Discovery of log-periodic oscillations in ultraquantum topological materials

Abstract

Discovery of log-periodic quantum oscillations may open a new chapter in the nearly 90-year history of quantum oscillations.

Scaling symmetry meets topology

“…Similar to the Efimov effect discussed above, the short range boundary condition breaks it down to the discrete scale invariance and results in an infinite number of quasi-bound states forming a geometric sequence [10,11]. The experiment by Wang et al [12] reported the observation of such discrete scale invariance in single-crystal three-dimensional Dirac semi-metal ZrTe 5 . The ZrTe 5 crystallizes in a layered orthorhombic structure with the space group Cmcm.…”

“…Nevertheless, these studies have so far been limited to atomic and nuclear systems. The recently published experiment by Wang et al [12] brings the Efimov physics into condensed matter system by observing such a universal discrete scaling symmetry in the topological semi-metals. The topological semi-metal has received considerable attentions in the past decades.…”

Discrete scale invariance and ln(B) periodic quantum oscillations in topological semimetals

“…The clearest case is the recent discovery in the layered bulk material ZrTe 5 , where 5 cycles of oscillations have been observed by further increasing the magnetic field when the lowest Landau level is occupied. Amazingly, the oscillations show clear ln(B) behavior [9], as seen in Figure 1, taken from this reference. The periodicity is entirely new: the peaks in the resistance are periodic in ln(B), not B or 1/B.…”

Magnetic field-induced electronic phase transition in the Dirac semimetal state of black phosphorus under pressure

“…The recently discovered topological semimetal, a family of 3D topological materials including Dirac semimetal, Weyl semimetal and node-line semimetal [13][14][15][16][17][18][19][20][21][22], serves as a good system to test the behaviors of 3D pseudorelativistic electron gas under high magnetic field, as its members usually have low QL fields and weak impurity scatterings [23][24][25]. Different anomalies on both magnetoresistance and magnetic torque have been observed in the QL regime in topological semimetal ZrTe 5 , TaAs and NbAs [25][26][27][28]. Lately, annihilation of Weyl nodes above the QL field, a unique feature reflecting topological nontriviality, is also observed in Weyl semimetal TaP and TaAs [29,30].…”