Misfit compounds (also known as incommensurate compounds) are alternating stacking of two layer compounds (Fig. 1.7a) defined by the formula: (MX)1+x(TX2)n, with M=Sn,
Pb, Bi, Sb, rare earth elements; T=V, Ti, Cr, Nb, Ta; X=S, Se, Te; 0.08≤x≤0.28; n=1, 2, 3. The MX and TX2 sets possess its own symmetry and lattice constants. The misfit behaviour arises from the non-stoichiometry of the lattice constants between the adjacent layers in a certain direction. Let the misfit lattice constant be a1 and a2for MX and TX2, respectively. Lattice constant b and c are the same for the two sets, where c is chosen as the stacking direction (Fig. 1.7a). Misfit compound can be viewed as the host compound TX2 intercalated by MX, which is a two-atom layer with distorted NaCl structure (Fig. 1.7b).
The TX2set is a three-atom layer with structure depending on the atom T. The non-integer number 1 + x in the formula is determined by the ratio of the periodicities of the two sets (1 + x = 2(a2/a1)), and n is the number of TX2 sets sandwiched between the MX sets. The adjacent layers are held together simply by van-der-Waals force. Thus misfit compound is also a quasi-low-dimensional system.
Some of the host compounds (TX2) display charge density wave (CDW) transition.
CDW is a special phase of periodic modulation of the conduction electron density and the lattice atoms’ positions [31, 5, 32]. The modulation is usually a few percent in electron density and about one percent in lattice constant. Figure 1.8b shows the charge density, atom positions, and band structure of a normal conductor (the upper figure) and a CDW phase (the lower figure). The normal conductor has evenly distributed electron density and lattice atoms. The CDW shows periodic modulation of electron density and lattice atom distance. Such modulation opens up a narrow gap near Fermi surface and lowers the system’s total energy (right part of Fig. 1.8b). CDW is similar to superconductors in the way that they both opens up a gap near Fermi surface and have a collective conduction mode. When an electric field is applied, the CDW can “slide” relative to the lattice atoms.
The oscillating lattice atoms produces a travelling potential which results in a current (Fig. 1.8a). It is widely believed that CDW competes with superconductivity [33] and a lot of efforts have been made on reducing CDW transition temperature and increase superconductivity transition temperature [34, 35, 36]. However, some evidences showed
that CDW may coexist with superconductivity [37, 38, 34]. How do the same electrons participate in both transitions remains an open question. It is, therefore, a major task to search for new materials with coexisting CDW and superconductivity, which can provide a platform for studying the interplay between the two transitions. Misfit compound can be useful in studying this issue in the sense that superconductivity can occur within TX2, which originally displays CDW transition.
Another interesting topic in misfit compounds is the charge transfer between TX2 and MX sets. The MX and TX2 sets usually have carrier concentrations comparable to semiconductors separately, but the resulting misfit compound often displays carrier con-centration comparable to a metal. It is believed that electrons are transferred to TX2from MX layers [39]. The rigid band model was adopted to explain the charge transfer. It assumes that the electron D.O.S. of the misfit compound can be inferred from the super-position of its constituents’ D.O.S. [40]. Figure 1.7c is an example of how electrons are transferred from MX layers (PbSe) to the TX2layers (TiSe2). While the rigid band model can qualitatively explain the charge transfer in many misfit compounds, it fails to provide quantitative explanation [41]. Therefore, the detailed relation between charge transfer and the suppression of CDW or emergence of superconductivity is still unclear. Detailed experimental characterization of the electronic structure of misfit compounds will help to understand the issue.
c
Figure 1.7: (a)Schematic drawing of the structure of a typical misfit compound. (b)The structure of a typical MX compound. (c)An example of how the rigid band model explains charge transfer in misfit compounds. This picture is from Ref. [42]
)b* )c*
Figure 1.8: (a)Schematic of how the collective behaviour of CDW results in a net current when electric field is applied. The solid lines and open circles indicate snapshots of the CDW and lattice atoms at successive times, respectively. (b)Schematic of how atom positions and electron density are modulated in CDW. The band structure is shown on the right. A narrow band gap opens up at±kF and the system’s total energy is lowered. The pictures are from Ref. [5].
Experimental Setup
2.1 Superconducting Magnet System
The superconducting magnet system (Oxford Instrument) is used for measurements that require high magnetic field. With a home-made two-jacket insert, sample temperature can be easily controlled from 4.2K to 300K with great stability better than 0.1%. A schematic drawing of the system is shown in Fig. 2.1a.
The superconducting coils are immersed in liquid helium (LHe) main bath at 4.2K.
The cryostat is shielded from the outside by a 77K liquid nitrogen reservoir and an outer vacuum shroud. The two-jacket insert is loaded from the top of the cryostat, and the sample probe is placed inside the inner jacket. The magnet is connected to a power sup-ply (IPS120, Oxford Instruments) that can be controlled by LabView program. At LHe temperature, the superconducting coils can sustain a supercurrent that produces a mag-netic field up to 15T. By using Lamda point fridge, LHe temperature around the coils can further drop to 2.2K, allowing the magnet to supply a field up to 17T.
The sample probe consists of a copper sample stage, which has 8 twisted pairs of phosphor bronze wires thermally anchored on it by Stycast Epoxy. A schematic drawing of sample stage is shown in Fig. 2.1(b) and (c). The stage is vacuum sealed by a taper copper can, and can be rotated and fixed at arbitrary angles from 0 to 90 degrees, allowing
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different field orientation with respect to the sample. A 25Ω wire resistor is fixed on the sample stage to act as a sample heater. A Cernox temperature sensor (Lakeshore) is mounted on the back of sample stage to monitor the sample temperature. Both heater and sensor are connected to a temperature controller (Lakeshore 340). We can obtain proper cooling power through the LHe main bath by tuning the amount of helium exchange gas in the two jackets and the sample space. Precise temperature control is achieved by carefully tuning the PID parameters and the amount of helium exchange gas. The two jackets and sample space are kept under high vacuum with pressure∼ 10−6 torr using a pumping station before loading into the dewar. A liquid nitrogen (LN2) cold-trap is placed along the pump line to reduce possible oil vapour contamination.