoul

In this talk 1. Intrinsic Magnetoresistance in 3D topological materials 2. Theory of weak localization and anti-localization in 3D topological materials 3. Anomaly-induced magnetoresistivity in massive Dirac materials Dr. Bo Fu Mr. Huan-Wen Wang Postdoc., HKU Ph.D candidate., HKU B. Fu, H. W. Wang & S. Q. Shen, arXiv: 1909.09297 B. Fu, H. W. Wang & S. Q. Shen, PRL 122, 246601 (2019) H. W. Wang, B. Fu, and S. Q. Shen, PRB 98, 081202(R) (2018) Magnetoresistance/Aug 22, 2019, Seoul

From Dirac to Weyl When the mass m=0, the Dirac equation is reduced into The Pauli matrices Electron spin • Anti-particle • Dirac sea • Magnetoresistance/Aug 22, 2019, Seoul