Weak-localization effects reveal intrinsic semiconductor ground state in iodine-free TiSe{}_{2}

Weak-localization effects reveal intrinsic semiconductor
ground state in iodine-free TiSe

Jaime M. Moya Department of Physics and Astronomy, Rice University    C.-L. Huang clh@rice.edu Department of Physics and Astronomy, Rice University    Jesse Choe Department of Electrical and Computer Engineering, Rice University    Gelu Costin Department of Earth, Environmental and Planetary Sciences, Rice University    Matthew S. Foster Department of Physics and Astronomy, Rice University    E. Morosan Department of Physics and Astronomy, Rice University
July 26, 2019
Abstract

Dilute impurities and growth conditions can drastically affect the transport properties of TiSe, especially below the charge density wave transition. In this paper, we discuss the effects of cooling rate, annealing time and annealing temperature on the transport properties of TiSe: slow cooling of polycrystalline TiSe post-synthesis drastically increases the low temperature resistivity, which is in contrast to the metallic behavior of single-crystalline TiSe due to charge doping from the residual iodine transport agent. A logarithmic increase of resistivity upon cooling and negative magnetoresistance with a sharp cusp around zero field are observed for the first time for the polycrystalline TiSe samples, pointing to weak-localization effects due to low dimensionality. Annealing at low temperatures has a similar, but less drastic effect. Furthermore, rapid quenching of the polycrystalline samples from high temperatures freezes in disorder, leading to a decrease in the low temperature resistivity.

I Introduction

Transition metal dichalcogenides (TMDCs) are a class of layered quasi-two dimensional materials. Owing to their low dimensionality, they span a vast area of physical properties. TiSe is one such TMDC that has attracted lots of attention due to its complex electronic properties, including charge ordering Di Salvo et al. (1976), superconductivity with intercalation of copper or palladium Morosan et al. (2006, 2010), and with the application of pressure Kusmartseva et al. (2009) or electrostatic gating Li et al. (2016). On the other extreme, TiSe becomes insulating with platinum doping Chen et al. (2015a), and displays potential Luttinger liquid states within domain boundaries Choe (2019) revealing the versatility of the chemical tuning of this TMDC compound.

The origin of the charge density wave (CDW) transition, occurring in TiSe around 202 K Di Salvo et al. (1976), has been an ongoing debate for decades, with proposed mechanisms including an excitonic insulator phase Jérome et al. (1967) and the band-type Jahn-Teller effect Hughes (1977). For the former, it can arise either in a small band gap semiconductor or a semimetal Jérome et al. (1967). Below the CDW transition, several angle-resolved photoemission spectroscopy experiments all pointed to a larger indirect gap, but whether the small normal state indirect band gap is positive or negative is still under debate Watson et al. (2019a); Bachrach et al. (1976); Traum et al. (1978); Pillo et al. (2000); Kidd et al. (2002); Rossnagel et al. (2002); Cercellier et al. (2007); May et al. (2011); Chen et al. (2015b). The latter proposed CDW mechanism is independent of the free carrier concentration Hughes (1977), and this cannot account for the incommensurate diffraction spots seen in TiSe Di Salvo et al. (1976). Recent experimental evidence favors the excitonic insulator scenario Hildebrand et al. (2016); Monney et al. (2009, 2011); Cercellier et al. (2007); Cazzaniga et al. (2012); Kogar et al. (2017), but theories predict that the exciton condensation can either be a superfluid Snoke (2002), or an insulator Kohn and Sherrington (1970). Most recently, Watson presented simulations of dome-like resistivity curves centered around 150 K, simply based on a semiconducting normal state band structure with an indirect band gap, without implementing the CDW physics at all Watson et al. (2019b). Huang et al. Huang et al. (2017) showed insulating behavior for their polycrystalline TiSe samples closest to stoichiometry, with metalicity induced by increasing Se deficiency Huang et al. (2017), while Campbell et al. recently revealed insulating behavior in iodine-free single crystals Campbell et al. (2018). Historically though, single crystal samples grown by iodine vapor transport have shown metallic behavior in resistivity Di Salvo et al. (1976); Rossnagel et al. (2002); Li et al. (2007). Bearing all of the above in mind, it is essential to reach experimental resolution of the intrinsic ground state of TiSe.

