# Presentation: 831898

## Quantum Fluctuations & Vortex Dynamics in Cuprate Superconductor 

***Nai-Chang Yeh,**** ***California Institute of Technology, DMR 0405088**

- (Dominant thermal &
- disorder fluctuations)

- _Fig.1:     Effects of quantum, thermal and disorder fluctuations on vortex phase diagrams of cuprates _

- (Dominant thermal & disorder fluctuations, weak quantum fluc.)

**Intellectual Merit:** It is well established that high-temperature superconducting cuprates are extreme type-II superconductors that exhibit strong fluctuation effects in their vortex state. However, little has been considered for the *microscopic* origin that leads to these *macroscopic* phenomena. We have recently established the connection between the strong fluctuation effects in the vortex state and the proximity of the cuprates to a quantum criticality that separates a pure superconducting (SC) state from a coexisting state of SC and competing orders (CO). By applying magnetic fields parallel to the CuO2 plane and studying its vortex dynamics at the lowest temperature (T ~ 0) to minimize the disorder and thermal fluctuations, we still find strong suppression of the magnetically irreversible vortex state, implying large quantum fluctuations. The degree of quantum fluctuations of the cuprates, as manifested by the *macroscopic* magnetic properties and vortex phase diagrams (Fig.1), is correlated with the its *microscopic* proximity to the quantum criticality and the quasiparticle spectra.
_**Publications emanated from this support in FY2005**_**:**
-  V. S. Zapf *et al*, Phys. Rev. B **71**, 134526 (2005).
-  N.-C. Yeh *** ****et al*, Int. J. Mod. Phys. B **19**, 285 (2005).
-  N.-C. Yeh *et al*, Chinese J. Phys. **43**, 505 Suppl. 2 (2005).
-  N.-C. Yeh *et al*, Proceedings of SPIE **5932** (2005), invited paper,
-   accepted for publication.
-  N.-C. Yeh *et al*, Physica C **408-410**, 792 (2004).

- (Strong quantum fluctuations at T  0 due to competing orders)

- Hirr(T): irreversible field
- Hc2(T): upper critical field
- Hc20 = Hc2(T=0)
- S(X): vortex smectic (crystal)
- IS(IX): incommensurate S(X)
- VL: vortex liquid

- Representative experimental results from Hg-1234 (HgBa2Ca3Cu4Ox) and
- La-112 (Sr0.9La0.1CuO2) for H || ab, consistent with strong quantum fluctuations at T  0.

**Experimental:**

**Theoretical:**

**Notes:**
	At the microscopic level, high-temperature superconducting cuprates differ fundamentally from conventional superconductors in that the latter consists of a pure superconducting phase at low temperatures, whereas the former often consists of multiple “competing orders”. That is, superconductivity is not necessarily the dominant low-temperature phase in the cuprate superconductors -- Depending on subtle tuning of either the chemical compositions of the cuprates or other controllable variables such as the temperature and magnetic field applied to the cuprates, high-temperature superconductivity can either homogeneously coexist with a competing phase, spatially separated from a competing phase in a “Swiss cheese” like pattern, or completely taken over by a competing phase. This phenomenon gives rise to extremely rich and complicated physical properties that appear to be “non-universal” among different families of cuprate superconductors. 
	At the macroscopic scale, it is also well known that the behavior of the superconducting cuprates in a magnetic field, known as the vortex dynamics, is fundamentally different from that of the conventional superconductors because of strong “fluctuation” effects. To date, the vortex dynamics of cuprate superconductors can be reasonably explained by the phenomenology of taking the strong fluctuation effects as given (i.e. without asking what the physical origin is), and then consider the resulting vortex dynamics due to the interplay of different fluctuation effects induced by temperature, disorder, and unknown quantum origin. 
	Our recent research has begun to bridge between the macroscopic fluctuations and the microscopic presence of competing orders in the cuprate superconductors. Our experimental studies of both the microscopic and macroscopic physical properties of the cuprates reveal that those with more significant contribution from the competing orders to their spectroscopy also reveal stronger quantum fluctuation effects on their vortex dynamics. This finding is potentially important in unifying a wide range of novel phenomena of high-temperature superconductivity, a step forward to ultimate revelation of the superconducting mechanism. We are currently conducting numerical calculations for the microscopic spectroscopy of cuprate superconductors by taking into consideration of the macroscopic quantum fluctuations. These numerical results, once completed, will be compared with our experimental data to provide a better theoretical foundation for our experimental findings. 

## Quantum Fluctuations & Vortex Dynamics in Cuprate Superconductors

***Nai-Chang Yeh,**** ***California Institute of Technology, DMR  0405088**

- Fig.3: Determining the proximity of different cuprates to the quantum criticality (at = c) from experiments

- Hg-1245: HgBa2Ca4Cu5Ox
- Hg-1234: HgBa2Ca3Cu4Ox
- La-112: Sr0.9La0.1CuO2
- Y-123: YBa2Cu3O7-x
- SC: superconductivity
- CO: competing order
- N: normal state

**Broader Impact: **Better understanding of the vortex dynamics in superconductors is crucial for a wide range of applications. In general, strong fluctuations in the vortex state are not desirable because they lead to dissipation at a finite time scale. With the establishment of the microscopic origin for strong fluctuations in the vortex state of cuprate superconductors, we can better decide on which cuprates to use in device applications. Specifically, our studies suggest that it is advisable to choose cuprates farther away from the “quantum criticality” that separates a pure SC phase from a coexisting SC and CO phase in zero magnetic field (H) so as to minimize fluctuation effects. In Fig. 3 we compile a list of cuprates that have been studied by us to reveal their different proximity to the quantum criticality at c (: a material parameter, closer to c corresponds to stronger quantum fluctuations), and we recommend that cuprates such as YBa2Cu3O7-x are better candidates for device applications.
**Education:**
- _Trainees involved in this research_
-   *Graduate students*: Ching-Tzu Chen, Andrew D. Beyer,
-                                   Cameron R. Hughes, Marcus Teague
-   *Postdoctoral scholar*: Slobodan Mitrovic
-   *Undergraduate student*: Victor Alvarez
- _Honor received by the PI_
-   Elected Fellow, American Physical Society (2004).

**h*(********):** A characteristic field obtained from the vortex-state magnetic measurements, normalized to the upper critical field Hc2 || CuO2 planes

- (See publications listed in the previous slide for details)

- Fig.4: Microscopic verification of quantum fluctuations using scanning tunneling spectroscopy

**Notes:**
 	In the context of broader impact, our realization of the relevance of competing orders to the vortex dynamics and dissipation of cuprate superconductors  can help determine the best materials for applications. Specifically, cuprate superconductors with weaker quantum fluctuations (i.e. farther away from the quantum criticality and therefore less influence from the competing orders) generally exhibit better physical properties (e.g. higher critical current densities) at finite temperatures and under finite magnetic fields, and are therefore more suitable for used in device or wire fabrication. 
	In addition to the relevance to applications, our studies of the quantum fluctuations and vortex dynamics of cuprate superconductors involve instrumentation development, a wide variety of experimental techniques, as well as theoretical modeling and numerical simulations. Hence, the project offers excellent research trainings for students and postdoctoral scholars, so is of much educational value.