We present a magneto-infrared spectroscopy study on a newly identified three-dimensional (3D) Dirac semimetal ZrTe 5 . We observe clear transitions between Landau levels and their further splitting under magnetic field. Both the sequence of transitions and their field dependence follow quantitatively the relation expected for 3D massless Dirac fermions. The measurement also reveals an exceptionally low magnetic field needed to drive the compound into its quantum limit, demonstrating that ZrTe 5 is an extremely clean system and ideal platform for studying 3D Dirac fermions. The splitting of the Landau levels provides a direct and bulk spectroscopic evidence that a relatively weak magnetic field can produce a sizeable Zeeman effect on the 3D Dirac fermions, which lifts the spin degeneracy of Landau levels. Our analysis indicates that the compound evolves from a Dirac semimetal into a topological line-node semimetal under current magnetic field configuration.PACS numbers: 71.55. Ak, 71.70.Di 3D topological Dirac/Weyl semimetals are new kinds of topological materials that possess linear band dispersion in the bulk along all three momentum directions [1][2][3][4][5][6][7]. Their low-energy quasiparticles are the condensed matter realization of Dirac and Weyl fermions in relativistic high energy physics [8,9]. These materials are expected to host many unusual phenomena [10][11][12], in particular the chiral and axial anomaly associated with Weyl fermions [3,[13][14][15]. It is well known that the Dirac nodes are protected by both timereversal and space inversion symmetry. Since magnetic field breaks the time-reversal symmetry, a Dirac node may be split into a pair of Weyl nodes along the magnetic field direction in the momentum space [16][17][18] or transformed into linenodes [17,19]. Therefore, a Dirac semimetal can be considered as a parent compound to realize other topological variant quantum states. However, past 3D Dirac semimetal materials (e.g. Cd 3 As 2 ) suffer from the problem of large residual carrier density which requires very high magnetic field (e.g. above 60 Tesla) to drive them to their quantum limit [20,21]. This makes it extremely difficult to explore the transformation from Dirac to Weyl or line-node semimetals. Up to now, there are no direct evidences of such transformations.ZrTe 5 appears to be a new topological 3D Dirac material that exhibits novel and interesting properties. The compound crystallizes in the layered orthorhombic crystal structure, with prismatic ZrTe 6 chains running along the crystallographic aaxis and linked along the c-axis via zigzag chains of Te atoms to form two-dimensional (2D) layers. Those layers stack along the b-axis. A recent ab initio calculation suggests that bulk ZrTe 5 locates close to the phase boundary between weak and strong topological insulators [22]. However, more recent transport and ARPES experiments identify it to be a 3D Dirac semimetal with only one Dirac node at the Γ point [23]. Interestingly, a chiral magnetic effect associated with the transform...

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Three-dimensional topological insulators (3D TIs) represent states of quantum matters in which surface states are protected by timereversal symmetry and an inversion occurs between bulk conduction and valence bands. However, the bulk-band inversion, which is intimately tied to the topologically nontrivial nature of 3D Tis, has rarely been investigated by experiments. Besides, 3D massive Dirac fermions with nearly linear band dispersions were seldom observed in TIs. Recently, a van der Waals crystal, ZrTe 5 , was theoretically predicted to be a TI. Here, we report an infrared transmission study of a high-mobility [∼33,000 cm 2 /(V · s)] multilayer ZrTe 5 flake at magnetic fields (B) up to 35 T. Our observation of a linear relationship between the zero-magnetic-field optical absorption and the photon energy, a bandgap of ∼10 meV and a ffiffiffi B p dependence of the Landau level (LL) transition energies at low magnetic fields demonstrates 3D massive Dirac fermions with nearly linear band dispersions in this system. More importantly, the reemergence of the intra-LL transitions at magnetic fields higher than 17 T reveals the energy cross between the two zeroth LLs, which reflects the inversion between the bulk conduction and valence bands. Our results not only provide spectroscopic evidence for the TI state in ZrTe 5 but also open up a new avenue for fundamental studies of Dirac fermions in van der Waals materials. T opologically nontrivial quantum matters, such as topological insulators (1-8), Dirac semimetals (9-19), and Weyl semimetals (20-27), have sparked enormous interest owing both to their exotic electronic properties and potential applications in spintronic devices and quantum computing. Therein, intrinsic topological insulators have insulating bulk states with odd Z 2 topological invariants and metallic surface or edge states protected by time-reversal symmetry (4-6, 28). Most of the experimental evidence to date for TIs is provided by the measurements of the spin texture of the metallic surface states. As a hallmark of the nontrivial Z 2 topology of TIs (4-6, 28), an inversion between the characteristics of the bulk conduction and valence bands occurring at an odd number of time-reversal invariant momenta has seldom been probed by experiments. An effective approach for identifying the bulk-band inversion in TIs is to follow the evolution of two zeroth Landau levels (LLs) that arise from the bulk conduction and valence bands, respectively. As shown in Fig. 1A, for TIs, due to the bulk-band inversion and Zeeman effects, the two zeroth bulk Landau levels are expected to intersect in a critical magnetic field and then separate (3, 29); and for trivial insulators, the energy difference between their two zeroth Landau levels would become larger with increasing magnetic field. Therefore, an intersection between the two zeroth bulk LLs is a significant signature of the bulk-band inversion in TIs. However, a spectroscopic study of the intersection between the two zeroth bulk LLs in 3D TIs is still missing. In addi...

The layered lanthanum silver antimonide LaAgSb 2 was known to experience two charge density (CDW) phase transitions, which were proposed recently to be closely related to the newly identified Dirac cone. We present optical spectroscopy and ultrafast pump probe measurement on the compound. The development of energy gaps were clearly observed below the phase transition temperatures in optical conductivity, which removes most part of the free carrier spectral weight. Time resolved measurement demonstrated the emergence of strong oscillations upon entering the CDW states, which were illuminated to come from the amplitude mode of CDW collective excitations. The frequencies of them are surprisingly low: only 0.12 THz for the CDW order with higher transition temperature and 0.34 THz for the lower one, which shall be caused by their small modulation wave vectors. Furthermore, the amplitude and relaxation time of photoinduced reflectivity stayed unchanged across the two phase transitions, which might be connected to the extremely low energy scales of amplitude modes. PACS numbers: 71.45.Lr, 78.47.+p Charge-density-waves (CDW) is one of the most fundamental collective quantum phenomena in solids. Charge density waves display periodic modulations of the charge with a period which is commensurate or incommensurate to the underlying lattice. Most CDW states are driven by the nesting topology of Fermi surfaces (FSs), i.e., the matching of sections of FS to others by a wave vector q = 2k F , where the electronic susceptibility has a divergence. A single-particle energy gap opens in the nested regions of the FSs at the transition, which leads to the lowering of the electronic energies of the system. Simultaneously, the phonon mode of acoustic branch becomes softened to zero frequency at q = 2k F as a result of electron-phonon interaction, which further leads to the periodic modulation of lattice structure.CDW also has collective excitations referred to as an amplitude mode (AM) and a phase mode. Phase excitation corresponds to the translational motion of the undistorted condensate. In the q=0 limit, the phase mode should locate at zero energy in ideal case since the translational motion does not change the condensation energy [1,2]. In reality, due to the presence of impurity or defects, the phase mode is pinned at finite frequency, usually in the microwave frequency range. The pinning/depinning of phase mode has dramatic effect on charge transport properties. By applying dc electric field, the phase mode can be driven into a current-carrying state, leading to nonlinear current-voltage characteristics [3][4][5]. On the other hand, the amplitude mode involves the ionic displacement and has a finite energy even at q=0 limit. For most CDW materials, the amplitude mode has an energy scale of about 10 meV (or ∼ 2 THz) [6][7][8][9][10][11][12]. Due to presence of such a gap for the amplitude mode (i.e. the mode energy at q=0), its effect on low temperature physical properties of CDW condensate has been much less studied. Generally...