One problem faced in studying TiSe is the inconsistency in the physical properties from sample to sample. The temperature-dependent resistivity (T) shows discrepancy between single-crystalline TiSe grown by I vapor transport Di Salvo et al. (1976); Rossnagel et al. (2002); Li et al. (2007) and polycrystalline TiSe, synthesized by solid state reaction Chen et al. (2015b); Morosan et al. (2006); Huang et al. (2017). This is illustrated by the normalized (T) data of TiSe in Fig. 1. Even though the (T) behavior is qualitatively similar between single-crystalline and polycrystalline samples with a local maximum between 100 and 200 K, at the lower temperatures (T) varies drastically: metallic behavior (d/dT ) is registered in the single-crystalline sample (dashed line and open circles), explained by either a doped semiconductor picture Watson et al. (2019b) or partial gapping of the Fermi surface Di Salvo et al. (1976), while semiconductor-like behavior (d/dT ) is found in the polycrystalline sample (solid line). To our knowledge, no systematic study of this discrepancy exists. It is imperious to understand the intrinsic properties of TiSe, and the effect of the synthesis conditions on the observed resistivity measurements, before the more complex effects of chemical doping, intercalation, or pressure can be understood.

It is well known that, for TiSe single crystals, the transport agent iodine might partially substitute for Se and dope the system Di Salvo et al. (1976); Rossnagel et al. (2002). Se deficiency also serves as a method of self-doping Chen et al. (2016). Both dopants presumably contribute additional density of states near the Fermi surface and hence enhance the conductivity on cooling. Here, we report systematic variations in the electrical transport properties of polycrystalline TiSe without doping or Se deficiency, as a function of cooling rate, annealing time, and annealing temperature. By decreasing the rate at which samples are cooled post-synthesis, a logarithmic increase in low temperature resistivity is observed. We surmize that this increase is due to weak-localization (WL) effects in low dimensional systems. Annealing polycrystalline samples post-synthesis at low temperatures (200C) has a similar, but less drastic effect. Our results suggest an intrinsic semiconducting ground state in TiSe, with low temperature electrical transport properties dominated by the WL effects.

Figure 1: A comparison of the resistivity (normalized to room temperature values) for iodine-grown TiSe single crystals with the current (dashed line) or (open circles), and polycrystalline (solid line). The full triangle is used to identify samples that are ‘As Grown, Air Quenched’ throughout the text.

Ii Methods

Polycrystalline samples of TiSe were synthesized by solid state reaction with a Ti:Se ratio of 1:2.02. The excess Se was added to compensate for the partial evaporation inherent during synthesis. The samples were sealed in evacuated quartz ampoules and heated at 50C/hr to 650C, followed by a 48 hour dwell at this temperature. Subsequently, the samples were either cooled at different rates, or annealed at different temperatures or different times. TiSe single crystals were grown by chemical vapor transport with I as the transport agent. Ground elemental Ti and Se were sealed in evacuated quartz tubes with a ratio of 1:2.02 and 5 mg/cm of iodine. The tubes were then placed in a 550C - 650C temperature gradient and held for 14 days, followed by controlled cooling to room temperature.

Structural characterization was done using a Bruker X-ray diffractometer with Cu k radiation. Refinements were performed using the FullProf software package Rodriguez-Carvajal (1990). The quantitative chemical composition was determined by electron probe microanalysis (EPMA) using a JEOL JXA 8530F Hyperprobe located at Rice University, Department of Earth, Environmental and Planetary Sciences, and equipped with a Schottky field emitter and five wavelength dispersive spectrometers. The analytical conditions were set to 15 kV accelerating voltage, 20 nA beam current, and beam spot size (300 nm). The Se L and Ti K X-ray lines were simultaneously measured using counting times of 10 seconds per peak and 5 seconds per each lower and upper background, respectively. Each element was simultaneously measured on two different spectrometers in order to increase the accuracy and the statistics of the measurement. Se L was analyzed on two TAP diffracting crystals, and Ti K was analyzed on a PETL and a LiFH diffracting crystal, respectively. The standards used to calibrate the spectrometers were Se metal (Se = 99.9990 wt. ) and rutile (TiO, where Ti = 59.9400 wt. ). For quantification, the ZAF matrix correction was used. The error of analysis, determined after analyzing secondary standards is below 2. The instrumental standard deviation (1) for Se and Ti in each analysis is 0.24 and 0.47, respectively. The quantitative analyses given in element wt. were converted to atomic ratios, and then the stoichiometry of the analyzed compound was normalized to one Ti atom.

