# Quantum critical scaling in graphene.

@article{Sheehy2007QuantumCS, title={Quantum critical scaling in graphene.}, author={Daniel E. Sheehy and J{\"o}rg Schmalian}, journal={Physical review letters}, year={2007}, volume={99 22}, pages={ 226803 } }

We show that the emergent relativistic symmetry of electrons in graphene near its quantum critical point (QCP) implies a crucial importance of the Coulomb interaction. We derive scaling laws, valid near the QCP, that dictate the nontrivial magnetic and charge response of interacting graphene. Our analysis yields numerous predictions for how the Coulomb interaction will be manifested in experimental observables such as the diamagnetic response and electronic compressibility.

## 153 Citations

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A key problem in the field of quantum criticality is to understand the nature of quantum phase transitions in systems of interacting itinerant fermions, motivated by experiments on a variety of…

## References

SHOWING 1-10 OF 12 REFERENCES

### Phys

- Rev. Lett. 98, 216401
- 2007

### Phys

- Rev. B 75, 121406
- 2007

### Phys

- Rev. B 74, 161402
- 2006

### Phys

- Rev. Lett. 53, 2449
- 1984

### Phys

- Rev. Lett. 98, 216801
- 2007

### Phys

- Rev. B 75, 235423
- 2007

### Phys

- Rev. B 75, 115123
- 2007

### Phys

- Rev. B 48, 7183
- 1993

### Nucl

- Phys. B. 424, 595 (1994); Phys. Rev. B 59, R2474
- 1999

### Phys

- Rev. B 11, 3504
- 1975