Quantum oscillation
Huanlong Liu 01.Dec.2020
Condensed Matter Physics (PHY 401)
Content
Quantum oscillations family
[1] L. Schubnikow and W. J. De Haas, Nature (London) 126,500 (1930).
[2] R. A. Webb, S. Washburn, C. Umbach, and R. A. Laibowitz, Phys. Rev. Lett. 54, 2696 (1985).
Theoretically proposed in 1959 by Aharonov and Bohm.
[3] H. Wang, etc. Science Advances, 4, eaau5096 (2018)
SdH Quantum oscillations
ћω
c> k
BT
Thermal Condition:
When Landau level splitting > thermal energy ， The state density of the material will be periodic with the change of the reciprocal of magnetic field, which leads to the quantum oscillation of various physical quantities related to the state density.
Quantum oscillations family
*J
0� � = 2 π2� � � m∗/e ћ ���� θ
sinh (2π2� � � m∗/e ћ ���� θ)
� �=exp(− � �(�)
� )
π � m∗
2(1+ λ) � � ��� θ
� �=¿ cos ¿
where
Low temperature
Strong magnetic field
High-quality single crystals
Lidshitz-Kosevich (LK ) Function:
Measured Conditions:
B. J. Ramshaw, etc. Nature Phys 7, 234–238 (2011)
SdH Quantum oscillations--Quasiparticle mass
High-Tc superconductor:
YBa2Cu3O6+δ
B. J. Ramshaw, etc. Science 348 (6232), 317-320
Quasiparticle mass enhancement approaching optimal doping in a high-Tc superconductor
Fig. 1. Cuprate temperature-doping phase diagram.
The charge order, the onset of the pseudogap (open red circles), the polar Kerr effect (open red diamonds), and the change in the slope of resistivity with temperature (open red triangles) terminate near p = 0.18, suggesting the possibility of a quantum critical point (QCP) at this doping.
AFM
SC
SdH Quantum oscillations--Quasiparticle mass
Fig. 2. Quantum oscillations of the magnetoresistance in YBa2Cu3O6+δ
B. J. Ramshaw, etc. Science 348 (6232), 317-320
SdH Quantum oscillations--Quasiparticle mass
�(� )= 2π2� �� /ћ ω �
sinh (2π2 � � � /ћ ω�) ω �=e � /m∗
Fig. 3.The quasiparticle effective mass in YBa2Cu3O6+δ B. J. Ramshaw, etc. Science 348 (6232), 317-320
SdH Quantum oscillations--Quasiparticle mass
Fig. 4. A quantum critical point near optimal doping.
Firstly, the critical fluctuations surrounding pcrit ≈ 0.08 and pcrit ≈ 0.18 provide two independent pairing
mechanisms for YBCO.
Secondly, a single underlying pairing mechanism leads to varies smoothly of upper critical field with doping.
B. J. Ramshaw, etc. Science 348 (6232), 317-320
SdH Quantum oscillations--Quasiparticle mass
Fig. 4. A quantum critical point near optimal doping.
.
FIG. 2. (Color online) Doping dependence in zero magnetic field of the CDW peak intensity in YBCO
Firstly, the CDW reconstructs the Fermi surface and the other hidden form of order drives quantum criticality near p ≈ 0.18.
Secondly, CDW order is coexistent with another form of order that also terminates near pcrit ≈0.18.
Doping dependence of the antiferromagnetic ordering temperature TN, the incommensurate spin-density wave order TSDW the superconducting temperature Tc and the pseudogap temperature T*. Below temperature scale TH a larger and negative Hall coefficient was observed and interpreted in terms of a Fermi surface reconstruction.
B. J. Ramshaw, etc. Science 348 (6232), 317-320 J. Chang et al., Nat. Phys. 8, 871–876 (2012).
M. Hücker et al., Phys. Rev. B 90, 054514 (2014).
Thanks for your attention ！
SdH Quantum oscillations—Fermi surface
Devarakonda et al., Science 370, 231–236 (2020)
SdH Quantum oscillations—Fermi surface
Devarakonda et al., Science 370, 231–236 (2020)
The oscillation frequency can be related to the Fermi surface cross-secction using the Onsager relationship:
π �� 2= 2 π 2 � / Φ 0