Polycrystalline samples were pressed into pellets without sintering, and shaped into bars for resistivity measurements. DC electrical resistivity measurements were made in a Quantum Design Physical Properties Measurement System with a standard four-point probe technique for temperatures K. The technique described in Ref. Maeno et al., 1994 was used for resistance measurements with curent .

Iii Results and Discussion

iii.1 Post synthesis cooling rate r

When trying to improve the quality of crystals (e.g. decrease extrinsic disorder), two commonly used techniques for metals are: (i) slow cooling to avoid quenching in disorder, and (ii) post synthesis annealing below the synthesis temperature to relieve microstrain and increase grain size Cullity and Stock (2001). In the present study, both methods were employed to minimize disorder. By contrast, quenching from high temperature was used to study the effect of enhanced disorder.

The first experiment was dedicated to testing the effect of the cooling rate post synthesis on the electrical resistivity. Three samples were synthesized as described in the Methods. Sample A was air quenched (C/hr), sample B was fast-cooled to room temperature at a rate 20C/hr, and sample C was slow-cooled at 4C/hr. The scaled semi-log (300 K)(T) plot is displayed in Fig. 2(a). While all three samples show a nearly 5 time increase in (300 K) on cooling to 150 K, the air-quenched sample A displays a broad local minimum centered around 60 K, while both samples B and C exhibit nearly two orders of magnitude resistivity increase down to 2 K. The large change in the resistivity as a function of cooling rate prompted the need to check sample composition for possible non-stoichiometry. The results of the EPMA analysis, displayed in Table 1, indicate that all three samples are stoichiometric, with the same Ti:Se ratio of 1:2. Room temperature X-ray diffraction data (Fig. 3) does not show any measurable change in either the peak position or peak shape among the three samples, consistent with invariable lattice parameters.

Figure 2: (a) A comparison of the normalized resistivity (300 K) as a function of temperature for samples: A, air quenched; B, cooled at 20C/hr; C, cooled at 4C/hr. (b) A semi-logarithmic plot of (T). (c) and (d) show the magnetoresistance MR measured at 15 K for the polycrystalline samples A-C and the single crystal, respectively.
Cooling rate (C/hr) Se
A: 2000 (air quench)
B: 20
C: 4
Table 1: EPMA results for polycrystalline TiSe with variable cooling rates post synthesis corresponding to Figs. 2 and 3. Data is normalized to 1 Ti.

When plotting on a semi-log scale (Fig. 2(b)), all three samples A-C show a lnT dependence of upon cooling below the CDW broad local maximum. Since no magnetic impurities are present in any of the samples, the lnT increase of cannot be attributed to Kondo or other extrinsic magnetic effects. In TiSe, the low dimensionality enhances two quantum corrections to the resistivity: Altshuler-Aronov corrections due to the coherent scattering of electrons by impurity-induced Friedel oscillations L. and G. (1985); Zala et al. (2001); Lara-Avila et al. (2011), and WL due to self-intersecting scattering paths Hikami et al. (1980); Lee and Ramakrishnan (1985). Upon an application of finite transverse magnetic field , the shape of the magnetoresistance MR is insensitive to Altshuler-Aronov corrections, while WL can be suppressed in finite magnetic fields leading to a negative MR. Fig. 2(c) shows a pronounced peak of MR centered at zero field for samples A-C, which is typical for WL effect. If we neglect contributions to the electrical transport from an inhomogeneous environment, such as grain boundaries, and interpret the data simply based on the WL theory, the MR curves are consistent with varying coherence lengths , i.e., the distance an electron goes before dephasing, with Sample A having the shortest and Sample C having the longest L. and G. (1985). For comparison, the single crystal sample with iodine inclusions does not show WL behavior either in (T) or in MR (Fig. 2(d)). EPMA reveals a 1 iodine impurity per formula unit. In our single crystal sample, the iodine inclusions might dope the system and dominate the transport property which leads to a suppression of WL behavior. A recent electrical transport study on iodine-free TiSe single crystals does show a large increase in electrical resistivity on cooling, qualitatively consistent with what is seen in our polycrystalline Samples B and C Campbell et al. (2018). It will be informative to investigate the magnetic field effects on the transport properties in these iodine-free single crystals to quantitatively analyze the characteristic parameters from the WL correction. The WL effect noted here for the first time in TiSe had been previously reported in another TMDC, VSeCao et al. (2017). Even though our transport data alone cannot completely rule out the possibility of the system being a semimetal, a recent simulation shows that the dome-like (T) behavior around 150 K can only be replicated in a narrow band gap semiconductor framework at room temperature, but not in a semimetallic scenario Watson et al. (2019b). Given the fact that d/dT is observed at high temperatures (Fig. 1), we argue that TiSe is best described as a semiconductor with a small indirect band gap. At low temperatures, impurities contribute to the carrier density and the insulating transport is dominated by WL effects. As the temperature approaches absolute zero, polycrystalline TiSe becomes an Anderson insulator where the conduction diverges not because of a band gap, but because the localizing effects of disorder.

Figure 3: Room temperature powder X-ray diffraction patterns for the polycrystalline samples (symbols), with refinements shown as solid black lines, and the difference between measurement and calculation shown in red. The vertical marks below each pattern correspond to the calculated peak position for TiSe. Inset: a zoomed in view of all three of the measured patterns plotted.

Cooling samples slowly after synthesis was expected to decrease the extent of disorder in the crystals and increase the average grain size. In an attempt to characterized disorder, we turn again to the X-ray refinements. There are at least four contributions to peak width in powder X-ray diffraction Cullity and Stock (2001): instrumental broadening, thermal vibrations, grain size, and microstrain. Instrumental broadening is a function of beam optics and geometry. Thermal vibrations increase the peak widths with increasing temperature. Peak width decrease as grain size increases, and increases as microstrain is increased. No variations in X-ray peak widths are measured as seen in the inset of Fig. 3, where a selection of high 2 peaks are shown. Because all peaks are of similar width, all contributions to peak width are similar, and therefore no disorder from microstrain can be measured.

iii.2 Post synthesis annealing time

The next set of experiments focuses on the effect of annealing time . Different pieces of sample A were annealed at T = 200C, for times ranging from 1 to 6 days, followed by air quenching. The low anneal temperature was chosen to relieve quenched-in disorder without adding more disorder from quenching at a high temperature. Resistivity shows a general upward trend at low temperatures on cooling for increasing (Fig. 4a). No change in stoichiometry is detected (Table 2), indicating that the change in low temperature resistivity is not due to a change in the density of states near the Fermi energy from charge doping. As before, no change is recorded in the X-ray peak width and lattice parameters (not shown).

A similar study with anneal time was done on single crystals. The normalized (T) is plotted in Fig. 4b. Annealing did not change the low temperature transport properties when compared to the polycrystalline samples. EPMA studies looking for only Ti and Se show all similar ratios as seen in Table 2. However, as stated earlier, EPMA measurements reveal iodine inclusions around 1 in single crystals for which the Ti:Se ratio is found to be 1:2. The additional density of states near the Fermi energy due to iodine accounts for the metal-like low temperature electrical transport down to 2 K in single crystalline TiSe.

Figure 4: (a) Comparison of polycrystalline K) for TiSe samples annealed at 200C in one day increments up to six days. With increase in anneal time, the low temperature resistivity increases. (b) The same comparison for TiSe single crystals. The low temperature resistivity is dominated by iodine impurities.

iii.3 Post synthesis annealing temperature

The next experiment aims to purposefully induce disorder into the TiSe by quenching, followed by annealing at different temperatures . Different single crystal pieces were annealed for 2 days at different temperatures between 200 and 1200C. After annealing, all samples were quenched. Normalized (T) data is plotted in Fig. 5.

Figure 5: (a) A comparison of normalized (T) for polycrystalline TiSe samples annealed at different temperatures post synthesis. For anneal temperatures below the growth temperature, there is an increase in normalized (T), while at higher temperature anneals, their is a decrease in low temperature normalized (T). (b) The corresponding study for single crystals.

For anneal temperatures below the growth temperature = 650C (triangles, Fig. 5(a)), the low temperature resistivity of the polycrystalline samples increases compared to that of the as-grown sample, much the same as the result shown in Fig. 4(a). For anneal temperatures at (square) or above (star) the synthesis temperature, the low temperature resistivity decreases. However, below 20 K the resistivity increases on cooling for all annealing temperatures . Our EPMA data shows no systematic loss of selenium with increased anneal temperature (Table 3), whereas X-ray diffraction patterns (Fig. 6) indicate significant peak broadening for samples quenched from 1200C (star) indicating microstrain caused by quenching at such a high temperature. Though there are small variations in lattice parameters, the variations are less than 0.1 of the as grown (upwards triangle), so the change in resistivity is not due to a change in the unit cell.

Figure 6: Zoomed in comparison of X-ray patterns for different anneal temperatures. At 1200C there is an increase in disorder from microstrain as evidence by severe broadening of the peaks.

For comparison, analogous data is shown in Fig. 5(b) for TiSe single crystals. Besides the differences in low temperature resistivity, which can be explained by iodine impurities, the normalized (T) shows qualitatively similar features as the polycrystalline samples. The trend of decreasing peak height below the CDW transition is qualitatively similar to that previously attributed to non-stoichiometry Di Salvo et al. (1976) . Though a Se deficiency is seen in the sample annealed at 1200C, the polycrystalline counterpart suggests that the decrease in the anomaly height is not due to doping, but rather an increase in quenched disorder. Remarkably, the 1200C single crystal (star, Fig. 5(b)) shows metallic behavior for the whole temperature range, and no anomaly in (T). Consistent with the observations of the most substantive structural changes at this temperature (Fig. 6), this signals that self doping, disorder, grain boundary freezing, or more, inhibit the intrinsic properties of TiSe at excessively high annealing temperatures.

Anneal t Polycrystal Single Crystal
(days) Se Se
As Grown
2
3
4
5
6
Table 2: Se normalized to 1 Ti in TiSe samples annealed at 200C in one day increments up to six days corresponding to Fig. 4.
Anneal T (C) Polycrystal Single Crystal
Se Se
As Grown
200
400
650
1200
Table 3: EPMA results for TiSe samples annealed for 2 days at variable temperatures corresponding to Fig. 5.

A seeming consensus concerning electrical transport studies is that single crystal data is often more reliable than pollycrystaline samples, because the data the latter can be plagued by grain boundary effects and lack of anisotropy details Ryden (1971). We confirm that the electrical transport in TiSe single crystals is nearly isotropic (Fig. 1), consistent with previous reports Di Salvo et al. (1976). This rules out anisotropy as the cause of differences in transport between polycrystalline and single crystalline samples. Furthermore, we expect that the overall behavior of pollycrystaline samples and single crystals to be similar, since the grain boundaries should contribute only an additive temperature-independent term to the bare Drude conductivity. Our study indicates that TiSe behaves like a small gap semiconductor where the electrical transport is largely localized by residual impurities towards zero temperature. In addition, the drastic decrease in the CDW anomaly upon annealing is also consistent with disorder (Fig. 5). Hildebrand et al. reported a decrease in CDW domains with increasing disorder Hildebrand et al. (2016). As the CDW domain size becomes smaller than the bulk exciton Bohr radius, the holes and electrons break into individual charge carriers, reducing the magnitude of the CDW anomaly Hildebrand et al. (2016). Though no systematic differences of disorder were measurable in our work, the trend in resistivity is consistent with a decrease in disorder for a decrease in cooling rate and an increase in annealing time, and both of which are expected in resulting better crystallization. Also, because no measured selenium deficiency is found in powdered samples, the disorder is a different effect than doping reported by Huang et al. Huang et al. (2017).

Iv Conclusions

We have systematically studied the effects of the cooling rate, and temperature and time dependence of post-synthesis annealing on the observed electrical transport properties of TiSe. For the first time, the weak-localization effect is found in polycrystalline TiSe samples, embodying the quantum corrections to the electrical transport properties in low dimensional systems. At low temperatures results on polycrystalline TiSe are consistent with a semiconducting-like ground state with low temperature and MR being dominated by the weak localization effect due to residual impurities. We have systematically studied the effects of the cooling rate, and temperature and time dependence of post-synthesis annealing on the observed electrical transport properties of TiSe. This study is intended to serve as a guide in the synthesis of TiSe, by pointing out to the intrinsic and extrinsic properties as a function of the preparation method.

Acknowledgements.

V Acknowledgements

JMM, JC, CLH and EM acknowledge support from NSF DMREF grant 1629374. The use of the EPMA facility at the Department of Earth Science, Rice University, Houston, TX is kindly acknowledged. Furthermore, the authors are grateful for fruitful discussions with A. M. Hallas and M. D. Watson.

References

  • Di Salvo et al. (1976) F Jr Di Salvo, DE Moncton,  and JV Waszczak, “Electronic properties and superlattice formation in the semimetal TiSe,” Physical Review B 14, 4321 (1976).
  • Morosan et al. (2006) Emilia Morosan, Henny W Zandbergen, BS Dennis, JWG Bos, Y Onose, Tomasz Klimczuk, AP Ramirez, NP Ong,  and Robert J Cava, “Superconductivity in CuTiSe,” Nature Physics 2, 544 (2006).
  • Morosan et al. (2010) Emilia Morosan, Keith E Wagner, Liang L Zhao, Y Hor, Anthony J Williams, Jing Tao, Yimei Zhu,  and Robert Joseph Cava, “Multiple electronic transitions and superconductivity in PdTiSe,” Physical Review B 81, 094524 (2010).
  • Kusmartseva et al. (2009) Anna F Kusmartseva, B Sipos, H Berger, Laszlo Forro,  and Eduard Tutiš, “Pressure induced superconductivity in pristine 1T-TiSe,” Physical review letters 103, 236401 (2009).
  • Li et al. (2016) LJ Li, ECT O’farrell, KP Loh, Goki Eda, B Özyilmaz,  and AH Castro Neto, “Controlling many-body states by the electric-field effect in a two-dimensional material,” Nature 529, 185 (2016).
  • Chen et al. (2015a) Justin S Chen, Jiakui K Wang, Scott V Carr, Sven C Vogel, Olivier Gourdon, Pengcheng Dai,  and E Morosan, “Chemical tuning of electrical transport in TiPtSe,” Physical Review B 91, 045125 (2015a).
  • Choe (2019) Jesse Choe, “Chemical tuning of electrical an magnetic properties in the transition metal dichalcogenides,” PhD diss., Rice University  (2019).
  • Jérome et al. (1967) D Jérome, TM Rice,  and W Kohn, “Excitonic insulator,” Physical Review 158, 462 (1967).
  • Hughes (1977) HP Hughes, “Structural distortion in TiSe and related materials-a possible jahn-teller effect?” Journal of Physics C: Solid State Physics 10, L319 (1977).
  • Watson et al. (2019a) Matthew D Watson, Oliver J Clark, Federico Mazzola, Igor Marković, Veronika Sunko, Timur K Kim, Kai Rossnagel,  and Philip DC King, “Orbital-and k-selective hybridization of Se 4p and Ti 3d states in the charge density wave phase of TiSe,” Physical review letters 122, 076404 (2019a).
  • Bachrach et al. (1976) RZ Bachrach, M Skibowski,  and Frederick C Brown, “Angle-resolved photoemission from TiSe using synchrotron radiation,” Physical Review Letters 37, 40 (1976).
  • Traum et al. (1978) MM Traum, G Margaritondo, NV Smith, JE Rowe,  and FJ Di Salvo, “TiSe: Semiconductor, semimetal, or excitonic insulator,” Physical Review B 17, 1836 (1978).
  • Pillo et al. (2000) Th Pillo, J Hayoz, Helmuth Berger, F Lévy, Louis Schlapbach,  and Philipp Aebi, “Photoemission of bands above the fermi level: The excitonic insulator phase transition in 1T-TiSe,” Physical Review B 61, 16213 (2000).
  • Kidd et al. (2002) TE Kidd, T Miller, MY Chou,  and T-C Chiang, “Electron-hole coupling and the charge density wave transition in TiSe,” Physical review letters 88, 226402 (2002).
  • Rossnagel et al. (2002) K Rossnagel, L Kipp,  and M Skibowski, ‘‘Charge-density-wave phase transition in 1T-TiSe: Excitonic insulator versus band-type Jahn-Teller mechanism,” Physical Review B 65, 235101 (2002).
  • Cercellier et al. (2007) H Cercellier, C Monney, F Clerc, C Battaglia, L Despont, MG Garnier, H Beck, P Aebi, L Patthey, H Berger, et al., “Evidence for an excitonic insulator phase in 1T-TiSe,” Physical review letters 99, 146403 (2007).
  • May et al. (2011) Matthias M May, Christine Brabetz, Christoph Janowitz,  and Recardo Manzke, “Charge-density-wave phase of 1T-TiSe: The influence of conduction band population,” Physical review letters 107, 176405 (2011).
  • Chen et al. (2015b) P. Chen, Y. H. Chan, X. Y. Fang, Y. Zhang, M. Y. Chou, S. K. Mo, Z. Hussain, A. V. Fedorov,  and T. C. Chiang, “Charge density wave transition in single-layer titanium diselenide,” Nature Communications 6, 8–12 (2015b).
  • Hildebrand et al. (2016) Baptiste Hildebrand, Thomas Jaouen, Clément Didiot, Elia Razzoli, Gaël Monney, M-L Mottas, A Ubaldini, Helmuth Berger, C Barreteau, Hans Beck, et al., “Short-range phase coherence and origin of the 1T-TiSe charge density wave,” Physical Review B 93, 125140 (2016).
  • Monney et al. (2009) Claude Monney, Hervé Cercellier, Florian Clerc, Corsin Battaglia, EF Schwier, Clement Didiot, Michael Gunnar Garnier, Hans Beck, Philipp Aebi, Helmut Berger, et al., “Spontaneous exciton condensation in 1T-TiSe: BCS-like approach,” Physical Review B 79, 045116 (2009).
  • Monney et al. (2011) Claude Monney, Corsin Battaglia, Hervé Cercellier, Philipp Aebi,  and Hans Beck, “Exciton condensation driving the periodic lattice distortion of 1T-TiSe,” Physical review letters 106, 106404 (2011).
  • Cazzaniga et al. (2012) Marco Cazzaniga, Hervé Cercellier, Markus Holzmann, Claude Monney, Philipp Aebi, Giovanni Onida,  and Valerio Olevano, ‘‘Ab initio many-body effects in TiSe: A possible excitonic insulator scenario from GW band-shape renormalization,” Physical Review B 85, 195111 (2012).
  • Kogar et al. (2017) Anshul Kogar, Melinda S Rak, Sean Vig, Ali A Husain, Felix Flicker, Young Il Joe, Luc Venema, Greg J MacDougall, Tai C Chiang, Eduardo Fradkin, et al., “Signatures of exciton condensation in a transition metal dichalcogenide,” Science 358, 1314–1317 (2017).
  • Snoke (2002) David Snoke, “Spontaneous bose coherence of excitons and polaritons,” Science 298, 1368–1372 (2002).
  • Kohn and Sherrington (1970) W Kohn and D Sherrington, “Two kinds of bosons and bose condensates,” Reviews of Modern Physics 42, 1 (1970).
  • Watson et al. (2019b) Matthew D Watson, Adam M Beales,  and Philip DC King, “On the origin of the anomalous peak in the resistivity of TiSe ,” arXiv preprint arXiv:1903.00756  (2019b).
  • Huang et al. (2017) SH Huang, GJ Shu, Woei Wu Pai, HL Liu,  and FC Chou, “Tunable se vacancy defects and the unconventional charge density wave in 1T-TiSe,” Physical Review B 95, 045310 (2017).
  • Campbell et al. (2018) Daniel J Campbell, Chris Eckberg, Peter Y Zavalij,  and Johnpierre Paglione, ‘‘Intrinsic Insulating Ground State in Transition Metal Dichalcogenide TiSe,” arXiv preprint arXiv:1809.09467  (2018).
  • Li et al. (2007) G Li, WZ Hu, D Qian, D Hsieh, MZ Hasan, E Morosan, RJ Cava,  and NL Wang, “Semimetal-to-semimetal charge density wave transition in 1T-TiSe,” Physical review letters 99, 027404 (2007).
  • Chen et al. (2016) P Chen, Y-H Chan, X-Y Fang, S-K Mo, Z Hussain, A-V Fedorov, MY Chou,  and T-C Chiang, “Hidden order and dimensional crossover of the charge density waves in TiSe,” Scientific reports 6, 37910 (2016).
  • Rodriguez-Carvajal (1990) J Rodriguez-Carvajal, “Fullprof: A Program for Rietveld Refinement and Pattern Matching Analysis,” Satellite meeting on powder diffraction on the XV congress of the IUCr  (1990).
  • Maeno et al. (1994) Y Maeno, H Hashimoto, K Yoshida, S Nishizaki, T Fujita, JG Bednorz,  and F Lichtenberg, “Superconductivity in a layered perovskite without copper,” Nature 372, 532 (1994).
  • Cullity and Stock (2001) B. D. Cullity and R. S. Stock, Elements of X-ray Diffraction, third edit ed. (Prentice Hall, 2001).
  • L. and G. (1985) Altshuler B. L. and Aronov A. G., Electron-Electron Interaction IN Disordered Conductors Chapter 1, edited by Efros A. L. and Pollak M. (Elsevier, 1985).
  • Zala et al. (2001) Gábor Zala, BN Narozhny,  and IL Aleiner, “Interaction corrections at intermediate temperatures: Longitudinal conductivity and kinetic equation,” Physical Review B 64, 214204 (2001).
  • Lara-Avila et al. (2011) Samuel Lara-Avila, Alexander Tzalenchuk, Sergey Kubatkin, Rositza Yakimova, TJBM Janssen, Karin Cedergren, Tobias Bergsten,  and Vladimir Fal’ko, “Disordered fermi liquid in epitaxial graphene from quantum transport measurements,” Physical review letters 107, 166602 (2011).
  • Hikami et al. (1980) Shinobu Hikami, Anatoly I Larkin,  and Yosuke Nagaoka, “Spin-orbit interaction and magnetoresistance in the two dimensional random system,” Progress of Theoretical Physics 63, 707–710 (1980).
  • Lee and Ramakrishnan (1985) Patrick A Lee and TV Ramakrishnan, ‘‘Disordered electronic systems,” Reviews of Modern Physics 57, 287 (1985).
  • Cao et al. (2017) Qiang Cao, Frank F Yun, Lina Sang, Feixiang Xiang, Guolei Liu,  and Xiaolin Wang, “Defect introduced paramagnetism and weak localization in two-dimensional metal VSe,” Nanotechnology 28, 475703 (2017).
  • Ryden (1971) DJ Ryden, “A comparison between the transport properties of single crystal, polycrystal and powder anisotropic semiconductors,” Journal of Physics C: Solid State Physics 4, 1193 (1971).
Comments 0
Request Comment
You are adding the first comment!
How to quickly get a good reply:
  • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
  • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
  • Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
""
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
   
Add comment
Cancel
Loading ...
350948
This is a comment super asjknd jkasnjk adsnkj
Upvote
Downvote
""
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters
Submit
Cancel

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test
Test description